eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-08-21
63:1
63:15
10.4230/LIPIcs.MFCS.2023.63
article
Distributed Merlin-Arthur Synthesis of Quantum States and Its Applications
Le Gall, François
1
Miyamoto, Masayuki
1
Nishimura, Harumichi
2
Graduate School of Mathematics, Nagoya University, Japan
Graduate School of Informatics, Nagoya University, Japan
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol272-mfcs2023/LIPIcs.MFCS.2023.63/LIPIcs.MFCS.2023.63.pdf
distributed quantum Merlin-Arthur
distributed verification
quantum computation