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BY 4.0 license Open Access Published by De Gruyter Open Access April 6, 2021

Graph isomorphism and Gaussian boson sampling

Kamil Brádler, Shmuel Friedland, Josh Izaac, Nathan Killoran and Daiqin Su
From the journal Special Matrices

Abstract

We introduce a connection between a near-term quantum computing device, specifically a Gaussian boson sampler, and the graph isomorphism problem. We propose a scheme where graphs are encoded into quantum states of light, whose properties are then probed with photon-number-resolving detectors. We prove that the probabilities of different photon-detection events in this setup can be combined to give a complete set of graph invariants. Two graphs are isomorphic if and only if their detection probabilities are equivalent. We present additional ways that the measurement probabilities can be combined or coarse-grained to make experimental tests more amenable. We benchmark these methods with numerical simulations on the Titan supercomputer for several graph families: pairs of isospectral nonisomorphic graphs, isospectral regular graphs, and strongly regular graphs.

MSC 2010: 05C50; 05C60; 15A15; 68Q12; 81P68

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Received: 2020-11-06
Accepted: 2021-03-14
Published Online: 2021-04-06

© 2021 Kamil Brádler et al., published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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