# Publications

@article{C13,

Year = {2013},

Abstract = {Due to the great di±culty in scalability, quantum computers are limited in the number of

qubits during the early stages of the quantum computing regime. In addition to the required

qubits for storing the corresponding eigenvector, suppose we have additional k qubits available.

Given such a constraint k, we propose an approach for the phase estimation for an eigenphase

of exactly n-bit precision. This approach adopts the standard recursive circuit for quantum

Fourier transform (QFT) in [R. Cleve and J. Watrous, Fast parallel circuits for quantum

fourier transform, Proc. 41st Annual Symp. on Foundations of Computer Science (2000),

pp. 526536.] and adopts classical bits to implement such a task. Our algorithm has the complexity

of O(n log k), instead of O(n^2) in the conventional QFT, in terms of the total invocation

of rotation gates. We also design a scheme to implement the factorization algorithm by using

k available qubits via either the continued fractions approach or the simultaneous Diophantine

approximation.},

author = {Chiang, Chen-Fu},

title = {Quantum phase estimation with an arbitrary number of qubits},

journal = {Int. J. Quant. Info.},

volume = {11},

pages = {1350008},

local-url = {C13.pdf}}

Year = {2013},

Abstract = {Due to the great di±culty in scalability, quantum computers are limited in the number of

qubits during the early stages of the quantum computing regime. In addition to the required

qubits for storing the corresponding eigenvector, suppose we have additional k qubits available.

Given such a constraint k, we propose an approach for the phase estimation for an eigenphase

of exactly n-bit precision. This approach adopts the standard recursive circuit for quantum

Fourier transform (QFT) in [R. Cleve and J. Watrous, Fast parallel circuits for quantum

fourier transform, Proc. 41st Annual Symp. on Foundations of Computer Science (2000),

pp. 526536.] and adopts classical bits to implement such a task. Our algorithm has the complexity

of O(n log k), instead of O(n^2) in the conventional QFT, in terms of the total invocation

of rotation gates. We also design a scheme to implement the factorization algorithm by using

k available qubits via either the continued fractions approach or the simultaneous Diophantine

approximation.},

author = {Chiang, Chen-Fu},

title = {Quantum phase estimation with an arbitrary number of qubits},

journal = {Int. J. Quant. Info.},

volume = {11},

pages = {1350008},

local-url = {C13.pdf}}