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Efficient sampling from shallow Gaussian quantum-optical circuits with local interactions

Haoyu Qi, Diego Cifuentes, Kamil Brádler, Robert Israel, Timjan Kalajdzievski, and Nicolás Quesada
Phys. Rev. A 105, 052412 – Published 6 May 2022

Abstract

We prove that a classical computer can efficiently sample from the photon-number probability distribution of a Gaussian state prepared by using an optical circuit that is shallow and local. Our paper generalizes previous known results for qubits to the continuous-variable domain. The key to our proof is the observation that the adjacency matrices characterizing the Gaussian states generated by shallow and local circuits have small bandwidth. To exploit this structure, we devise fast algorithms to calculate loop Hafnians of banded matrices. Since sampling from deep optical circuits with exponential-scaling photon loss is classically simulable, our results pose a challenge to the feasibility of demonstrating quantum supremacy on photonic platforms with local interactions.

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  • Received 9 February 2022
  • Accepted 15 April 2022

DOI:https://doi.org/10.1103/PhysRevA.105.052412

©2022 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & TechnologyAtomic, Molecular & Optical

Authors & Affiliations

Haoyu Qi1, Diego Cifuentes2, Kamil Brádler1, Robert Israel1, Timjan Kalajdzievski1, and Nicolás Quesada1,*

  • 1Xanadu, Toronto, Ontario M5G 2C8, Canada
  • 2Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139-4307, USA

  • *nquesada@tutanota.com

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Vol. 105, Iss. 5 — May 2022

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