2026-07-23T01:18:39Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:18597 2024-03-06T11:02:13Z ddc:004 open_access

Distributed Merlin-Arthur Synthesis of Quantum States and Its Applications Le Gall, François Miyamoto, Masayuki Nishimura, Harumichi distributed quantum Merlin-Arthur distributed verification quantum computation 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik François Le Gall and Masayuki Miyamoto and Harumichi Nishimura 2023 Is Part Of LIPIcs, Volume 272, 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.MFCS.2023.63 urn:nbn:de:0030-drops-185975 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.63 eng https://creativecommons.org/licenses/by/4.0/legalcode