%% EPIQ - Poulin
%% 2019-09-19
@misc{KP19a,
Author = {Anirudh Krishna and David Poulin},
Eprint = {arXiv:1909.07419},
Title = {Topological wormholes},
Year = {2019},
local-url = {KP19a.pdf}}
@misc{KP19b,
Author = {Anirudh Krishna and David Poulin},
Eprint = {1909.07424},
Title = {Fault-tolerant gates on hypergraph product codes},
Year = {2019},
local-url = {KP19b.pdf}}
@article{WSPS18a,
Abstract = {At the Mott transition, electron-electron interaction changes a metal, in which electrons are itinerant, to an insulator, in which electrons are localized. This phenomenon is central to quantum materials. Here we contribute to its understanding by studying the two-dimensional Hubbard model at finite temperature with plaquette cellular dynamical mean-field theory. We provide an exhaustive thermodynamic description of the correlation-driven Mott transition of the half-filled model by calculating pressure, charge compressibility, entropy, kinetic energy, potential energy and free energy across the first-order Mott transition and its high-temperature crossover (Widom line). The entropy is extracted from the Gibbs-Duhem relation and shows complex behavior near the transition, marked by discontinuous jumps at the first-order boundary, singular behavior at the Mott endpoint and inflections marking sharp variations in the supercritical region. The free energy allows us to identify the thermodynamic phase boundary, to discuss phases stability and metastability, and to touch upon nucleation and spinodal decomposition mechanisms for the transition. We complement this thermodynamic description of the Mott transition by an information-theoretic description. We achieve this by calculating the local entropy, which is a measure of entanglement, and the single-site total mutual information, which quantifies quantum and classical correlations. These information-theoretic measures exhibit characteristic behaviors that allow us to identify the first-order coexistence regions, the Mott critical endpoint and the crossovers along the Widom line in the supercritical region. },
Author = {C. Walsh and P. S{'e}mon and D. Poulin and G. Sordi and A. -M. S. Tremblay},
Eprint = {arXiv:1807.10409},
Journal = {Phys. Rev. B},
Pages = {075122},
Title = {Thermodynamic and information-theoretic description of the Mott transition in the two-dimensional Hubbard model},
Volume = {99},
Year = {2019},
local-url = {WSPS18c.pdf}}
@article{WSPS18b,
Abstract = {Entanglement and information are powerful lenses to probe phases transitions in many-body systems. Motivated by recent cold atom experiments, which are now able to measure the corresponding information-theoretic quantities, we study the Mott transition in the half-filled two-dimensional Hubbard model using cellular dynamical mean-field theory, and focus on two key measures of quantum correlations: entanglement entropy and mutual information. We show that they detect the first-order nature of the transition, the universality class of the endpoint, and the crossover emanating from the endpoint.},
Author = {C. Walsh and P. S{'e}mon and D. Poulin and G. Sordi and A. -M. S. Tremblay},
Eprint = {arXiv:1807.10408},
Journal = {Phys. Rev. Lett.},
Pages = {067203},
Title = {Entanglement entropy and mutual information across the Mott transition in the two-dimensional Hubbard model},
Volume = {122},
Year = {2019},
local-url = {WSPS18d.pdf}}
@article{PMH18a,
Abstract = { Motivated by the growing interest in self-correcting quantum memories, we study the feasibility of self-correction in classical lattice systems composed of bounded degrees of freedom with local interactions. We argue that self-correction, including a requirement of stability against external perturbation, cannot be realized in system with broken global symmetries such as the 2d Ising model, but that systems with local, i.e. gauge, symmetries have the required properties. Previous work gave a three-dimensional quantum system which realized a self-correcting classical memory. Here we show that a purely classical three dimensional system, Wegner's 3D Ising lattice gauge model, can also realize this self-correction despite having an extensive ground state degeneracy. We give a detailed numerical study to support the existence of a self-correcting phase in this system, even when the gauge symmetry is explicitly broken. More generally, our results obtained by studying the memory lifetime of the system are in quantitative agreement with the phase diagram obtained from conventional analysis of the system's specific heat, except that self-correction extends beyond the topological phase, past the lower critical temperature.},
Author = {David Poulin and Roger G. Melko and Matthew B. Hastings},
Eprint = {arXiv:1812.03936},
Journal = {Phys. Rev. B},
Pages = {094103},
Title = {Self-correction in Wegner's 3D Ising lattice gauge theory},
Volume = {99},
Year = {2019},
Local-url = {PMH19a.pdf}}
@article{LP18a,
Abstract = {Belief-propagation (BP) decoders play a vital role in modern coding theory, but they are not
suitable to decode quantum error-correcting codes because of a unique quantum feature called error degeneracy. Inspired by an exact mapping between BP and deep neural networks, we train neural BP decoders for quantum low-density parity-check (LDPC) codes with a loss function tailored to error degeneracy. Training substantially improves the performance of BP decoders for all families of codes we tested and may solve the degeneracy problem which plagues the decoding of quantum LDPC codes.},
Author = {Ye-Hua Liu and David Poulin},
Eprint = {arXiv:1811.07835},
Journal = {Phys. Rev. Lett.},
Pages = {200501},
Title = {Neural Belief-Propagation Decoders for Quantum Error-Correcting Codes},
Volume = {122},
Year = {2019},
local-url = {LP19a.pdf}}
@article{BPS18a,
Abstract = {Foliated quantum codes are a resource for fault-tolerant measurement-based quantum error correction for quantum repeaters and for quantum computation. They represent a general approach to integrating a range of possible quantum error correcting codes into larger fault-tolerant networks. Here we present an ecient heuristic decoding scheme for foliated quantum codes, based on message passing between primal and dual code `sheets'. We test this decoder on two different families of sparse quantum error correcting code: turbo codes and bicycle codes, and show reasonably high numerical performance thresholds. We also present a construction schedule for building such code states.},
Author = {A. Bolt and D. Poulin and T. M. Stace},
Journal = {Phys. Rev. A},
Volume = {98},
Pages = {062302},
Title = {Decoding Schemes for Foliated Sparse Quantum Error Correcting Codes },
Year = {2018},
local-url = {BPS18a.pdf}}
@article{DP18a,
Abstract = {A quantum error correcting protocol can be substantially improved by taking into account features of the physical noise process. We present an ecient decoder for the surface code which can account for general noise features, including coherences and correlations. We demonstrate that the decoder signicantly outperforms the conventional matching algorithm on a variety of noise models, including non-Pauli noise and spatially correlated noise. The algorithm is based on an approximate calculation of the logical channel using a tensor-network description of the noisy state.},
Author = {Andrew S. Darmawan and David Poulin},
Eprint = {arXiv:1801.01879},
Journal = {Phys. Rev. E},
Pages = {051302(R)},
Title = {An ecient general decoding algorithm for the surface code},
Volume = {97},
Year = {2018},
Local-url = {DP18b.pdf}}
@misc{BTP18a,
Abstract = {Arikan's recursive code construction was designed for memoryless channels, but was recently shown to also polarize channels with finite-state memory. The resulting successive cancellation decoder has a complexity that scales like the third power of the channel's memory size. Furthermore, the polar code construction was extended by replacing the block polarization kernel by a convoluted kernel. Here, we extend the polar code efficient decoding algorithm for channels with memory to the family of convolutional polar code. We use numerical simulations to study the performance of these algorithms for practically relevant code sizes and find that the convolutional structure outperforms the standard polar codes on a variety of channels with memory.},
Author = {Benjamin Bourassa and Maxime Tremblay and David Poulin },
Eprint = {arxiv:1805.09378},
Title = {Convolutional Polar Codes on Channels with Memory},
Year = {2018},
local-url = {BTP18a.pdf}}
@article{CIP17a,
Abstract = {We consider the problem of fault-tolerant quantum computation in the presence of slow error diagnostics, either caused by measurement latencies or slow decoding algorithms. Our scheme offers a few improvements over previously existing solutions, for instance it does not require active error correction and results in a reduced error-correction overhead when error diagnostics is much slower than the gate time. In addition, we adapt our protocol to cases where the underlying error correction strategy chooses the optimal correction amongst all Clifford gates instead of the usual Pauli gates. The resulting Clifford frame protocol is of independent interest as it can increase error thresholds and could find applications in other areas of quantum computation.},
Author = {Christopher Chamberland and Pavithran Iyer and David Poulin},
Date-Added = {2017-04-25 12:26:29 +0000},
Date-Modified = {2018-01-09 13:54:01 +0000},
Eprint = {arxiv:1704.06662},
Journal = {Quantum},
Pages = {43},
Title = {Fault-Tolerant Quantum Computing in the Pauli or Clifford Frame with Slow Error Diagnostics},
Volume = {2},
Year = {2018},
Local-url = {CIP17a.pdf}}
@article{DSHT17a,
Abstract = {We present two techniques that can greatly reduce the number of gates required to realize an energy measurement, with application to ground state preparation in quantum simulations. The first technique realizes that to prepare the ground state of some Hamiltonian, it is not necessary to implement the time-evolution operator: any unitary operator which is a function of the Hamiltonian will do. We propose one such unitary operator which can be implemented exactly, circumventing any Taylor or Trotter approximation errors. The second technique is tailored to lattice models, and is targeted at reducing the use of generic single-qubit rotations, which are very expensive to produce by standard fault tolerant techniques. In particular, the number of generic single-qubit rotations used by our method scales with the number of parameters in the Hamiltonian, which contrasts with a growth proportional to the lattice size required by other techniques.},
Author = {David Poulin and Alexei Kitaev and Damian S. Steiger and Matthew B. Hastings and Matthias Troyer},
Eprint = {arXiv:1711.11025},
Journal = {Phys. Rev. Lett},
Pages = {010501},
Title = {Quantum Algorithm for Spectral Measurement with a Lower Gate Count},
Volume = {121},
Year = {2018},
Local-url={PKSH17a.pdf}}
@article{HHPW17b,
Abstract = {Recently we proposed a family of magic state distillation protocols that obtains asymptotic performance that is conjectured to be optimal. This family depends upon several codes, called "inner codes" and "outer codes." We presented some small examples of these codes as well as an analysis of codes in the asymptotic limit. Here, we analyze such protocols in an intermediate size regime, using hundreds to thousands of qubits. We use BCH inner codes, combined with various outer codes. We extend our protocols by adding error correction in some cases. We present a variety of protocols in various input error regimes; in many cases these protocols require significantly fewer input magic states to obtain a given output error than previous protocols.},
Author = {Jeongwan Haah and Matthew B. Hastings and David Poulin and Dave Wecker},
Eprint = {arXiv:1709.02789},
Journal = {Quantum Inf. Comput.},
Keywords = {Distillation},
Pages = {114},
Title = {Magic State Distillation at Intermediate Size},
Volume = {18},
Year = {2018},
local-url = {HHPW17d.pdf}}
@misc{TBP18a,
Abstract = {Polar codes were introduced in 2009 by Arikan as the first efficient encoding and decoding scheme that is capacity achieving for symmetric binary-input memoryless channels. Recently, this code family was extended by replacing the block-structured polarization step of polar codes by a convolutional structure. This article presents a numerical exploration of this so-called convolutional polar codes family to find efficient generalizations of polar codes, both in terms of decoding speed and decoding error probability. The main conclusion drawn from our study is that increasing the convolution depth is more efficient than increasing the polarization kernel's breadth as previously explored.},
