经典模拟无界Toffoli和扇出门量子电路的硬度

IF 0.7 4区 物理与天体物理 Q3 COMPUTER SCIENCE, THEORY & METHODS Quantum Information & Computation Pub Date : 2013-08-27 DOI:10.26421/QIC14.13-14-7
Y. Takahashi, Takeshi Yamazaki, Kazuyuki Tanaka
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引用次数: 9

摘要

我们研究了只有一个单量子位测量的等深度多项式大小量子电路的经典可模拟性,其中电路由最多两个量子位的通用门和无限大数量的量子位的附加门组成。首先,我们考虑无界Toffoli门作为附加门,并处理弱仿真,即对输出概率分布进行采样。我们证明了存在一个只有一个无界Toffoli门且不可弱模拟的等深度量子电路,除非BQP≠PostBPP∩AM。然后,我们考虑无界扇出门作为附加门,并处理强仿真,即计算输出概率。我们证明了存在一个只有两个无界扇出门的恒定深度量子电路,除非P = PP,否则它是不可强模拟的。这些结果与任何在无界量子位上没有附加门的恒定深度量子电路是强和弱可模拟的事实形成对比。
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Hardness of classically simulating quantum circuits with unbounded Toffoli and fan-out gates
We study the classical simulatability of constant-depth polynomial-size quantum circuits followed by only one single-qubit measurement, where the circuits 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 on an unbounded number of qubits is strongly and weakly simulatable.
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来源期刊
Quantum Information & Computation
Quantum Information & Computation 物理-计算机:理论方法
CiteScore
1.70
自引率
0.00%
发文量
42
审稿时长
3.3 months
期刊介绍: Quantum Information & Computation provides a forum for distribution of information in all areas of quantum information processing. Original articles, survey articles, reviews, tutorials, perspectives, and correspondences are all welcome. Computer science, physics and mathematics are covered. Both theory and experiments are included. Illustrative subjects include quantum algorithms, quantum information theory, quantum complexity theory, quantum cryptology, quantum communication and measurements, proposals and experiments on the implementation of quantum computation, communications, and entanglement in all areas of science including ion traps, cavity QED, photons, nuclear magnetic resonance, and solid-state proposals.
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