Title: Classical Simulation of Boson Sampling Based on Graph Structure

Abstract

Boson sampling is a fundamentally and practically important task that can be used to demonstrate quantum supremacy using noisy intermediate-scale quantum devices. In this Letter, we present classical sampling algorithms for single-photon and Gaussian input states that take advantage of a graph structure of a linear-optical circuit. The algorithms’ complexity grows as so-called treewidth, which is closely related to the connectivity of a given linear-optical circuit. Using the algorithms, we study approximated simulations for local Haar-random linear-optical circuits. For equally spaced initial sources, we show that, when the circuit depth is less than the quadratic in the lattice spacing, the efficient simulation is possible with an exponentially small error. Notably, right after this depth, photons start to interfere each other and the algorithms’ complexity becomes subexponential in the number of sources, implying that there is a sharp transition of its complexity. Finally, when a circuit is sufficiently deep enough for photons to typically propagate to all modes, the complexity becomes exponential as generic sampling algorithms. We numerically implement a likelihood test with a recent Gaussian boson sampling experiment and show that the treewidth-based algorithm with a limited treewidth renders a larger likelihood than the experimental data.

Authors:

Oh, Changhun  ^[1];

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• Search DOE PAGES for ORCID "0000-0003-2002-1928"

Lim, Youngrong  ^[2];

• Search DOE PAGES for author "Lim, Youngrong"
• Search DOE PAGES for ORCID "0000-0003-3678-0080"

Fefferman, Bill  ^[1];

• Search DOE PAGES for author "Fefferman, Bill"
• Search DOE PAGES for ORCID "0000-0002-9627-0210"

Jiang, Liang  ^[1]

• Search DOE PAGES for author "Jiang, Liang"
• Search DOE PAGES for ORCID "0000-0002-0000-9342"

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+ Show Author Affiliations

1. Univ. of Chicago, IL (United States)
2. Korea Institute of Advanced Study, Seoul (South Korea)

Publication Date:

Fri May 13 00:00:00 EDT 2022

Research Org.:

Yale Univ., New Haven, CT (United States)

Sponsoring Org.:

USDOE Office of Science (SC); National Science Foundation (NSF); US Army Research Office (ARO); US Air Force Office of Scientific Research (AFOSR); National Research Foundation of Korea (NRF); Packard Foundation

OSTI Identifier:

1980281

Grant/Contract Number:  

SC0019406; W911NF-15-2-0067; W911NF-18-1-0020; W911NF-18-1-0212; 911NF-16-1-0349; A9550-15-1-0015; FA9550-19-1-0399; EFMA-1640959; OMA-1936118; 2013-39273; 2020M3E4A1077861; FA9550-18-1-0148; FA9550-21-1-0008; CCF-2044923

Resource Type:

Accepted Manuscript

Journal Name:

Physical Review Letters

Additional Journal Information:

Journal Volume: 128; Journal Issue: 19; Journal ID: ISSN 0031-9007

Publisher:

American Physical Society (APS)

Country of Publication:

United States

Language:

English

Subject:

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Physics; boson sampling