Author = {Maxime Tremblay and Benjamin Bourassa and David Poulin },
Date-Added = {2018-05-25 12:24:47 +0000},
Date-Modified = {2018-05-25 12:25:42 +0000},
Eprint = {arxiv:1805.09306},
Title = {Depth versus Breadth in Convolutional Polar Codes},
Year = {2018},
local-url = {TBP18a}}
@article{IP17a,
Abstract = {As far as we know, a useful quantum computer will require fault-tolerant gates, and existing schemes demand a prohibitively large space and time overhead. We argue that a first generation quantum computer will be very valuable to design, test, and optimize fault-tolerant protocols tailored to the noise processes of the hardware. Our argument is essentially a critical analysis of the current methods envisioned to optimize fault-tolerant schemes, which rely on hardware characterization, noise modelling, and numerical simulations. We show that, even within a very restricted set of noise models, error correction protocols depend strongly on the details of the noise model. Combined to the intrinsic diculty of hardware characterization and of numerical simulations of fault-tolerant protocols, we arrive at the conclusion that the currently envisioned optimization cycle is of very limited scope. On the other hand, the direct characterization of a fault-tolerant scheme on a small quantum computer bypasses these diculties, and could provide a bootstrapping path to full-scale fault-tolerant quantum computation.},
Author = {Pavithran {Iyer Sridharan} and David Poulin},
Eprint = {arXiv:1711.04736},
Journal = {Quantum Sci. Technol.},
Pages = {030504},
Title = {A Small Quantum Computer is Needed to Optimize Fault-Tolerant Protocols},
Volume = {3},
Year = {2018},
local-url = {IP18a.pdf}}
@misc{FHP17a,
Author = {Andrew Ferris and Christoph Hirche and David Poulin},
Eprint = {arXiv:1704.00715},
Keywords = {Polar codes; Tensor networks},
Title = {Convolutional Polar Codes},
Year = {2017},
Local-URL = {FHP17a.pdf},
Abstract = {Arikan's Polar codes attracted much attention as the first efficiently decodable and capacity achieving codes. Furthermore, Polar codes exhibit an exponentially decreasing block error probability with an asymptotic error exponent upper bounded by 1/2. Since their discovery, many attempts have been made to improve the error exponent and the finite block-length performance, while keeping the bloc-structured kernel. Recently, two of us introduced a new family of efficiently decodable error-correction codes based on a recently discovered efficiently-contractible tensor network family in quantum many-body physics, called branching MERA. These codes, called branching MERA codes, include Polar codes and also extend them in a non-trivial way by substituting the bloc-structured kernel by a convolutional structure. Here, we perform an in-depth study of a particular example that can be thought of as a direct extension to Arikan's Polar code, which we therefore name Convolutional Polar codes. We prove that these codes polarize and exponentially suppress the channel's error probability, with an asymptotic error exponent log_2(3)/2 which is provably better than for Polar codes under successive cancellation decoding. We also perform finite block-size numerical simulations which display improved error-correcting capability with only a minor impact on decoding complexity.}}
@article{DP16b,
Abstract = {The surface code is a many-body quantum system, and simulating it in generic conditions is computationally hard. While the surface code is believed to have a high threshold, the numerical simulations used to establish this threshold are based on simplified noise models. We present a tensor-network algorithm for simulating error correction with the surface code under arbitrary local noise. Our simulation is exact within statistical fluctuations and we use it to study the threshold and the sub-threshold behaviour of the amplitude-damping and systematic rotation channels. We also compare these exact results to those obtained by making standard approximations to the noise models.},
Author = {Andrew S. Darmawan and David Poulin},
Date-Added = {2016-07-25 15:46:30 +0000},
Date-Modified = {2017-07-28 13:28:20 +0000},
Eprint = {arXiv:1607.06460},
Journal = {Phys. Rev. Lett.},
Keywords = {Topological QC},
Pages = {040502},
Title = {Tensor-network simulations of the surface code under realistic noise},
Volume = {119},
Year = {2017},
local-url = {DP16c.pdf}}
@article{DP16a,
Abstract = {While topological quantum computation is intrinsically fault-tolerant at zero temperature, it looses its topological protection at any finite temperature. We present a scheme to protect the information stored in a system supporting non-cyclic anyons against thermal and measurement errors. The correction procedure builds on the work of G'acs cite{Gacs_86} and Harrington cite{Harrington_04} and operates as a local cellular automaton. In contrast to previously studied schemes, our scheme is valid for both abelian and non-abelian anyons and accounts for measurement errors. We prove the existence of a fault-tolerant threshold and numerically simulate the procedure for a system of Ising anyons. The result of our simulations are consistent with a threshold between $10^{-4}$ and $10^{-3}$.},
Author = {Guillaume Dauphinais and David Poulin},
Eprint = {arXiv:1607.02159},
Journal = {Comm. Math. Phys.},
Pages = {519},
Title = {Fault-Tolerant Quantum Error Correction for non-Abelian Anyons},
Volume = {355},
Year = {2017},
local-url = {DP16a.pdf}}
@article{HHPW17a,
Author = {Jeongwan Haah and Matthew B. Hastings and David Poulin and Dave Wecker},
Eprint = {arXiv:1703.07847},
Journal = {Quantum},
Pages = {31},
Title = {Magic state distillation with low space overhead and optimal asymptotic input count},
Volume = {1},
Year = {2017},
Local-url = {HHPW17a.pdf}}
@article{BDPS16a,
Abstract = {We show how to construct a large class of quantum error correcting codes, known as CSS codes, from highly entangled cluster states. This becomes a primitive in a protocol that foliates a series of such cluster states into a much larger cluster state, implementing foliated quantum error correction. We exemplify this construction with several familiar quantum error correction codes, and propose a generic method for decoding foliated codes. We numerically evaluate the error-correction performance of a family of finite-rate CSS codes known as turbo codes, finding that it performs well over moderate depth foliations. Foliated codes have applications for quantum repeaters and fault-tolerant measurement-based quantum computation. },
Author = {Andrew Bolt, Guillaume Duclos-Cianci, David Poulin and Tom M. Stace},
Eprint = {arXiv:1607.02579},
Journal = {Phys. Rev. Lett.},
Pages = {070501},
Title = {Foliated quantum error-correcting codes},
Volume = {117},
Year = {2016},
Local-url = {BDPS16b.pdf}}
@article{BFP16a,
Abstract = {We introduce a numerical method for identifying topological order in two-dimensional models based on one-dimensional bulk operators. The idea is to identify approximate symmetries supported on thin strips through the bulk that behave as string operators associated to an anyon model. We can express these ribbon operators in matrix product form and define a cost function that allows us to efficiently optimize over this ansatz class. We test this method on spin models with abelian topological order by finding ribbon operators for ℤd quantum double models with local fields and Ising-like terms. In addition, we identify ribbons in the abelian phase of Kitaev's honeycomb model which serve as the logical operators of the encoded qubit for the quantum error-correcting code. We further identify the topologically encoded qubit in the quantum compass model, and show that despite this qubit, the model does not support topological order. Finally, we discuss how the method supports generalizations for detecting nonabelian topological order. },
Author = {Jacob C. Bridgeman, Steven T. Flammia and David Poulin},
Date-Added = {2016-04-27 20:51:06 +0000},
Date-Modified = {2016-11-15 18:27:56 +0000},
Eprint = {arXiv:1603.02275},
Journal = {Phys. Rev. B},
Pages = {205123},
Title = {Detecting Topological Order with Ribbon Operators},
Volume = {94},
Year = {2016},
Local-url = {BFP16b.pdf}}
@misc{DIP16a,
Author = {Nicolas Delfosse, Pavithran Iyer and David Poulin},
Abstract = {We consider a notion of relative homology (and cohomology) for surfaces with two types of boundaries. Using this tool, we study a generalization of Kitaev's code based on surfaces with mixed boundaries. This construction includes both Bravyi and Kitaev's and Freedman and Meyer's extension of Kitaev's toric code. We argue that our generalization offers a denser storage of quantum information. In a planar architecture, we obtain a three-fold overhead reduction over the standard architecture consisting of a punctured square lattice.},
Eprint = {arXiv:1606.7116},
Keywords = {LDPC; Topological QC},
Title = {Generalized surface codes and packing of logical qubits},
Year = {2016},
Local-url = {DIP16a.pdf}}
@misc{DIP16b,
Abstract = {Quantum information processors need to be protected against errors and faults. One of the most widely considered fault-tolerant architecture is based on surface codes. While the general principles of these codes are well understood and basic code properties such as minimum distance and rate are easy to characterize, a code's average performance depends on the detailed geometric layout of the qubits. To date, optimizing a surface code architecture and comparing different geometric layouts relies on costly numerical simulations. Here, we propose a benchmarking algorithm for simulating the performance of surface codes, and generalizations thereof, that runs in linear time. We implemented this algorithm in a software that generates performance reports and allows to quickly compare different architectures. },
Author = {Nicolas Delfosse, Pavithran Iyer and David Poulin},
Date-Added = {2016-11-15 18:31:35 +0000},
Date-Modified = {2016-11-15 18:34:18 +0000},
Eprint = {arXiv:1611.04256},
Title = {A linear-time benchmarking tool for generalized surface codes},
Year = {2016},
local-url = {DIP16b.pdf}}
@article{PHWW14a,
Abstract = { The simulation of molecules is a widely anticipated application of quantum computers. However, recent studies have cast a shadow on this hope by revealing that the complexity in gate count of such simulations increases with the number of spin orbitals N as N^8, which becomes prohibitive even for molecules of modest size N = 100. This study was partly based on a scaling analysis of the Trotter step required for an ensemble of random artificial molecules. Here, we revisit this analysis and find instead that the scaling is closer to N^6 in worst case for real model molecules we have studied, indicating that the random ensemble fails to accurately capture the statistical properties of real-world molecules. Actual scaling may be significantly better than this due to averaging effects. We then present an alternative simulation scheme and show that it can sometimes outperform existing schemes, but that this possibility depends crucially on the details of the simulated molecule. We obtain further improvements using a version of the coalescing scheme of cite{WBCH13a}; this scheme is based on using different Trotter steps for different terms. The method we use to bound the complexity of simulating a given molecule is efficient, in contrast to the approach of cite{WBCH13a,HWBT14a} which relied on exponentially costly classical exact simulation.},
Author = {David Poulin, M.B. Hastings, Dave Wecker, Nathan Wiebe, Andrew C. Doherty and Matthias Troyer,},
Date-Added = {2014-06-19 17:31:01 +0000},
Date-Modified = {2015-03-31 13:42:48 +0000},
Journal = {Quant. Info. and Comp.},
Keywords = {Simulation},
Pages = {0361},
Title = {The Trotter Step Size Required for Accurate Quantum Simulation of Quantum Chemistry},
Volume = {15},
Year = {2015},
local-url = {PHWW14b.pdf}}
@article{DP14a,
