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arXiv:1911.06855 · Physical Review Research

Quantum gate verification and its application in property testing

Pei Zeng, You Zhou, Zhenhuan Liu

Published Jun 9, 2020• 22 citations
arXivHTMLPDF

Abstract

This paper establishes a general framework of verifying a unitary gate based on few rounds of state preparation and measurements. The authors study the efficiency and optimality of the verification strategies in both non-adversarial and adversarial scenario. Furthermore, they provide examples for the commonly-used quantum gates and show the application in channel property testing

DOI
10.1103/physrevresearch.2.023306

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This paper establishes a general framework of verifying a unitary gate based on few rounds of state preparation and measurements. The authors study the efficiency and optimality of the verification strategies in both non-adversarial and adversarial scenario. Furthermore, they provide examples for the commonly-used quantum gates and show the application in channel property testing
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Efficient verification of pure quantum states in the adversarial scenario is crucial to many applications in quantum information processing, such as blind measurement-based quantum computation and quantum networks. However, little is known about this topic so far. Here, we establish a general framework for verifying pure quantum states in the adversarial scenario and clarify the resource cost. Moreover, we propose a simple and general recipe to constructing efficient verification protocols for the adversarial scenario from protocols for the nonadversarial scenario. With this recipe, arbitrary pure states can be verified in the adversarial scenario with almost the same efficiency as in the nonadversarial scenario. Many important quantum states can be verified in the adversarial scenario using local projective measurements with unprecedented high efficiencies.
Bipartite and multipartite entangled states are of central interest in quantum information processing and foundational studies. Efficient verification of these states, especially in the adversarial scenario, is a key to various applications, including quantum computation, quantum simulation, and quantum networks. However, little is known about this topic in the adversarial scenario. Here we initiate a systematic study of pure-state verification in the adversarial scenario. In particular, we introduce a general method for determining the minimal number of tests required by a given strategy to achieve a given precision. In the case of homogeneous strategies, we can even derive an analytical formula. Furthermore, we propose a general recipe to verifying pure quantum states in the adversarial scenario by virtue of protocols for the nonadversarial scenario. Thanks to this recipe, the resource cost for verifying an arbitrary pure state in the adversarial scenario is comparable to the counterpart for the nonadversarial scenario, and the overhead is at most three times for high-precision verification. Our recipe can readily be applied to efficiently verify bipartite pure states, stabilizer states, hypergraph states, weighted graph states, and Dicke states in the adversarial scenario, even if only local projective measurements are accessible. This paper is an extended version of the companion paper Zhu and Hayashi, Phys. Rev. Lett. 123, 260504 (2019).
Efficient verification of quantum states and gates is crucial to the development of quantum technologies. Although the sample complexities of quantum state verification and quantum gate verification have been studied by many researchers, the number of experimental settings has received little attention and is poorly understood. In this work we study systematically quantum state verification and quantum gate verification with a focus on the number of experimental settings. We show that any bipartite pure state can be verified by only two measurement settings based on local projective measurements. Any bipartite unitary in dimension ddd can be verified by 2d2d2d experimental settings based on local operations. In addition, we introduce the concept of entanglement-free verification and clarify its connection with minimal-setting verification. Finally, we show that any two-qubit unitary can be verified with at most five experimental settings; moreover, a generic two-qubit unitary (except for a set of measure zero) can be verified by an entanglement-free protocol based on four settings. In the course of study we clarify the properties of Schmidt coefficients of two-qubit unitaries, which are of independent interest.
Quantum processes, such as quantum circuits, quantum memories, and quantum channels, are essential ingredients in almost all quantum information processing tasks. However, the characterization of these processes remains a daunting task due to the exponentially increasing amount of resources required by traditional methods. Here, by first proposing the concept of quantum process verification, we establish two efficient and practical protocols for verifying quantum processes which can provide an exponential improvement over the standard quantum process tomography and a quadratic improvement over the method of direct fidelity estimation. The efficacy of our protocols is illustrated with the verification of various quantum gates as well as the processes of well-known quantum circuits. Moreover, our protocols are readily applicable with current experimental techniques since only local measurements are required. In addition, we show that our protocols for verifying quantum processes can be easily adapted to verify quantum measurements.