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Distributed Merlin-Arthur Synthesis of Quantum States and Its Applications

Authors François Le Gall, Masayuki Miyamoto, Harumichi Nishimura

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Author Details

François Le Gall
  • Graduate School of Mathematics, Nagoya University, Japan
Masayuki Miyamoto
  • Graduate School of Mathematics, Nagoya University, Japan
Harumichi Nishimura
  • Graduate School of Informatics, Nagoya University, Japan

Funding

FLG was supported by the JSPS KAKENHI grants JP16H01705, JP19H04066, JP20H00579, JP20H04139, JP20H05966, JP21H04879 and by the MEXT Q-LEAP grants JPMXS0118067394 and JPMXS0120319794. MM would like to take this opportunity to thank the “Nagoya University Interdisciplinary Frontier Fellowship” supported by Nagoya University and JST, the establishment of university fellowships towards the creation of science technology innovation, Grant Number JPMJFS212. HN was supported by the JSPS KAKENHI grants JP19H04066, JP20H05966, JP21H04879, JP22H00522 and by the MEXT Q-LEAP grants JPMXS0120319794.

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François Le Gall, Masayuki Miyamoto, and Harumichi Nishimura. Distributed Merlin-Arthur Synthesis of Quantum States and Its Applications. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 63:1-63:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.MFCS.2023.63

Abstract

The generation and verification of quantum states are fundamental tasks for quantum information processing that have recently been investigated by Irani, Natarajan, Nirkhe, Rao and Yuen [CCC 2022], Rosenthal and Yuen [ITCS 2022], Metger and Yuen [QIP 2023] under the term state synthesis. This paper studies this concept from the viewpoint of quantum distributed computing, and especially distributed quantum Merlin-Arthur (dQMA) protocols. We first introduce a novel task, on a line, called state generation with distributed inputs (SGDI). In this task, the goal is to generate the quantum state U|ψ⟩ at the rightmost node of the line, where |ψ⟩ is a quantum state given at the leftmost node and U is a unitary matrix whose description is distributed over the nodes of the line. We give a dQMA protocol for SGDI and utilize this protocol to construct a dQMA protocol for the Set Equality problem studied by Naor, Parter and Yogev [SODA 2020], and complement our protocol by showing classical lower bounds for this problem. Our second contribution is a dQMA protocol, based on a recent work by Zhu and Hayashi [Physical Review A, 2019], to create EPR-pairs between adjacent nodes of a network without quantum communication. As an application of this dQMA protocol, we prove a general result showing how to convert any dQMA protocol on an arbitrary network into another dQMA protocol where the verification stage does not require any quantum communication.

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed algorithms
  • Theory of computation → Quantum computation theory
Keywords
  • distributed quantum Merlin-Arthur
  • distributed verification
  • quantum computation

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