Abstract = {In leading fault-tolerant quantum computing schemes, accurate transformation are obtained by a two-stage process. In a first stage, a discrete, universal set of fault-tolerant operations is obtained by error-correcting noisy transformations and distilling resource states. In a second stage, arbitrary transformations are synthesized to desired accuracy by combining elements of this set into a circuit. Here, we present a scheme which merges these two stages into a single one, directly distilling complex transformations. We find that our scheme can reduce the total overhead to realize certain gates by up to a few orders of magnitude. In contrast to other schemes, this efficient gate synthesis does not require computationally intensive compilation algorithms, and a straightforward generalization of our scheme circumvents compilation and synthesis altogether.},
Author = {G. Duclos-Cianci and D. Poulin},
Eprint = {arXiv:1403.5280},
Journal = {Phys. Rev. A},
Pages = {042315},
Title = {Reducing the quantum computing overhead with complex gate distillation},
Volume = {91},
Year = {2015},
local-url = {DP15a.pdf}}
@article{IP13a,
Abstract = {In this article we address the computational hardness of optimally decoding a quantum stabilizer code. Much like classical linear codes, errors are detected by measuring certain check operators which yield an error syndrome, and the decoding problem consists of determining the most likely recovery given the syndrome. The corresponding classical problem is known to be {NP-complete}, and a similar decoding problem for quantum codes is also known to be {NP-complete.} However, this decoding strategy is not optimal in the quantum setting as it does not take into account error degeneracy, which causes distinct errors to have the same effect on the code. Here, we show that optimal decoding of stabilizer codes is computationally much harder than optimal decoding of classical linear codes, it is {\#P.}},
Author = {Iyer, Pavithran and Poulin, David},
Date-Added = {2013-10-31 21:20:38 +0000},
Date-Modified = {2015-12-14 16:29:46 +0000},
Eprint = {arXiv:1310.3235},
Journal = {IEEE Trans. Info. Theor.},
Keywords = {Quantum Physics},
Pages = {5209},
Title = {Hardness of decoding quantum stabilizer codes},
Volume = {61},
Year = {2015},
local-url = {IP15a.pdf}}
@misc{LYPP15a,
Author = {Olivier Landon-Cardinal, Beni Yoshida, John Preskill and David Poulin},
Journal = {Phys. Rev. A},
Volume = {91},
Pages = {032303},
Eprint = {arXiv:1501.04112 },
Keywords = {Topological phase},
Title = {Perturbative instability of quantum memory based on effective long-range interactions},
Year = {2015},
Local-url = {LYPP15b.pdf}}
@misc{WBP15a,
Abstract = {We analyse a model for fault-tolerant quantum computation with low overhead suitable for situations where the noise is biased. The basis for this scheme is a gadget for the fault-tolerant preparation of magic states that enable universal fault-tolerant quantum computation using only Clifford gates that preserve the noise bias. We analyse the distillation of |T⟩-type magic states using this gadget at the physical level, followed by concatenation with the 15-qubit quantum Reed-Muller code, and comparing our results with standard constructions. In the regime where the noise bias (rate of Pauli Z errors relative to other single-qubit errors) is greater than a factor of 10, our scheme has lower overhead across a broad range of relevant noise rates. },
Author = {Paul Webster, Stephen D. Bartlett and David Poulin},
Date-Added = {2015-12-14 19:40:37 +0000},
Date-Modified = {2015-12-14 19:42:32 +0000},
Eprint = { arXiv:1509.05032},
Journal = {Phys. Rev. A},
Pages = {062309},
Title = {Reducing the overhead for quantum computation when noise is biased},
Volume = {92},
Year = {2015},
local-url = {WBP15b.pdf}}
@article{ADP14a,
Abstract = {Steane's 7-qubit quantum error-correcting code admits a set of fault-tolerant gates that generate the Clifford group, which in itself is not universal for quantum computation. The 15-qubit Reed-Muller code also does not admit a universal fault-tolerant gate set but possesses fault-tolerant T and control-control-Z gates. Combined with the Clifford group, either of these two gates generate a universal set. Here, we combine these two features by demonstrating how to fault-tolerantly convert between these two codes, providing a new method to realize universal fault-tolerant quantum computation. One interpretation of our result is that both codes correspond to the same subsystem code in different gauges. Our scheme extends to the entire family of quantum Reed-Muller codes.},
Author = {Anderson, Jonas T. and Duclos-Cianci, Guillaume and Poulin, David},
Journal = {Phys. Rev. Lett.},
Volume = {113},
Pages = {080501},
Eprint = {arXiv:1403.2734},
Title = {Fault-tolerant conversion between the Steane and Reed-Muller quantum codes},
Year = {2014},
Local-url = {ADP14b.pdf}}
@inproceedings{FP14a,
Author = {Andrew Ferris and David Poulin},
Booktitle = {International Symposium on Information Theory },
Organization = {IEEE},
Title = {Branching {MERA} codes: a natural extension of classical and quantum polar codes},
Year = {2014},
local-url = {FP14a.pdf}}
@article{FP14d,
Abstract = {We establish several relations between quantum error correction ({QEC)} and tensor network ({TN)} methods of quantum many-body physics. We exhibit correspondences between well-known families of {QEC} codes and {TNs}, and demonstrate a formal equivalence between decoding a {QEC} code and contracting a {TN.} We build on this equivalence to propose a new family of quantum codes and decoding algorithms that generalize and improve upon quantum polar codes and successive cancellation decoding in a natural way.},
Author = {Ferris, Andrew J. and Poulin, David},
Journal = {Phys. Rev. Lett.},
Volume = {113},
Pages = {030501},
Eprint = {arXiv:1312.4578},
Title = {Tensor Networks and Quantum Error Correction},
Year = {2014},
local-url = {FP13a.pdf}}
@article{DP13b,
Abstract = {We present a three-dimensional generalization of a renormalization group decoding algorithm for topological codes with Abelian anyonic excitations that we previously introduced for two dimensions. This 3D implementation extends our previous 2D algorithm by incorporating a failure probability of the syndrome measurements, i.e., it enables fault-tolerant decoding. We report a fault-tolerant storage threshold of 1.9(4)% for Kitaev's toric code subject to a 3D bit-flip channel (i.e. including imperfect syndrome measurements). This number is to be compared with the 2.9% value obtained via perfect matching. The 3D generalization inherits many properties of the 2D algorithm, including a complexity linear in the space-time volume of the memory, which can be parallelized to logarithmic time.},
Author = {Guillaume Duclos-Cianci and David Poulin},
Journal = {Quant. Info. and Comp.},
Volume = {14},
Pages = {0721},
Eprint = {arXiv:1304.6100},
Title = {Fault-Tolerant Renormalization Group Decoder for Abelian Topological Codes},
Year = {2014},
local-url = {DP13a1.pdf}}
@misc{BBDFP13,
Abstract = {We consider two-dimensional lattice models that support Ising anyonic excitations and are coupled to a thermal bath. We propose a phenomenological model for the resulting short-time dynamics that includes pair-creation, hopping, braiding, and fusion of anyons. By explicitly constructing topological quantum error-correcting codes for this class of system, we use our thermalization model to estimate the lifetime of the quantum information stored in the encoded spaces. To decode and correct errors in these codes, we adapt several existing topological decoders to the non-Abelian setting. We perform large-scale numerical simulations of these two-dimensional Ising anyon systems and find that the thresholds of these models range between 13% to 25%. To our knowledge, these are the first numerical threshold estimates for quantum codes without explicit additive structure. },
Author = {C.G. Brell and S.D. Burton and G. Dauphinais and S.T. Flammia and D. Poulin},
Eprint = {arXiv:1311.0019},
Year = {2013},
Title = {Thermalization, Error-Correction, and Memory Lifetime for Ising Anyon Systems },
local-url = {BBDFa1.pdf}}
@article{KP13a,
Author = {D. Kribs and D. Poulin},
Title = {Operator quantum error correction},
Editor = {D.A. Lidar and T.A. Brun},
Number = {6},
Pages = {163},
Publisher = {Cambridge University Press, Cambridge},
Journal = {Chapter in book Quantum Error Correction},
Local-url = {KP08av2.pdf},
Year = {2013}}
@article{P13a,
Author = {D. Poulin},
Title = {Iterative quantum coding systems},
Editor = {D.A. Lidar and T.A. Brun},
Number = {11},
Pages = {279},
Publisher = {Cambridge University Press},
Journal = {Chapter in book Quantum error correction},
Local-url = {Pou08a},
Year = {2013}}
@article{PP12a,
Author = {Emilie Pelchat and David Poulin},
Date-Added = {2012-04-12 08:39:46 -0400},
Date-Modified = {2013-05-29 14:36:44 +0000},
Eprint = {arXiv:1204.2439},
Journal = {IEEE Trans. Info. Theor.},
Keywords = {Error correction},
Pages = {3915},
Title = {Degenerate Viterbi decoding},
Volume = {59},
Year = {2013},
local-url = {PP13a1.pdf}}
@article{FP13a,
Abstract = {The Markov entropy decomposition {(MED)} is a recently-proposed, cluster-based simulation method for finite temperature quantum systems with arbitrary geometry. In this paper, we detail numerical algorithms for performing the required steps of the {MED}, principally solving a minimization problem with a preconditioned Newton's algorithm, as well as how to extract global susceptibilities and thermal responses. We demonstrate the power of the method with the spin-1/2 {XXZ} model on the {2D} square lattice, including the extraction of critical points and details of each phase. Although the method shares some qualitative similarities with exact-diagonalization, we show the {MED} is both more accurate and significantly more flexible.},
Author = {Ferris, Andrew J. and Poulin, David},
Date-Added = {2012-12-07 09:34:47 -0500},
Date-Modified = {2013-05-28 20:04:18 +0000},
Eprint = {arXiv:1212.1442},
Journal = {Phys. Rev. B},
Keywords = {Belief Propagatio; Markov entropy},
Pages = {205126},
Title = {Algorithms for the Markov Entropy Decomposition},
Urldate = {2012-12-07},
Volume = {87},
Year = {2013},
local-url = {FP13a1.pdf}}
@misc{FP13c,
Abstract = {We introduce a new class of circuits for constructing efficiently decodable error-correction codes, based on a recently discovered contractible tensor network. We perform an in-depth study of a particular example that can be thought of as an extension to Arikan's polar code. Notably, our numerical simulation show that this code polarizes the logical channels more strongly while retaining the log-linear decoding complexity using the successive cancellation decoder. These codes also display improved error-correcting capability with only a minor impact on decoding complexity. Efficient decoding is realized using powerful graphical calculus tools developed in the field of quantum many-body physics. In a companion paper, we generalize our construction to the quantum setting and describe more in-depth the relation between classical and quantum error correction and the graphical calculus of tensor networks.},
Author = {Ferris, Andrew J. and Poulin, David},
Date-Added = {2013-12-19 19:12:39 +0000},
Date-Modified = {2013-12-19 19:13:41 +0000},
Eprint = {arXiv:1312.4575},
Title = {Branching {MERA} codes: a natural extension of polar codes},
Year = {2013},
local-url = {FP13c1.pdf}}
@article{STIMUL2013,
Year = {2013},
Abstract = {},
title = {Simulations of Magnetic Field Gradients due to Micro-Magnets on a Triple Quantum Dot Circuit},
author = {G. Poulin-Lamarre, C. Bureau-Oxton, A. Kam, P. Zawadzki, S. Studenikin, G. Aers, M. Pioro-Ladrière and A. S. Sachrajda},
journal = {AIP Conference Proceedings 1566, 556}}
@article{DP13a,
Year = {2013},
Journal = {Phys. Rev. A},
Volume = {87},
Pages = {062338},
Abstract = {We study the quantum error correction threshold of Kitaev's toric code over the group Z_d subject to a generalized bit-flip noise. This problem requires novel decoding techniques, and for this purpose we generalize the renormalization group method we previously introduced for Z_2 topological codes.},
title = {Kitaev's Z_d-Codes Threshold Estimates},
author = {Guillaume Duclos-Cianci and David Poulin},
eprint = {arXiv:1302.3638},
local-url = {DP13c1.pdf}}
@article{LP13a,
Abstract = {We study the robustness of quantum information stored in the degenerate ground space of a local, frustration-free Hamiltonian with commuting terms on a {2D} spin lattice. On one hand, a macroscopic energy barrier separating the distinct ground states under local transformations would protect the information from thermal fluctuations. On the other hand, local topological order would shield the ground space from static perturbations. Here we demonstrate that local topological order implies a constant energy barrier, thus inhibiting thermal stability.},
