TY - GEN

T1 - Hardness of classically simulating quantum circuits with unbounded Toffoli and fan-out gates

AU - Takahashi, Yasuhiro

AU - Yamazaki, Takeshi

AU - Tanaka, Kazuyuki

PY - 2013

Y1 - 2013

N2 - We study the classical simulatability of constant-depth quantum circuits followed by only one single-qubit measurement, where they consist of universal gates on at most two qubits and additional gates on an unbounded number of qubits. First, we consider unbounded Toffoli gates as additional gates and deal with the weak simulation, i.e., sampling the output probability distribution. We show that there exists a constant-depth quantum circuit with only one unbounded Toffoli gate that is not weakly simulatable, unless BQP ⊆ PostBPP ∩ AM. Then, we consider unbounded fan-out gates as additional gates and deal with the strong simulation, i.e., computing the output probability. We show that there exists a constant-depth quantum circuit with only two unbounded fan-out gates that is not strongly simulatable, unless P = PP. These results are in contrast to the fact that any constant-depth quantum circuit without additional gates is strongly and weakly simulatable.

AB - We study the classical simulatability of constant-depth quantum circuits followed by only one single-qubit measurement, where they consist of universal gates on at most two qubits and additional gates on an unbounded number of qubits. First, we consider unbounded Toffoli gates as additional gates and deal with the weak simulation, i.e., sampling the output probability distribution. We show that there exists a constant-depth quantum circuit with only one unbounded Toffoli gate that is not weakly simulatable, unless BQP ⊆ PostBPP ∩ AM. Then, we consider unbounded fan-out gates as additional gates and deal with the strong simulation, i.e., computing the output probability. We show that there exists a constant-depth quantum circuit with only two unbounded fan-out gates that is not strongly simulatable, unless P = PP. These results are in contrast to the fact that any constant-depth quantum circuit without additional gates is strongly and weakly simulatable.

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U2 - 10.1007/978-3-642-40313-2_70

DO - 10.1007/978-3-642-40313-2_70

M3 - Conference contribution

AN - SCOPUS:84885237253

SN - 9783642403125

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

SP - 801

EP - 812

BT - Mathematical Foundations of Computer Science 2013 - 38th International Symposium, MFCS 2013, Proceedings

T2 - 38th International Symposium on Mathematical Foundations of Computer Science, MFCS 2013

Y2 - 26 August 2013 through 30 August 2013

ER -