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.
UR - http://www.scopus.com/inward/record.url?scp=84885237253&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84885237253&partnerID=8YFLogxK
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 -