Author = {Landon-Cardinal, Olivier and Poulin, David},
Eprint = {arXiv:1209.5750},
Journal = {Phys. Rev. Lett.},
Pages = {090502},
Title = {Local topological order inhibits thermal stability in {2D}},
Volume = {110},
Year = {2013},
local-url = {LP13a1.pdf}}
@article{BDPS12a,
Author = {S. Bravyi, G. Duclos-Cianci, D. Poulin and M. Suchara},
Eprint = {arXiv:1207.1443},
Journal = {Quant. Info. and Comp.},
Keywords = {Topological QC},
Pages = {0963},
Title = {Subsystem surface codes with three-qubit check operators},
Volume = {13},
Year = {2013},
Abstract = {We propose a simplied version of the Kitaev's surface code in which error correction requires only three-qubit parity measurements for Pauli operators XXX and ZZZ. The new code belongs to the class of subsystem stabilizer codes. It inherits many favorable properties of the standard surface code such as encoding of multiple logical qubits on a planar lattice with punctured holes, ecient decoding by either minimum-weight matching or renormalization group methods, and high error threshold. The new subsystem surface code (SSC) gives rise to an exactly solvable Hamiltonian with 3-qubit interactions, topologically ordered ground state, and a constant energy gap. We construct a local unitary transformation mapping the SSC Hamiltonian to the one of the ordinary surface code thus showing that the two Hamiltonians belong to the same topological class. We describe error correction protocols for the SSC and determine its error thresholds under several natural error models. In particular, we show that the SSC has error threshold approximately 0:6% for the standard circuit-based error model studied in the literature. We also consider a model in which three-qubit parity operators can be measured directly. We show that the SSC has error threshold approximately 0:97% in this setting.},
local-url = {BDPS12a1.pdf}}
@misc{BP12a,
Abstract = {Quantum Markov networks are a generalization of quantum Markov chains to arbitrary graphs. They provide a powerful classification of correlations in quantum many-body systems---complementing the area law at finite temperature---and are therefore useful to understand the powers and limitations of certain classes of simulation algorithms. Here, we extend the characterization of quantum Markov networks and in particular prove the equivalence of positive quantum Markov networks and Gibbs states of Hamiltonians that are the sum of local commuting terms on graphs containing no triangles. For more general graphs we demonstrate the equivalence between quantum Markov networks and Gibbs states of a class of Hamiltonians of intermediate complexity between commuting and general local Hamiltonians.},
Author = {Brown, Winton and Poulin, David},
Date-Added = {2012-06-06 10:36:53 -0400},
Date-Modified = {2012-06-06 10:37:49 -0400},
Eprint = {arXiv:1206.0755},
Title = {Quantum Markov Networks and Commuting Hamiltonians},
Year = {2012},
local-url = {BP12a1.pdf}}
@article{DBP12a,
Author = {Gabrielle Denhez and Alexandre Blais and David Poulin},
Journal = {Phys. Rev. A},
Pages = {032318},
Title = {Quantum error correction benchmarks for continuous weak parity measurements},
Volume = {86},
Year = {2012},
Eprint = {arXiv:1204.3793},
local-url = {DBP12b1.pdf}}
@article{BDP11a,
Abstract = {Topological phases can be defined in terms of local equivalence:
two systems are in the same topological phase if it is possible to transform
one into the other by a local reorganization of its degrees of freedom. The
classification of topological phases therefore amounts to the classification of
long-range entanglement. Such local transformation could result, for instance,
from the adiabatic continuation of one system’s Hamiltonian to the other. Here,
we use this definition to study the topological phase of translationally invariant
stabilizer codes in two spatial dimensions, and show that they all belong to one
universal phase. We do this by constructing an explicit mapping from any such
code to a number of copies of Kitaev’s code. Some of our results extend to some
two-dimensional (2D) subsystem codes, including topological subsystem codes.
Error correction benefits from the corresponding local mappings. In particular, it
enables us to use decoding algorithm developed for Kitaev’s code to decode any
2D stabilizer code and subsystem code.},
Author = {Hector Bombin and Guillaume Duclos-Cianci and David Poulin},
Eprint = {arXiv:1103.4606},
Keywords = {Topological QC},
Title = {Universal topological phase of 2D stabilizer codes},
Year = {2012},
Journal = {New J. Phys.},
Volume = {14},
Pages = {073048},
local-url = {BDP12a1.pdf}}
@article{LP12a,
Abstract = {We describe a method for reconstructing multi-scale entangled states from a small number of efficiently-implementable measurements and fast post-processing. The method only requires singleparticle measurements and the total number of measurements is polynomial in the number of particles. Data post-processing for state reconstruction uses standard tools, namely matrix diagonalisation and conjugate gradient method, and scales polynomially with the number of particles. Our method prevents the build-up of errors from both numerical and experimental imperfections.},
Journal = {New J. Phys.},
Volume = {14},
Pages = {085004},
Author = {Olivier Landon-Cardinal and David Poulin},
Eprint = {arXiv:1204.0792},
local-url = {LP12b1.pdf},
Title = {Practical learning method for multi-scale entangled states},
Year = {2012}}
@article{PQSV11a,
Author = {David Poulin and Angie Quarry and Rolando D. Somma and Frank Verstraete},
Eprint = {arXiv:1102.1360},
Journal = {Phys. Rev. Lett.},
Volume = {106},
Pages = {170501},
Title = {Quantum simulation of time-dependent Hamiltonians and the convenient illusion of Hilbert space},
Local-Url = {PQSV11b1.pdf},
Year = {2011},
Abstract = {We consider the manifold of all quantum many-body states that can be generated by arbitrary time-dependent local Hamiltonians in a time that scales polynomially in the system size, and showthat it occupies an exponentially small volume in Hilbert space. This implies that the overwhelming majority of states in Hilbert space are not physical as they can only be produced after an exponentially long time. We establish this fact by making use of a time-dependent generalization of the Suzuki-Trotter expansion, followed by a well-known counting argument. This also demonstrates that a computational model based on arbitrarily}}
@article{PH11a,
Abstract = {We present a lower bound for the free energy of a quantum many-body system at finite temperature. This lower bound is expressed as a convex optimization problem with linear constraints, and is derived using strong subadditivity of von Neumann entropy and a relaxation of the consistency condition of local density operators. The dual to this minimization problem leads to a set of quantum belief propagation equations, thus providing a firm theoretical foundation to that approach. The minimization problem is numerically tractable, and we find good agreement with quantum Monte Carlo for the spin-1/2 Heisenberg anti-ferromagnet in two dimensions. This lower bound complements other variational upper bounds. We discuss applications to Hamiltonian complexity theory and give a generalization of the structure theorem to trees in an appendix.},
Author = {David Poulin and Matthew B. Hastings},
Eprint = {arXiv:1012.2050},
Journal = {Phys. Rev. Lett},
Pages = {080403},
Title = {Markov entropy decomposition: a variational dual for quantum belief propagation},
Volume = {106},
Year = {2011},
local-url = {PH11b1.pdf}}
@article{TOVP11a,
Year = {2011},
Abstract = {The original motivation to build a quantum computer came from
Feynman, who imagined a machine capable of simulating generic
quantum mechanical systems—a task that is believed to be intractable
for classical computers. Such a machine could have farreaching
applications in the simulation of many-body quantum
physics in condensed-matter, chemical and high-energy systems.
Part of Feynman’s challenge was met by Lloyd, who showed how to
approximately decompose the time evolution operator of interacting
quantum particles into a short sequence of elementary gates,
suitable for operation on a quantum computer. However, this left
open the problem of how to simulate the equilibrium and static
properties of quantum systems. This requires the preparation of
ground and Gibbs states on a quantum computer. For classical
systems, this problem is solved by the ubiquitous Metropolis algorithm,
a method that has basically acquired a monopoly on the
simulation of interacting particles. Here we demonstrate how to
implement a quantum version of the Metropolis algorithm. This
algorithm permits sampling directly from the eigenstates of the
Hamiltonian, and thus evades the sign problem present in classical
simulations. A small-scale implementation of this algorithm
should be achievable with today’s technology.},
author = {K. Temme and T.J. Osborne and K. Vollbrecht and David Poulin and F. Verstraete},
title = {Quantum Metropolis Sampling},
journal = {Nature},
volume = {471},
pages = {87},
month = {March},
eprint = {arXiv:0911.3635},
local-url = {TOVP11a.pdf}}
@article{SLP11a,
Abstract = {Quantum tomography is the main method used to assess the quality of quantum information processing devices. However, the amount of resources needed for quantum tomography is exponential in the device size. Part of the problem is that tomography generates much more information than is usually sought. Taking a more targeted approach, we develop schemes that enable (i) estimating the fidelity of an experiment to a theoretical ideal description, (ii) learning which description within a reduced subset best matches the experimental data. Both these approaches yield a significant reduction in resources compared to tomography. In particular, we demonstrate that fidelity can be estimated from a number of simple experiments that is independent of the system size, removing an important roadblock for the experimental study of larger quantum information processing units.},
Author = {Marcus P. {da Silva} and Olivier Landon-Cardinal and David Poulin},
Eprint = {arXiv:1104.3835},
Journal = {Phys. Rev. Lett.},
Pages = {210404},
Title = {Practical characterization of quantum devices without tomography},
Volume = {107},
Year = {2011},
Local-url = {dLP11a1.pdf}}
@article{P10a,
Abstract = {The Lieb-Robinson bound shows the existence of a maximum speed of signal propagation in discrete quantum mechanical systems with local interactions. This generalizes the concept of relativistic causality beyond field theory, and provides a powerful tool in theoretical condensed matter physics and quantum information science. Here, we extend the scope of this seminal result by considering general Markovian quantum evolution, where we prove that an equivalent bound holds. In addition, we use the generalized bound to demonstrate that correlations in the stationary state of a Markov process decay on a length-scale set by the Lieb-Robinson velocity and the system's relaxation time. },
Author = {David Poulin},
Date-Added = {2010-04-22 09:52:11 -0400},
Date-Modified = {2010-05-06 13:38:06 -0400},
Journal = {Phys. Rev. Lett.},
Volume = {104},
Pages = {190401},
Local-Url = {P10a.pdf},
Title = {Lieb-Robinson bound and locality for general Markovian quantum dynamics},
Year = {2010},
Eprint = {1003.3675}}
@article{BP10b,
Abstract = {We continue our numerical study of quantum belief propagation initiated in cite{PB08a}. We demonstrate how the method can be expressed in terms of an effective thermal potential that materializes when the system presents quantum correlations, but is insensitive to classical correlations. The thermal potential provides an efficient means to assess the precision of belief propagation on graphs with no loops. We illustrate these concepts using the one-dimensional quantum Ising model and compare our results with exact solutions. We also use the method to study the transverse field quantum Ising spin glass for which we obtain a phase diagram that is largely in agreement with the one obtained in cite{LSS07a} using a different approach. Finally, we introduce the coarse grained belief propagation (CGBP) algorithm to improve belief propagation at low temperatures. This method combines the reliability of belief propagation at high temperatures with the ability of entanglement renormalization to efficiently describe low energy subspaces of quantum systems with local interactions. With CGBP, thermodynamic properties of quantum systems can be calculated with a high degree of accuracy at all temperatures. },
