A complexity transition in displaced Gaussian Boson sampling
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Author(s)
Li, Zhenghao
Solomons, Naomi R
Bulmer, Jacob FF
Patel, Raj B
Walmsley, Ian A
Type
Journal Article
Abstract
Gaussian Boson Sampling (GBS) is the problem of sampling from the output of photon-number-resolving measurements of squeezed states input to a linear optical interferometer. For purposes of demonstrating quantum computational advantage as well as practical applications,
a large photon number is often desirable. However, producing squeezed states with high photon
numbers is experimentally challenging. In this work, we examine the computational complexity implications of increasing the photon number by introducing coherent states. This displaces the state in phase space and as such we call this modified problem Displaced GBS. By utilising a connection to the matching polynomial in graph theory, we first describe an efficient classical algorithm for Displaced GBS when displacement is high or when the output state is represented by a non-negative graph. Then we provide complexity theoretic arguments for the quantum advantage of the problem in the low-displacement regime and numerically quantify where the complexity transition occurs.
a large photon number is often desirable. However, producing squeezed states with high photon
numbers is experimentally challenging. In this work, we examine the computational complexity implications of increasing the photon number by introducing coherent states. This displaces the state in phase space and as such we call this modified problem Displaced GBS. By utilising a connection to the matching polynomial in graph theory, we first describe an efficient classical algorithm for Displaced GBS when displacement is high or when the output state is represented by a non-negative graph. Then we provide complexity theoretic arguments for the quantum advantage of the problem in the low-displacement regime and numerically quantify where the complexity transition occurs.
Date Issued
2025-07-09
Date Acceptance
2025-06-09
Citation
npj Quantum Information, 2025, 11
ISSN
2056-6387
Publisher
Nature Portfolio
Journal / Book Title
npj Quantum Information
Volume
11
Copyright Statement
© The Author(s) 2025. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
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Publication Status
Published
Article Number
ARTN 119