Closed-form analytic expressions for shadow estimation with brickwork circuits

IF 0.7 4区 物理与天体物理 Q3 COMPUTER SCIENCE, THEORY & METHODS
Mirko Arienzo, Markus Heinrich, Ingo Roth, Martin Kliesch
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引用次数: 13

Abstract

Properties of quantum systems can be estimated using classical shadows, which implement measurements based on random ensembles of unitaries. Originally derived for global Clifford unitaries and products of single-qubit Clifford gates, practical implementations are limited to the latter scheme for moderate numbers of qubits. Beyond local gates, the accurate implementation of very short random circuits with two-local gates is still experimentally feasible and, therefore, interesting for implementing measurements in near-term applications. In this work, we derive closed-form analytical expressions for shadow estimation using brickwork circuits with two layers of parallel two-local Haar-random (or Clifford) unitaries. Besides the construction of the classical shadow, our results give rise to sample-complexity guarantees for estimating Pauli observables.We then compare the performance of shadow estimation with brickwork circuits to the established approach using local Clifford unitaries and find improved sample complexity in the estimation of observables supported on sufficiently many qubits.
砖砌电路阴影估计的封闭解析表达式
量子系统的性质可以使用经典阴影来估计,它实现了基于酉元的随机系综的测量。最初是为全局Clifford单一性和单量子位Clifford门的产物推导的,实际实现仅限于后者的中等数量的量子位。除了局部门之外,用双局部门精确实现非常短的随机电路在实验上仍然是可行的,因此,在近期应用中实现测量很有趣。在这项工作中,我们推导了使用具有两层平行双局部Haar-random(或Clifford)酉元的砖砌电路的阴影估计的封闭形式解析表达式。除了构造经典阴影外,我们的结果还为估计泡利观测值提供了样本复杂度保证。然后,我们将砖砌电路的阴影估计性能与使用局部Clifford一元的既定方法进行比较,并发现在足够多的量子位支持的可观察值估计中改进了样本复杂性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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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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