Author = {E. Bilgin and David Poulin},
Date-Added = {2009-10-13 12:36:12 -0400},
Date-Modified = {2010-05-06 13:36:54 -0400},
Eprint = {arXiv:0910.2299},
Journal = {Phys. Rev. B},
Keywords = {Simulation; Belief Propagation},
Local-Url = {BP10b.pdf},
Pages = {054106},
Title = {Coarse grained belief propagation for simulation of interacting quantum systems at all temperatures},
Volume = {81},
Year = {2010}}
@article{DP10a,
Abstract = {We present a family of algorithms, combining real-space renormalization methods and belief propagation, to estimate the free energy of a topologically ordered system in the presence of defects. Such an algorithm is needed to preserve the quantum information stored in the ground space of a topologically ordered system and to decode topological error-correcting codes. For a system of linear size $ell$, our algorithm runs in time $logell$ compared to $ell^6$ needed for the minimum-weight perfect matching algorithm previously used in this context and achieves a higher depolarizing error threshold.},
Author = {Guillaume Duclos-Cianci and David Poulin},
Date-Added = {2009-11-09 09:11:43 -0500},
Date-Modified = {2010-05-06 13:37:27 -0400},
Eprint = {arXiv:0911.0581},
Journal = {Phys. Rev. Lett.},
Keywords = {Topological QC; Error correction},
Local-Url = {DP10a.pdf},
Pages = {050504},
Title = {Fast decoders for topological quantum codes},
Volume = {104},
Year = {2010}}
@inproceedings{DP10a1,
Year = {2010},
Abstract = {Topological quantum error-correcting codes are defined by geometrically local checks on a two-dimensional lattice of quantum bits (qubits), making them particularly well suited for fault-tolerant quantum information processing. Here, we present a decoding algorithm for topological codes that is faster than previously known algorithms and applies to a wider class of topological codes. Our algorithm makes use of two methods inspired from statistical physics: renormalization groups and mean-field approximations. First, the topological code is approximated by a concatenated block code that can be efficiently decoded. To improve this approximation, additional consistency conditions are imposed between the blocks, and are solved by a belief propagation algorithm.},
title = {A renormalization group decoding algorithm for topological quantum codes},
booktitle = {IEEE Information Theory Workshop},
author = {Guillaume Duclos-Cianci and David Poulin},
eprint = {arXiv:1006.1362},
local-url = {DP10a1.pdf}}
@article{CPFS10a,
Author = {M. Cramer and M.B. Plenio and S.T. Flammia and R. Somma and D. Gross and S.D. Bartlett and O. Landon-Cardinal and D. Poulin and Y.-K. Liu},
Journal = {Nature Comm.},
Pages = {149},
Title = {Efficient quantum state tomography},
Volume = {1},
Year = {2010},
Eprint = {1101.4366},
Abstract = {Quantum state tomography—deducing quantum states from measured data—is the gold standard for verification and benchmarking of quantum devices. It has been realized in systems with few components, but for larger systems it becomes unfeasible because the number of measurements and the amount of computation required to process them grows exponentially in the system size. Here, we present two tomography schemes that scale much more favourably than direct tomography with system size. One of them requires unitary operations on a constant number of subsystems, whereas the other requires only local measurements together with more elaborate post-processing. Both rely only on a linear number of experimental operations and post-processing that is polynomial in the system size. These schemes can be applied to a wide range of quantum states, in particular those that are well approximated by matrix product states. The accuracy of the reconstructed states can be rigorously certified without any a priori assumptions.},
Local-Url = {CPFS10a1.pdf}}
@article{BNPV10a,
Author = {R. Blume-Kohout and H.K. Ng and D. Poulin and L. Viola},
Date-Added = {2010-03-16 13:15:33 -0400},
Date-Modified = {2010-12-09 14:07:09 -0500},
Eprint = {arXiv:1006.1358},
Journal = {Phys. Rev. A},
Pages = {062306},
Title = {Information preserving structures: a general framework for quantum zero-error information},
Volume = {82},
Year = {2010},
Local-Url = {BNPV10b1.pdf},
Abstract = {Quantum systems carry information. Quantum theory supports at least two distinct kinds of
information (classical and quantum), and a variety of different ways to encode and preserve information
in physical systems. A system's ability to carry information is constrained and defined
by the noise in its dynamics. This paper introduces an operational framework, using informationpreserving
structures to classify all the kinds of information that can be perfectly (i.e., with zero
error) preserved by quantum dynamics. We prove that every perfectly preserved code has the same
structure as a matrix algebra, and that preserved information can always be corrected. We also
classify distinct operational criteria for preservation (e.g., ``noiseless'', ``unitarily correctible'', etc.)
and introduce two new and natural criteria for measurement-stabilized and unconditionally preserved
codes. Finally, for several of these operational critera, we present efficient [polynomial in the
state-space dimension] algorithms to find all of a channel's information-preserving structures.}}
@inproceedings{BPT10b,
Author = {S. Bravyi and D. Poulin and B.M. Terhal},
Booktitle = {Quantum Cryptography and Computing},
Editor = {R. Horodecki and S. Ya. Kilin and J. Kowalik},
Pages = {125},
Title = {Tradeoffs for reliable quantum information storage in 2D systems},
Year = {2010},
local-url = {BPT10a.pdf}}
@article{BPT10a,
Abstract = {We ask whether there are fundamental limits on storing quantum information reliably in a bounded volume of space. To investigate this question, we study quantum error correcting codes specified by geometrically local commuting constraints on a 2D lattice of finite-dimensional quantum particles. For these 2D systems, we derive a tradeoff between the number of encoded qubits $k$, the distance of the code $d$, and the number of particles $n$. It is shown that $kd^2=O(n)$ where the coefficient in $O(n)$ depends only on the locality of the constraints and dimension of the Hilbert spaces describing individual particles. The analogous tradeoff for the classical information storage is $ksqrt{d} =O(n)$.},
Author = {S. Bravyi and David Poulin and B.M. Terhal},
Date-Added = {2009-10-01 08:43:00 -0400},
Date-Modified = {2010-05-06 13:35:38 -0400},
Eprint = {arXiv:0909.5200},
Journal = {Phys. Rev. Lett.},
Keywords = {Error correction, Self correcting},
Local-Url = {BPT10b.pdf},
Pages = {050503},
Title = {Tradeoffs for reliable quantum information storage in {2D} systems},
Volume = {104},
Year = {2010}}
@article{PTO09a,
Abstract = {We present a theory of quantum serial turbo-codes, describe their iterative decoding algorithm, and study their performances numerically on a depolarization channel. Our construction offers several advantages over quantum LDPC codes. First, the Tanner graph used for decoding is free of 4-cycles that deteriorate the performances of iterative decoding. Secondly, the iterative decoder makes explicit use of the code's degeneracy. Finally, there is complete freedom in the code design in terms of length, rate, memory size, and interleaver choice.
We define a quantum analogue of a state diagram that provides an efficient way to verify the properties of a quantum convolutional code, and in particular its recursiveness and the presence of catastrophic error propagation. We prove that all recursive quantum convolutional encoder have catastrophic error propagation. In our constructions, the convolutional codes have thus been chosen to be non-catastrophic and non-recursive.
While the resulting families of turbo-codes have bounded minimum distance,
from a pragmatic point of view the effective minimum distances of the codes that we have simulated are large enough not to degrade the iterative decoding performance up to reasonable word error rates and block sizes. With well chosen constituent convolutional codes, we observe an important reduction of the word error rate as the code length increases. },
Author = {D. Poulin and J.-P. Tillich and H. Ollivier},
Date-Added = {2007-07-09 10:08:12 -0700},
Date-Modified = {2010-05-06 13:38:55 -0400},
Eprint = {arXiv:0712.2888},
Journal = {IEEE Trans. Info. Theor.},
Keywords = {Turbo Codes; Error correction},
Local-Url = {PTO09b.pdf},
Number = {6},
Pages = {2776},
Title = {Quantum serial turbo-codes},
Volume = {55},
Year = {2009}}
@article{PW09b,
Abstract = {We present a quantum algorithm to prepare the thermal Gibbs state of interacting quantum systems. This algorithm sets a universal upper bound $D^\alpha$ on the thermalization time of a quantum system, where $D$ is the system's Hilbert space dimension and $\alpha \leq \frac 12$ is proportional to the Helmholtz free energy density of the system. We also derive an algorithm to evaluate the partition function of a quantum system in a time proportional to the system's thermalization time and inversely proportional to the targeted accuracy squared. },
Author = {David Poulin and Pawel Wocjan},
Date-Added = {2009-06-05 14:51:04 -0400},
Date-Modified = {2010-05-06 13:40:25 -0400},
Eprint = {arXiv:0905.2199},
Journal = {Phys. Rev. Lett.},
Local-Url = {PW09e.pdf},
Pages = {220502},
Title = {Sampling from the quantum Gibbs state and evaluating partition functions with a quantum computer},
Volume = {103},
Year = {2009}}
@article{PW09a,
Abstract = {Preparing the ground state of a system of interacting classical particles is an NP-hard problem. Thus, there is in general no better algorithm to solve this problem than exhaustively going through all $N$ configurations of the system to determine the one with lowest energy, requiring a running time proportional to $N$. A quantum computer, if it could be built, could solve this problem in time $\sqrt N$. Here, we present a powerful extension of this result to the case of interacting {\em quantum} particles, demonstrating that a quantum computer can prepare the ground state of a quantum system as efficiently as it does for classical systems. },
Author = {David Poulin and Pawel Wocjan},
Date-Added = {2008-09-16 10:33:27 -0400},
Date-Modified = {2010-05-06 13:39:48 -0400},
Eprint = {arXiv:0809.2705},
Journal = {Phys. Rev. Lett.},
Keywords = {Complexity; Quantum simulation},
Local-Url = {PW09b.pdf},
Pages = {130503},
Title = {Preparing ground states of quantum many-body systems on a quantum computer},
Volume = {102},
Year = {2009}}
@article{PB08a,
Abstract = {Belief propagation --- a powerful heuristic method to solve inference problems involving a large number of random variables --- was recently generalized to quantum theory. Like its classical counterpart, this algorithm is exact on trees when the appropriate independence conditions are met and is expected to provide reliable approximations when operated on loopy graphs. In this paper, we benchmark the performances of loopy quantum belief propagation (QBP) in the context of finite-temperature quantum many-body physics. Our results indicate that QBP provides reliable estimates of the high-temperature correlation function when the typical loop size in the graph is large. As such, it is suitable e.g. for the study of quantum spin glasses on Bethe lattices and the decoding of sparse quantum error correction codes. },
Author = {D. Poulin and E. Bilgin},
Date-Added = {2007-11-19 16:02:55 -0800},
Date-Modified = {2010-05-06 13:46:46 -0400},
Eprint = {arXiv:0710.4304},
Journal = {Phys. Rev. A},
Keywords = {Simulation; Belief propagation},
Local-Url = {PB08a.pdf},
Pages = {052318},
Title = {Belief propagation algorithm for computing correlation functions in finite-temperature quantum many-body systems on loopy graphs},
Volume = {77},
Year = {2008}}
@article{PC08a,
Abstract = {We address the problem of decoding sparse quantum error correction codes. For Pauli channels, this task can be accomplished by a version of the belief propagation algorithm used for decoding sparse classical codes. Quantum codes pose two new challenges however. Firstly, their Tanner graph unavoidably contain small loops which typically undermines the performance of belief propagation. Secondly, sparse quantum codes are by definition highly degenerate. The standard belief propagation algorithm does not exploit this feature, but rather it is impaired by it. We propose heuristic methods to improve belief propagation decoding, specifically targeted at these two problems.
