TY - GEN

T1 - Commuting quantum circuits with few outputs are unlikely to be classically simulatable

AU - Takahashi, Yasuhiro

AU - Tani, Seiichiro

AU - Yamazaki, Takeshi

AU - Tanaka, Kazuyuki

N1 - Publisher Copyright:
© Springer International Publishing Switzerland 2015.

PY - 2015

Y1 - 2015

N2 - We study the classical simulatability of commuting quantum circuits with n input qubits and O(log n) output qubits, where a quantum circuit is classically simulatable if its output probability distribution can be sampled up to an exponentially small additive error in classical polynomial time. Our main result is that there exists a commuting quantum circuit that is not classically simulatable unless the polynomial hierarchy collapses to the third level. This is the first formal evidence that a commuting quantum circuit is not classically simulatable even when the number of output qubits is exponentially small. Then, we consider a generalized version of the circuit and clarify the condition under which it is classically simulatable. We apply these results to examining the ability of IQP circuits to implement fundamental operations, and to examining the classical simulatability of slightly extended Clifford circuits.

AB - We study the classical simulatability of commuting quantum circuits with n input qubits and O(log n) output qubits, where a quantum circuit is classically simulatable if its output probability distribution can be sampled up to an exponentially small additive error in classical polynomial time. Our main result is that there exists a commuting quantum circuit that is not classically simulatable unless the polynomial hierarchy collapses to the third level. This is the first formal evidence that a commuting quantum circuit is not classically simulatable even when the number of output qubits is exponentially small. Then, we consider a generalized version of the circuit and clarify the condition under which it is classically simulatable. We apply these results to examining the ability of IQP circuits to implement fundamental operations, and to examining the classical simulatability of slightly extended Clifford circuits.

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U2 - 10.1007/978-3-319-21398-9_18

DO - 10.1007/978-3-319-21398-9_18

M3 - Conference contribution

AN - SCOPUS:84951125574

SN - 9783319213972

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 223

EP - 234

BT - Computing and Combinatorics - 21st International Conference, COCOON 2015, Proceedings

A2 - Xu, Dachuan

A2 - Du, Donglei

A2 - Du, Dingzhu

PB - Springer Verlag

T2 - 21st International Conference on Computing and Combinatorics Conference, COCOON 2015

Y2 - 4 August 2015 through 6 August 2015

ER -