# Publications

@misc{BF13,

Year = {2013},

Abstract = {Decoupling has become a central concept in quantum information theory with applications including proving

coding theorems, randomness extraction and the study of conditions for reaching thermal equilibrium. However,

our understanding of the dynamics that lead to decoupling is limited. In fact, the only families of transformations

that are known to lead to decoupling are (approximate) unitary two-designs, i.e., measures over the unitary

group which behave like the Haar measure as far as the first two moments are concerned. Such families include

for example random quantum circuits with O(n2) gates, where n is the number of qubits in the system under

consideration. In fact, all known constructions of decoupling circuits use

(n2) gates.

Here, we prove that random quantum circuits with O(n log2 n) gates satisfy an essentially optimal decoupling

theorem. In addition, these circuits can be implemented in depth O(log3 n). This proves that decoupling can

happen in a time that scales polylogarithmically in the number of particles in the system, provided all the particles

are allowed to interact. Our proof does not proceed by showing that such circuits are approximate two-designs in

the usual sense, but rather we directly analyze the decoupling property.},

author = {W. Brown and O. Fawzi},

title = {Decoupling with random quantum circuits},

eprint = {arXiv:1307.0632},

local-url = {BF13.pdf}}

Year = {2013},

Abstract = {Decoupling has become a central concept in quantum information theory with applications including proving

coding theorems, randomness extraction and the study of conditions for reaching thermal equilibrium. However,

our understanding of the dynamics that lead to decoupling is limited. In fact, the only families of transformations

that are known to lead to decoupling are (approximate) unitary two-designs, i.e., measures over the unitary

group which behave like the Haar measure as far as the first two moments are concerned. Such families include

for example random quantum circuits with O(n2) gates, where n is the number of qubits in the system under

consideration. In fact, all known constructions of decoupling circuits use

(n2) gates.

Here, we prove that random quantum circuits with O(n log2 n) gates satisfy an essentially optimal decoupling

theorem. In addition, these circuits can be implemented in depth O(log3 n). This proves that decoupling can

happen in a time that scales polylogarithmically in the number of particles in the system, provided all the particles

are allowed to interact. Our proof does not proceed by showing that such circuits are approximate two-designs in

the usual sense, but rather we directly analyze the decoupling property.},

author = {W. Brown and O. Fawzi},

title = {Decoupling with random quantum circuits},

eprint = {arXiv:1307.0632},

local-url = {BF13.pdf}}