While our results exhibit a clear improvement due to the proposed heuristic methods, they also indicate that the main source of errors in the quantum coding scheme remains in the decoding. },
Author = {D. Poulin and Y. Chung},
Date-Added = {2007-11-19 11:11:22 -0800},
Date-Modified = {2010-05-06 13:42:31 -0400},
Eprint = {arXiv:0801.1241},
Journal = {Quant. Info. and Comp.},
Keywords = {LDPC; Belief propagation},
Local-Url = {PC08a.pdf},
Pages = {986},
Title = {On the iterative decoding of sparse quantum codes},
Volume = {8},
Year = {2008}}
@conference{PTO08a,
Abstract = {We present a theory of quantum serial turbo-codes and study their performance numerically on a depolarization channel. These codes can be considered as a generalization of classical serial turbo-codes. As their classical cousins, they can be iteratively decoded and with well chosen constituent convolutional codes, we observe an important reduction of the word error rate as the number of encoded qubits increases.
Our construction offers several advantages over quantum LDPC codes. First, the Tanner graph used for decoding can be chosen to be free of 4-cycles that deteriorate the performances of iterative decoding. Secondly, the iterative decoder makes explicit use of the code's degeneracy. Finally, there is complete freedom in the code design in terms of length, rate, memory size, and interleaver choice.
We address two issues related to the encoding of convolutional codes that are directly relevant for turbo-codes, namely the character of being recursive and non-catastrophic. We define a quantum analogue of a state diagram that provides an efficient way to verify these properties on a given quantum convolutional encoder. Unfortunately, we also prove that all recursive quantum convolutional encoder have catastrophic error propagation. In our constructions, the convolutional codes have thus been chosen to be non-catastrophic and non-recursive. While the resulting families of turbo-codes have bounded minimum distance, from a pragmatic point of view the effective minimum distances of the codes that we have simulated are large enough for not degrading iterative decoding performance up to reasonable word error rates and block sizes.},
Author = {David Poulin and Jean-Pierre Tillich and Harold Ollivier},
Booktitle = {ISIT'08},
Date-Added = {2008-05-13 10:27:47 -0700},
Date-Modified = {2010-05-06 13:45:01 -0400},
Keywords = {Turbo Codes; Error correction},
Local-Url = {PTO08a.pdf},
Publisher = {IEEE},
Title = {Quantum serial turbo-codes},
Year = {2008}}
@article{GP08a,
Abstract = {In the context of constrained quantum mechanics, reference systems are used to construct relational observables that are invariant under the action of the symmetry group. Upon measurement of a relational observable, the reference system undergoes an unavoidable measurement "back-action" that modifies its properties. In a quantum-gravitational setting, it has been argued that such a back-action may produce effects that are described at an effective level as a form of deformed (or doubly) special relativity. We examine this possibility using a simple constrained system that has been extensively studied in the context of quantum information. While our conclusions support the idea of a symmetry deformation, they also reveal a host of other effects that may be relevant to the context of quantum gravity, and could potentially conceal the symmetry deformation.},
Author = {F. Girelli and D. Poulin},
Date-Added = {2007-11-19 15:58:17 -0800},
Date-Modified = {2010-05-06 13:43:33 -0400},
Eprint = {arXiv:0710.4393},
Journal = {Phys. Rev. D},
Keywords = {Reference frame; Gravity; Foundations},
Local-Url = {GP07b.pdf},
Pages = {104012},
Title = {Quantum reference frames and deformed symmetries},
Volume = {77},
Year = {2008}}
@article{LP08a,
Abstract = {Belief Propagation algorithms acting on Graphical Models of classical probability distributions, such as Markov Networks, Factor Graphs and Bayesian Networks, are amongst the most powerful known methods for deriving probabilistic inferences amongst large numbers of random variables. This paper presents a generalization of these concepts and methods to the quantum case, based on the idea that quantum theory can be thought of as a noncommutative, operator-valued, generalization of classical probability theory. Some novel characterizations of quantum conditional independence are derived, and definitions of Quantum n-Bifactor Networks, Markov Networks, Factor Graphs and Bayesian Networks are proposed. The structure of Quantum Markov Networks is investigated and some partial characterization results are obtained, along the lines of the Hammersely-Clifford theorem. A Quantum Belief Propagation algorithm is presented and is shown to converge on 1-Bifactor Networks and Markov Networks when the underlying graph is a tree. The use of Quantum Belief Propagation as a heuristic algorithm in cases where it is not known to converge is discussed. Applications to decoding quantum error correcting codes and to the simulation of many-body quantum systems are described. },
Author = {M.S. Leifer and D. Poulin},
Date-Added = {2007-07-26 15:19:50 -0700},
Date-Modified = {2010-05-06 13:41:46 -0400},
Eprint = {arXiv:0708.1337},
Journal = {Ann. Phys.},
Keywords = {Simulation; LDPC; Turbo Codes; Belief propagation},
Local-Url = {LP08a.pdf},
Pages = {1899},
Title = {Quantum graphical models and belief propagation},
Volume = {323},
Year = {2008}}
@article{BNPV08a,
Abstract = {We introduce a general operational characterization of
information-preserving structures (IPS) -- encompassing noiseless
subsystems, decoherence-free subspaces, pointer bases, and
error-correcting codes -- by demonstrating that they are isometric to
fixed points of unital quantum processes. Using this, we show that
every IPS is a matrix algebra. We further establish a structure
theorem for the fixed states and observables of an arbitrary process,
which unifies the Schr{"o}dinger and Heisenberg pictures, places
restrictions on physically allowed kinds of information, and provides
an efficient algorithm for finding all noiseless and unitarily
noiseless subsystems of the process.},
Author = {R. Blume-Kohout and H.K. Ng and D. Poulin and L. Viola},
Date-Added = {2007-05-29 15:46:08 -0700},
Date-Modified = {2010-05-06 13:41:03 -0400},
Eprint = {arXiv:0705.4282},
Journal = {Phys. Rev. Lett.},
Keywords = {Error correction},
Local-Url = {BNPV08a.pdf},
Pages = {030501},
Title = {The structure of preserved information in quantum processes},
Volume = {100},
Year = {2008}}
@article{PY07a,
Abstract = {We analyze a quantum mechanical gyroscope which is modeled as a large
spin and used as a reference against which to measure the angular
momenta of spin-1/2 particles. These measurements induce a
back-action on the reference which is the central focus of our study.
We begin by deriving explicit expressions for the quantum channel
representing the back-action. Then, we analyze the dynamics
incurred by the reference when it is used to sequentially measure
particles drawn from a fixed ensemble. We prove that the reference
thermalizes with the measured particles and find that generically, the
thermal state is reached in time which scales linearly with the size
of the reference. This contrasts a recent conclusion of Bartlett et
al. that this takes a quadratic amount of time when the particles are
completely unpolarized. We now understand their result in terms of a
simple physical principle based on symmetries and conservation laws.
Finally, we initiate the study of the non-equilibrium dynamics of the
reference. Here we find that a reference in a coherent state will
essentially remain in one when measuring polarized particles, while
rotating itself to ultimately align with the polarization of the
particles. },
Author = {D. Poulin and J. Yard},
Date-Added = {2007-02-01 08:54:10 -0800},
Date-Modified = {2010-05-06 13:47:34 -0400},
Eprint = {quant-ph/0612126},
Journal = {New J. Phys.},
Keywords = {Reference frame},
Local-Url = {PY07a.pdf},
Pages = {156},
Title = {Dynamics of a Quantum Reference Frame},
Volume = {9},
Year = {2007}}
@conference{GP07a,
Abstract = {Deformed Special Relativity (DSR) is a candidate phenomenological theory to describe the Quantum Gravitational (QG) semi-classical regime. A possible interpretation of DSR can be derived from the notion of deformed reference frame. Observables in (quantum) General Relativity can be constructed from (quantum) reference frame -- a physical observable is then a relation between a system of interest and the reference frame. We present a toy model and study an example of such quantum relational observables. We show how the intrinsic quantum nature of the reference frame naturally leads to a deformation of the symmetries, comforting DSR to be a good candidate to describe the QG semi-classical regime.},
Author = {F. Girelli and D. Poulin},
Date-Added = {2007-09-19 13:49:01 -0700},
Date-Modified = {2010-05-06 13:48:22 -0400},
Journal = {J. of Phys.: Conf. Series, 12th Conference on Recent Developments in Gravity},
Keywords = {Reference frame; Gravity},
Local-Url = {GP07a.pdf},
Number = {012025},
Title = {Deformed symmetries from quantum relational observables},
Volume = {68},
Year = {2007}}
@article{NP07a,
Abstract = { Operator quantum error-correction is a technique for robustly
storing quantum information in the presence of noise. It
generalizes the standard theory of quantum error-correction, and
provides a unified framework for topics such as quantum
error-correction, decoherence-free subspaces, and noiseless
subsystems. This paper develops (a) easily applied algebraic and
information-theoretic conditions which characterize when operator
quantum error-correction is feasible; (b) a representation theorem
for a class of noise processes which can be corrected using operator
quantum error-correction; and (c) generalizations of the coherent
information and quantum data processing inequality to the setting of
operator quantum error-correction.},
Author = {Nielsen, M. A. and Poulin, D.},
Date-Added = {2005-07-05 14:02:02 +1000},
Date-Modified = {2010-05-06 13:45:43 -0400},
Eprint = {quant-ph/0506069},
Journal = {Phys. Rev. A},
Keywords = {Error correction; OQEC},
Local-Url = {NP07a.pdf},
Pages = {064304},
Title = {Algebraic and information-theoretic conditions for operator quantum error-correction},
Volume = {75},
Year = {2007}}
@article{Pou06b,
Abstract = {We consider the problem of optimally decoding a quantum error correction code --- that is to find the optimal recovery procedure given the outcomes of partial "check" measurements on the system. In general, this problem is NP-hard. However, we demonstrate that for concatenated block codes, the optimal decoding can be efficiently computed using a message passing algorithm. We compare the performance of the message passing algorithm to that of the widespread blockwise hard decoding technique. Our Monte Carlo results using the 5 qubit and Steane's code on a depolarizing channel demonstrate significant advantages of the message passing algorithms in two respects. 1) Optimal decoding increases by as much as 94% the error threshold below which the error correction procedure can be used to reliably send information over a noisy channel. 2) For noise levels below these thresholds, the probability of error after optimal decoding is suppressed at a significantly higher rate, leading to a substantial reduction of the error correction overhead.},
Author = {D. Poulin},
Date-Added = {2006-06-26 15:54:53 -0700},
Date-Modified = {2010-05-06 13:51:08 -0400},
Eprint = {quant-ph/0606126},
Journal = {Phys. Rev. A},
Keywords = {Error correction},
Local-Url = {Pou06b.pdf},
Pages = {052333},
Title = {Optimal and Efficient Decoding of Concatenated Quantum Block Codes},
Volume = {74},
Year = {2006}}
@article{Pou06a,
