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Cited by 64Quantum Computing Algorithms and ArchitectureQuantum Information and CryptographyQuantum Mechanics and Applications

Continuous-Variable Instantaneous Quantum Computing is Hard to Sample

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Douce, T., Markham, D., Kashefi, E., Diamanti, E., Coudreau, T., Milman, P., van Loock, P., Ferrini, G.·2017·Physical Review Letters
DOI 10.1103/physrevlett.118.070503
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Abstract

Instantaneous quantum computing is a subuniversal quantum complexity class, whose circuits have proven to be hard to simulate classically in the discrete-variable realm. We extend this proof to the continuous-variable (CV) domain by using squeezed states and homodyne detection, and by exploring the properties of postselected circuits. In order to treat postselection in CVs, we consider finitely resolved homodyne detectors, corresponding to a realistic scheme based on discrete probability distributions of the measurement outcomes. The unavoidable errors stemming from the use of finitely squeezed states are suppressed through a qubit-into-oscillator Gottesman-Kitaev-Preskill encoding of quantum information, which was previously shown to enable fault-tolerant CV quantum computation. Finally, we show that, in order to render postselected computational classes in CVs meaningful, a logarithmic scaling of the squeezing parameter with the circuit size is necessary, translating into a polynomial scaling of the input energy.

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  • CV quantum neural networks can be used to reproduce continuous-variable instantaneous quantum polynomial (CV-IQP) circuits by using Gaussian and non-Gaussian gates diagonal in the position basis, stacked, plus Fourier transform gates.

    “Additionally, CV quantum neural networks can be used to reproduce continuous-variable instantaneous quantum polynomial (CV-IQP) circuits [109], which consist of (i) input momentum eigenstates, (ii) a unitary transformation that is diagonal in the position basis, and (iii) momentum homodyne measurements.”

    From Continuous-variable quantum neural networks (2019) · cites this paper as [109]

    The model passage (labelled Abstract in our copy) describes CV-IQP circuits with position-diagonal gates and momentum homodyne measurements, supporting the cited circuit structure. It specifies finitely momentum-squeezed input states rather than momentum eigenstates. Neither that passage nor the Fourier-gadget discussion (p. 070503-2) establishes that CV quantum neural networks reproduce these circuits or that Fourier gates are part of the basic CV-IQP circuit. (LLM, conf=0.87)

    Experimental — accuracy not yet measured

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Cites

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Cited by

Sorted by citations

Authors
Douce, T., Markham, D., Kashefi, E., Diamanti, E., Coudreau, T., Milman, P., van Loock, P., & Ferrini, G.
Affiliations
Centre National de la Recherche Scientifique (FR)
ORCID
Venue
Physical Review Letters
Publisher
American Physical Society (APS)
Published
2017-02-17
Volume
118
Issue
7
Pages
070503-070503
ISSN
  • 0031-9007 (ISSN-L)
  • 1079-7114
DOI
10.1103/physrevlett.118.070503
OpenAlex
W2497224462
Cited by
64
References
4
Citations by year
2026: 2 · 2025: 5 · 2024: 6 · 2023: 6 · 2022: 7 · 2021: 8 · 2020: 7 · 2019: 10 · 2018: 7 · 2017: 6
FWCI
4.89
Type
journal article
Language
en
Open access
Licence
link.aps.org/licenses/aps-default-license (vor)
Locations
  • Physical Review Letters (publishedVersion)
  • arXiv (Cornell University) (publishedVersion)
  • PubMed (publishedVersion)
  • HAL (submittedVersion, other-oa)
  • Edinburgh Research Explorer (University of Edinburgh) (submittedVersion, other-oa)
  • arXiv (Cornell University)
Funders
  • Agence Nationale de la Recherche (ANR-13-BS04-0014)
  • Deutscher Akademischer Austauschdienst (35465RJ)
  • Seventh Framework Programme (704192)
Topics
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
Keywords
continuous-variable quantum computing, post-selection, squeezed states, homodyne detection, fault-tolerant quantum computing, classical simulation

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