Random Quantum Circuits and Pseudo-Random Operators: Theory and Applications
Joseph Emerson
备注：
This paper is a synopsis of Emerson et al., Science 302: 2098 (Dec 19, 2003) and some related unpublished work; it is based on a talk given at QCMC04; 4 pages, 1 figure, aipproc.sty
Pseudo-random operators consist of sets of operators that exhibit many of the important statistical features of uniformly distributed random operators. Such pseudo-random sets of operators are most useful whey they may be parameterized and generated on a quantum processor in a way that requires exponentially fewer resources than direct implementation of the uniformly random set. Efficient pseudo-random operators can overcome the exponential cost of random operators required for quantum communication tasks such as super-dense coding of quantum states and approximately secure quantum data-hiding, and enable efficient stochastic methods for noise estimation on prototype quantum processors. This paper summarizes some recently published work demonstrating a random circuit method for the implementation of pseudo-random unitary operators on a quantum processor [Emerson et al., Science 302:2098 (Dec.~19, 2003)], and further elaborates the theory and applications of pseudo-random states and operators.
Pseudorandom circuits generate quantum states and unitary operators which are approximately distributed according to the unitarily invariant Haar measure. We explore how several design parameters affect the efficiency of pseudo-random circuits, with the goal of identifying relevant trade-offs and optimizing convergence. The parameters we explore include the choice of single- and two-qubit gates, the topology of the underlying physical qubit architecture, the probabilistic application of two-qubit gates, as well as circuit size, initialization, and the effect of control constraints. Building on…
We explore the implementation of pseudo-random single-qubit rotations and multi-qubit pseudo-random circuits constructed only from Clifford gates and the T-gate, a phase rotation of pi/4. Such a gate set would be appropriate for computations performed in a fault tolerant setting. For single-qubit rotations the distribution of parameters found for unitaries constructed from Clifford plus T quickly approaches that of random rotations and require significantly fewer gates than the construction of arbitrary single-qubit rotations. For Clifford plus T pseudo-random circuits we find an exponential c…
Technical University of Munich（慕尼黑工业大学）；Stanford University（斯坦福大学）
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Mitsubishi Chemical Corporation（三菱化学公司）；Quantum Computing Center, Keio University（庆应义塾大学量子计算中心）；IBM Quantum, IBM Research – Tokyo（IBM量子，IBM研究-东京）；Department of Applied Physics and Physico-Informatics, Keio University（庆应义塾大学应用物理与物理信息系）
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Harish-Chandra Research Institute（哈里什-钱德拉研究所）；Homi Bhabha National Institute（霍米·巴巴国立研究所）；Indian Institute of Technology (ISM) Dhanbad（印度理工学院（ISMT）丹巴德分校）
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Freie Universität Berlin（柏林自由大学）；Google Quantum AI（谷歌量子人工智能）；Institute for Quantum Information and Matter, California Institute of Technology（加州理工学院量子信息与物质研究所）
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The College of William & Mary（威廉玛丽学院）；The University of Chicago（芝加哥大学）；Joint Center for Quantum Information and Computer Science, University of Maryland and NIST（马里兰大学和NIST联合量子信息与计算中心）；University of Waterloo（滑铁卢大学）
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