Abstract = {In the absence of an external frame of reference --- i.e. in background independent theories such as general relativity --- physical degrees of freedom must describe {em relations} between systems. Using a simple model, we investigate how such a relational quantum theory naturally arises by promoting reference systems to the status of dynamical entities. Our goal is twofold. First, we demonstrate using elementary quantum theory how any quantum mechanical experiment admits a purely relational description at a fundamental level. Second, we describe how the original "non-relational" theory approximately emerges from the fully relational theory when reference systems become semi-classical. Our technique is motivated by a Bayesian approach to quantum mechanics, and relies on the noiseless subsystem method of quantum information science used to protect quantum states against undesired noise. The relational theory naturally predicts a fundamental decoherence mechanism, so an arrow of time emerges from a time-symmetric theory. Moreover, our model circumvents the problem of the "collapse of the wave packet" as the probability interpretation is only ever applied to diagonal density operators. Finally, the physical states of the relational theory can be described in terms of "spin networks" introduced by Penrose as a combinatorial description of geometry, and widely studied in the loop formulation of quantum gravity. Thus, our simple bottom-up approach (starting from the semi-classical limit to derive the fully relational quantum theory) may offer interesting insights on the low energy limit of quantum gravity. },
Author = {David Poulin},
Date-Added = {2006-01-21 21:36:17 +1000},
Date-Modified = {2010-05-06 13:50:24 -0400},
Eprint = {quant-ph/0505081},
Journal = {Int. J. of Theor. Phys.},
Keywords = {Quantum Theory; Reference frame; Measurement; Gravity; Foundations},
Local-Url = {Pou06a.pdf},
Pages = {1229},
Title = {Toy model for a relational formulation of quantum theory},
Volume = {45},
Year = {2006}}
@article{KLPL05a,
Abstract = {This paper is an expanded and more detailed version of the work
cite{KLP04} in which the Operator Quantum Error Correction
formalism was introduced. This is a new scheme for the error
correction of quantum operations that incorporates the known
techniques --- i.e. the standard error correction model, the
method of decoherence-free subspaces, and the noiseless subsystem
method --- as special cases, and relies on a generalized
mathematical framework for noiseless subsystems that applies to
arbitrary quantum operations. We also discuss a number of examples
and introduce the notion of "unitarily noiseless subsystems".},
Author = {Kribs, D. W. and Laflamme, R. and Poulin, D. and Lesosky, M.},
Date-Added = {2005-07-12 11:51:59 +1000},
Date-Modified = {2010-05-06 13:49:54 -0400},
Eprint = {quant-ph/0504189},
Journal = {Quant. Info. and Comp.},
Keywords = {Error correction; OQEC},
Local-Url = {KLPL05a.pdf},
Pages = {382},
Title = {Operator quantum error correction},
Volume = {6},
Year = {2006}}
@article{MP06a,
Abstract = {Using an elementary example based on two simple harmonic oscillators, we show how a relational time may be defined that leads to an approximate Schr{"o}dinger dynamics for subsystems, with corrections leading to an intrinsic decoherence in the energy eigenstates of the subsystem. },
Author = {Milburn, G. J. and Poulin, D.},
Date-Added = {2005-05-09 14:26:54 +1000},
Date-Modified = {2010-05-06 13:49:09 -0400},
Eprint = {quant-ph/050517},
Journal = {Int. J. Quant. Info.},
Keywords = {Reference frame; Quantum Theory; Gravity; Foundations},
Local-Url = {MP06a.pdf},
Pages = {151},
Title = {Relational time for systems of oscillators},
Volume = {4},
Year = {2006}}
@article{REP+05a,
Abstract = {We present experimental results on the measurement of fidelity decay under contrasting system dynamics using a nuclear magnetic resonance quantum information processor. The measurements were performed by implementing a scalable circuit in the model of deterministic quantum computation with only one quantum bit. The results show measurable differences between regular and complex behaviour and for complex dynamics are faithful to the expected theoretical decay rate. Moreover, we illustrate how the experimental method can be seen as an efficient way for either extracting coarse-grained information about the dynamics of a large system, or measuring the decoherence rate from engineered environments.},
Author = {C. A. Ryan and J. Emerson and D. Poulin and C. Negrevergne and R. Laflamme},
Date-Added = {2006-01-06 10:48:26 +1000},
Date-Modified = {2010-05-06 13:55:20 -0400},
Eid = {250502},
Journal = {Phys. Rev. Lett.},
Keywords = {Quantum chaos; Quantum simulation},
Local-Url = {REP+05a.pdf},
Number = {25},
Numpages = {4},
Pages = {250502},
Publisher = {APS},
Title = {Characterization of Complex Quantum Dynamics with a Scalable NMR Information Processor},
Url = {http://link.aps.org/abstract/PRL/v95/e250502},
Volume = {95},
Year = {2005}}
@misc{PT05a,
Abstract = {We comment on a recent paper by D'Abramo [Chaos, Solitons \&
Fractals, 25 (2005) 29], focusing on the author's statement that an algorithm
can produce a list of strings containing at least one string whose
algorithmic complexity is greater than that of the entire
list. We show that this statement, although perplexing, is not as
paradoxical as it seems when the definition of algorithmic complexity is
applied correctly.},
Author = {David Poulin and Hugo Touchette},
Date-Added = {2006-01-06 10:50:01 +1000},
Date-Modified = {2010-05-06 13:56:21 -0400},
Eprint = {cs.OH/0503034},
Local-Url = {PT05a.pdf},
Title = {Comment on ``Some non-conventional idesa about algorithmic complexity"},
Year = {2005}}
@article{KLP05a,
Abstract = {We present a unified approach to quantum error correction, called
operator quantum error correction. Our scheme relies on a generalized notion of noiseless subsystem that is investigated here. By combining active error correction with this generalized noiseless subsystems method, we arrive at the unified approach which incorporates the known techniques --- i.e. the standard error correction model, the method of decoherence-free subspaces, and the noiseless subsystem method --- as special cases. Moreover, we demonstrate that the quantum error correction condition from the standard model is a necessary
condition for all known methods of quantum error correction.},
Author = {Kribs, D. and Laflamme, R. and Poulin, D.},
Date-Added = {2005-05-06 15:11:09 +1000},
Date-Modified = {2010-05-06 13:54:07 -0400},
Eprint = {quant-ph/0412076},
Journal = {Phys. Rev. Lett.},
Keywords = {Error correction; OQEC},
Local-Url = {KLP05a.pdf},
Pages = {180501},
Title = {A Unified and Generalized Approach to Quantum Error Correction},
Volume = {94},
Year = {2005}}
@article{OPZ05a,
Abstract = {We study the role of the information deposited in the environment of
an open quantum system in course of the decoherence process. Redundant
spreading of information --- the fact that some observables of the
system can be independently "read-off" from many distinct fragments
of the environment --- is investigated as the key to effective
objectivity, the essential ingredient of "classical reality". This
focus on the environment as a communication channel through which
observers learn about physical systems underscores importance of
quantum Darwinism --- selective proliferation of information about
"the fittest states" chosen by the dynamics of decoherence at the
expense of their superpositions --- as redundancy imposes the
existence of preferred observables. We demonstrate that the only
observables that can leave multiple imprints in the environment are
the familiar pointer observables singled out by
environment-induced superselection (einselection) for their
predictability. Many independent observers monitoring the environment
will therefore agree on properties of the system as they can only
learn about preferred observables. In this operational sense, the
selective spreading of information leads to appearance of an objective
"classical reality" from within quantum substrate.},
Author = {Ollivier, H. and Poulin, D. and Zurek, W. H.},
Correct_Ref = {Yes},
Date-Modified = {2010-05-06 13:53:18 -0400},
Eprint = {quant-ph/0408125},
Journal = {Phys. Rev. A},
Keywords = {Decoherence; Quantum Theory; Foundations},
Local-Url = {OPZ05a.pdf},
Pages = {042113},
Read = {Yes},
Source = {H. Ollivier},
Title = {Environment as a Witness: Selective Proliferation of Information and Emergence of Objectivity},
Url = {http://www.arxiv.org/abs/quant-ph/0408125},
Volume = {72},
Year = {2005}}
@article{Pou05a,
Abstract = {We study macroscopic observables defined as the total value of a physical quantity over a collection of quantum systems. We show that previous results obtained for infinite ensemble of identically prepared systems lead to incorrect conclusions for finite ensembles. In particular, exact measurement of a macroscopic observable significantly disturbs the state of any finite ensemble. However, we show how this disturbance can be made arbitrarily small when the measurement are of finite accuracy. We demonstrate a general tradeoff between state disturbance and measurement coarseness as a function of the size of the ensemble. Using this tradeoff, we show that the histories generated by any sequence of finite accuracy macroscopic measurements always generate a consistent family in the absence of large scale entanglement, for sufficiently large ensembles. Hence, macroscopic observables behave "classically" provided that their accuracy is coarser than the quantum correlation length-scale of the system. The role of these observable is also discussed in the context of NMR quantum information processing and bulk ensemble quantum state tomography. },
Author = {Poulin, D.},
Date-Modified = {2010-05-06 13:52:38 -0400},
Eprint = {quant-ph/0403212},
Journal = {Phys. Rev. A},
Keywords = {Quantum Theory; Emergent; Decoherence; Renormalization; Foundations},
Local-Url = {Pou05a.pdf},
Pages = {22102},
Title = {Macroscopic Observables},
Volume = {71},
Year = {2005}}
@article{Pou05b,
Abstract = {Operator quantum error correction is a recently developed theory that provides a generalized framework for active error correction and passive error avoiding schemes. In this paper, we describe these codes in the stabilizer formalism of standard quantum error correction theory. This is achieved by adding a "gauge" group to the standard stabilizer definition of a code that defines an equivalence class between encoded states. Gauge transformations leave the encoded information unchanged; their effect is absorbed by virtual gauge qubits that do not carry useful information. We illustrate the construction by identifying a gauge symmetry in Shor's 9-qubit code that allows us to remove 4 of its 8 stabilizer generators, leading to a simpler decoding procedure and a wider class of logical operations without affecting its essential properties. This opens the path to possible improvements of the error threshold of fault-tolerant quantum computing. },
Author = {Poulin, D.},
Date-Added = {2005-10-11 08:24:34 +1000},
Date-Modified = {2010-05-06 13:51:53 -0400},
Eprint = {quant-ph/0508131},
Journal = {Phys. Rev. Lett.},
Keywords = {Error correction; OQEC},
Local-Url = {Pou05b.pdf},
Pages = {230504},
Title = {Stabilizer formalism for operator quantum error correction},
Volume = {95},
Year = {2005}}
@article{BGL+04a,
Abstract = {We present two polarization-based protocols for quantum key
distribution. The protocols encode key bits in noiseless
subspaces or subsystems, and so can function over a quantum
channel subjected to an arbitrary degree of collective noise, as
occurs, for instance, due to rotation of polarizations in an
optical fiber. These protocols can be implemented using only
entangled photon-pair sources, single-photon rotations,
and single-photon detectors. Thus, our proposals offer practical and
realistic alternatives to existing schemes for quantum key
distribution over optical fibers without resorting to interferometry
or two-way quantum communication, thereby circumventing,
respectively, the need for high precision timing and the threat of
Trojan horse attacks.},
Author = {Boileau, J.-C. and Gottesman, D. and Laflamme, R. and Poulin, D. and Spekkens, R. W.},
Date-Modified = {2010-05-06 14:02:43 -0400},
Eprint = {quant-ph/0306199},
Journal = {Phys. Rev. Lett.},
Keywords = {Crypto; Error correction},
Local-Url = {BGL+04a.pdf},
Pages = {017901},
Title = {Robust Polarization-Based Quantum Key Distribution over a Collective-Noise Channel},
Volume = {92},
Year = {2004}}
@article{ELP+04a,
Abstract = { We report an efficient
quantum algorithm for estimating the local density of states (LDOS)
on a quantum computer.
The LDOS describes the redistribution of
energy levels of a quantum system under the influence of a
perturbation. Sometimes known as the "strength function" from
nuclear spectroscopy experiments, the shape of the LDOS is directly
related to the survivial probability of unperturbed eigenstates, and
has recently been related to the fidelity decay (or "Loschmidt
echo") under imperfect motion-reversal.
For quantum systems that can be simulated
efficiently on a quantum computer, the LDOS
estimation algorithm enables an exponential speed-up over
direct classical computation. },
Author = {Emerson, J. and Lloyd, S. and Poulin, D. and Cory, D.},
Date-Modified = {2010-05-06 14:02:15 -0400},
Eprint = {quant-ph/0308164},
Journal = {Phys. Rev. A},
Keywords = {Quantum chaos; Quantum simulation},
Local-Url = {ELP+04a.pdf},
Pages = {050305},
Source = {D. Poulin 2004-09-28},
Title = {Estimation of the Local Density of States on a Quantum Computer},
Volume = {69},
Year = {2004}}
@article{HKL+04a,
Abstract = {Collective rotation channels are a fundamental class of channels
in quantum computing and quantum information theory. The commutant
of the noise operators for such a channel is a c*-algebra which
is equal to the set of fixed points for the channel. Finding the
precise spatial structure of the commutant algebra for a set of
noise operators associated with a channel is a core problem in
quantum error prevention. We draw on methods of operator algebras,
quantum mechanics and combinatorics to explicitly determine the
structure of the commutant for the class of collective rotation
channels.},
Author = {Holbrook, J. A. and Kribs, D. W. and Laflamme, R. and Poulin, D.},
Date-Modified = {2010-05-06 14:00:52 -0400},
Eprint = {math.OA/0402105},
Journal = {Integ. Eqs. {&} Oper. Theo.},
Keywords = {Error correction},
Local-Url = {HKL+04a.pdf},
Note = {to appear},
Title = {Noiseless subsystems for collective rotation channels in quantum information theory},
Year = {2004}}
@article{OPZ04a,
Abstract = {We study the emergence of objective properties in open quantum
systems. In our analysis, the environment is promoted from a passive
role of reservoir selectively destroying quantum coherence, to an
active role of amplifier selectively proliferating information about
the system. We show that only preferred pointer states of the
system can leave a redundant and therefore easily detectable imprint on
the environment. Observers who---as it is almost always the
case---discover the state of the system indirectly (by probing a
fraction of its environment) will find out only about the
corresponding pointer observable. Many observers can act in this
fashion independently and without perturbing the system: they will
agree about the state of the system. In this operational sense, em
preferred pointer states exist objectively.},
Author = {Ollivier, H. and Poulin, D. and Zurek, W. H.},
Correct_Ref = {Yes},
Date-Modified = {2010-05-06 13:59:11 -0400},
Eprint = {quant-ph/0307229},
Journal = {Phys. Rev. Lett.},
Keywords = {Decoherence; Quantum Theory; Foundations},
Local-Url = {OPZ04a.pdf},
Pages = {220401},
Read = {Yes},
Source = {H. Ollivier 2004-12-03},
Title = {Objective properties from subjective quantum states: Environment as a witness},
Volume = {93},
Year = {2004}}
@article{PBLO04b,
Abstract = { We present an efficient quantum algorithm to measure the average
fidelity decay of a quantum map under perturbation using a single
bit of quantum information. Our algorithm scales only as the
complexity of the map under investigation, so for those maps
admitting an efficient gate decomposition, it provides an
exponential speed up over known classical procedures. Fidelity
decay is important in the study of complex dynamical systems, where
it is conjectured to be a signature of eigenvector statistics. Our
result also illustrates the role of chaos in the process of
decoherence.},
Author = {Poulin, D. and Blume-Kohout, R. and Laflamme, R. and Ollivier, H.},
Correct_Ref = {Yes},
Date-Added = {2006-01-05 17:11:02 -0500},
Date-Modified = {2010-05-06 13:58:48 -0400},
Eprint = {quant-ph/0310038},
Journal = {Phys. Rev. Lett.},
Keywords = {Quantum chaos; Quantum simulation},
Local-Url = {PBLO04b.pdf},
Number = {17},
Pages = {177906},
Read = {Yes},
Source = {H. Ollivier, 2006-01-05},
Title = {Exponential Speedup with a Single Bit of Quantum Information: Measuring the Average Fidelity Decay},
Volume = {92},
Year = {2004}}
@article{KLP+03a,
Abstract = {In a recent paper, Phys. Rev. Lett. 87, 167010/1-4 (2001), Moukouri and Jarrell presented evidence that in the two-dimensional (d=2) Hubbard model at half-filling there is a metal-insulator transition (MIT) at finite temperature even in weak coupling. While we agree with the numerical results of that paper, we arrive at different conclusions: The apparent gap at finite-temperature can be understood, at weak-coupling, as a crossover phenomenon involving large (but not infinite) antiferromagnetic (AFM) correlation length. Phase-space effects on the self-energy in d=2 are crucial, as are the ratio between AFM correlation length and single-particle thermal de Broglie wavelength. In weak coupling, d=2, there is in general no finite-temperature MIT transition in the thermodynamic sense.},
Author = {B. Kyung and J.S. Landry and D. Poulin and A.-M.S. Tremblay},
Date-Added = {2006-01-06 10:53:59 +1000},
Date-Modified = {2010-05-06 14:04:21 -0400},
Eprint = {cond-mat/ 0112273},
Journal = {Phys. Rev. Lett},
Keywords = {Condensed matter; Many-Body; Simulation},
Local-Url = {KLP+03a.pdf},
Pages = {099702},
Title = {Comment on 'Absence of a Slater Transition in the Two-Dimensional Hubbard Model'},
Volume = {90},
Year = {2003}}
@article{PB03a,
Abstract = {We introduce a measure of the compatibility between quantum states---the
likelihood that two density matrices describe the same object. Our measure
is motivated by two elementary requirements, which lead to a natural
definition. We list some properties of this measure, and discuss its relation to the
problem of combining two observers' states of knowledge.},
Author = {Poulin, D. and Blume-Kohout, R.},
Date-Modified = {2010-05-06 14:03:49 -0400},
Journal = {Phys. Rev. A},
Keywords = {Foundations},
Local-Url = {PB03a.pdf},
Pages = {010101(R)},
Source = {K. Kzyczkowski, 2004-11-18},
Title = {Compatibility of quantum states},
Volume = {67},
Year = {2003}}
@article{PLMP03a,
Abstract = {We show that deterministic quantum computing with a single bit
(DQC1) can determine whether the classical limit of a quantum system
is chaotic or integrable using $O(N)$ physical resources,
where $N$ is the dimension of the Hilbert space of the system under
study. This is a square root improvement over all known classical
procedures. Our study relies strictly on the random matrix
conjecture. We also present numerical results for the nonlinear
kicked top.},
Author = {Poulin, D. and Laflamme, R. and Milburn, G. J. and Paz, J.-P.},
Date-Modified = {2010-05-06 14:03:18 -0400},
Eprint = {quant-ph/0303042},
Journal = {Phys. Rev. A},
Keywords = {Quantum chaos; Quantum simulation},
Local-Url = {PLMP03b.pdf},
Pages = {022302},
Title = {Testing Intergrability with a single bit of quantum information},
Volume = {68},
Year = {2003}}
@misc{Pou02a,
Abstract = {This tutorial offers some insight into the question ``What is
quantum chaos and why is it interesting?'. Its main purpose is
to present some signatures of chaos in the quantum world. This is
{it not} a technical reference, it contains but a few simple
equations and no explicit references; rather, the main body of this
manuscript is followed by a reading guide. Some of the mathematical
tools used in the field are so cumbersome they often obscure the
physical relevance of the problem under investigation. However,
after having consulted this tutorial, the technical literature
should appear less mysterious and, we hope, one should have a better
intuition of what is interesting, and what is superficial!},
Author = {David Poulin},
Date-Added = {2006-01-06 10:42:45 +1000},
Date-Modified = {2010-05-06 14:05:02 -0400},
Keywords = {Quantum chaos},
Local-Url = {Pou02a.pdf},
Title = {A rough guide to quantum chaos},
Year = {2002}}
@article{Pou01a,
Abstract = {The ultimate goal of the classicality program is to quantify the
amount of quantumness of certain processes. Here, classicality is
studied for a restricted type of process: quantum information processing (QIP).
Under special conditions, one can force some qubits of a
quantum computer into a classical state without affecting
the outcome of the computation. The minimal set of conditions is described and
its structure is studied. Some implications of this formalism are the
increase of noise robustness, a proof of the quantumness of mixed
state quantum computing and a step forward in understanding the very
foundation of QIP.},
Author = {Poulin, D.},
Date-Modified = {2010-05-06 14:05:56 -0400},
Eprint = {quant-ph/0108102},
Journal = {Phys. Rev. A},
Keywords = {Foundations},
Local-Url = {Pou01a.pdf},
Pages = {42319},
Title = {Classicality of Quantum Information Processing},
Volume = {65},
Year = {2001}}
@techreport{TP00a,
Abstract = {Nous présentons dans ce rapport une introduction complète à deux algorithmes couramment utilisés en physique du solide dans le cadre du problème à N-corps quantique. Le premier est l'algorithme de Blankenbecler, Scalapino et Sugar (bss) (aussi appelé algorithme du déterminant), développé au début des années 80 dans le but de calculer numériquement les propriétés thermodynamiques de certains modèles d'électrons fortement corrélés, dont celui de Hubbard, étudié ici comme modèle pour la supraconductivité à haut Tc. Pour cette partie du rapport, notre étude présente d'abord le fonctionnement de l'algorithme pour s'attarder ensuite à certains de ses aspects numériques, en particulier ceux qui sont problématiques au niveau de la stabilité des calculs. Parmi ceux-ci, nous retrouvons les instabilités liées aux calculs à basse température, le choix de la décomposition de Trotter, le calcul des fonctions de Green et des observables à temps inégal, de même que le problème d'ergodicité. En deuxième partie, nous abordons le calcul des propriétés dynamiques du modèle de Hubbard, comme le poids spectral obtenu en prolongeant analytiquement les données Monte Carlo calculées en temps imaginaire. Pour cette section du rapport, nous présentons quelques éléments de la théorie de la régularisation et la méthode d'entropie maximum utilisés pour résoudre le problème numériquement mal posé que constitue le prolongement analytique des données Monte Carlo. Finalement, pour rendre ce rapport complet en soi, nous avons inclut en annexe une introduction à quelques outils d'analyse numérique ainsi qu'un guide de lecture renvoyant à des références de base sur la plupart des sujets traités dans ce rapport.},
Author = {Hugo Touchette and David Poulin},
Date-Added = {2008-04-23 13:58:54 -0700},
Date-Modified = {2010-05-06 14:07:54 -0400},
Institution = {Université de Sherbrooke},
Keywords = {Condensed matter; Many-Body; Simulation},
Local-Url = {TP00aa.pdf},
Title = {Aspects num{\'e}riques des simulations du modèle de Hubbard --- {M}omte {C}arlo quantique et méthode d'entropie maximum},
Year = {2000}}
@article{MAL+00a,
Abstract = {The opening of a critical-fluctuation induced pseudogap (or precursor pseudogap) in the one-particle spectral weight of the half-filled two-dimensional Hubbard model is discussed. This pseudogap, appearing in our Monte Carlo simulations, may be obtained from many-body techniques that use Green functions and vertex corrections that are at the same level of approximation. Self-consistent theories of the Eliashberg type (such as the Fluctuation Exchange Approximation) use renormalized Green functions and bare vertices in a context where there is no Migdal theorem. They do not find the pseudogap, in quantitative and qualitative disagreement with simulations, suggesting these methods are inadequate for this problem. Differences between precursor pseudogaps and strong-coupling pseudogaps are also discussed.},
Author = {S. Moukouri, S. Allen, F. Lemay and B. Kyung and D. Poulin and Y. M. Vilk and and A.-M. S. Tremblay},
Date-Added = {2006-01-06 10:57:21 +1000},
Date-Modified = {2010-05-06 14:07:27 -0400},
Eprint = {cond-mat/990853},
Journal = {Phys. Rev. B},
Keywords = {Simulation; Condensed matter; Many-Body},
Local-Url = {MAL+00a.pdf},
Pages = {7887},
Title = {Many-body theory versus simulations for the pseudogap in the Hubbard model},
Volume = {61},
Year = {2000}}