Efficient Classical Simulation of Continuous Variable Quantum Information Processes
Open accessAbstract
We obtain sufficient conditions for the efficient simulation of a continuous variable quantum algorithm or process on a classical computer. The resulting theorem is an extension of the Gottesman-Knill theorem to continuous variable quantum information. For a collection of harmonic oscillators, any quantum process that begins with unentangled Gaussian states, performs only transformations generated by Hamiltonians that are quadratic in the canonical operators, and involves only measurements of canonical operators (including finite losses) and suitable operations conditioned on these measurements can be simulated efficiently on a classical computer.
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These demonstrations remained well outside the domain of quantum computational advantage because they lacked non-Gaussian elements and were unable to synthesize states of sufficient complexity to evade efficient classical simulation.
“Although groundbreaking, these demonstrations have remained well outside the domain of quantum computational advantage, as they lacked non-Gaussian elements and were unable to synthesize states of sufficient complexity to evade efficient classical simulation27.”
From Quantum computational advantage with a programmable photonic processor (2022) · cites this paper as [27]
Cites
<i>Quantum Computation and Quantum Information</i>
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Feynman, R. P. (1986) · Foundations of Physics · doi:10.1007/bf01886518 · Cited by 1,770 · see citing works
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Quantum computational advantage with a programmable photonic processor
Madsen, L. S., Laudenbach, F., Askarani, M. F., Rortais, F., Vincent, T., Bulmer, J. F. F., Miatto, F. M., Neuhaus, L., Helt, L. G., Collins, M. J., et al. (2022) · Nature · doi:10.1038/s41586-022-04725-x · Cited by 1,031 · see citing works
Deterministic generation of a two-dimensional cluster state
Larsen, M. V., Guo, X., Breum, C. R., Neergaard-Nielsen, J. S., & Andersen, U. L. (2019) · Science · doi:10.1126/science.aay4354 · Cited by 433 · see citing works
All-Gaussian universality and fault tolerance with the Gottesman-Kitaev-Preskill code
Baragiola, B. Q., Pantaleoni, G., Alexander, R. N., Karanjai, A., & Menicucci, N. C. (2019) · Physical Review Letters · doi:10.1103/physrevlett.123.200502 · Cited by 173 · see citing works
Room-temperature photonic logical qubits via second-order nonlinearities
Krastanov, S., Heuck, M., Shapiro, J. H., Narang, P., Englund, D. R., & Jacobs, K. (2021) · Nature Communications · doi:10.1038/s41467-020-20417-4 · Cited by 44 · see citing works
Kendon, V. M., Nemoto, K., & Munro, W. J. (2010) · Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences · doi:10.1098/rsta.2010.0017 · Cited by 41 · see citing works
“The nonlinear operation in our CVQC will evolve the state into something that is no longer a Gaussian state: if it didn’t, the whole computation would be efficiently classically simulatable (Bartlett et al. 2002).”
BackgroundSelf-citationSchmidt, F., & van Loock, P. (2022) · Physical Review A · doi:10.1103/physreva.105.042427 · Cited by 20 · see citing works
- Authors
- Bartlett, S. D., Sanders, B. C., Braunstein, S. L., & Nemoto, K.
- Affiliations
- Macquarie University (AU)
- Bangor University (GB)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2002-02-14
- Volume
- 88
- Issue
- 9
- Pages
- 097904-097904
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2147282524
- Cited by
- 425
- References
- 2
- Citations by year
- 2026: 21 · 2025: 29 · 2024: 40 · 2023: 22 · 2022: 25 · 2021: 38 · 2020: 26 · 2019: 29 · 2018: 18 · 2017: 20 · 2016: 15 · 2015: 12 · 2014: 16 · 2013: 5 · 2012: 17
- FWCI
- 5.19
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review Letters (publishedVersion)
- arXiv (Cornell University) (publishedVersion)
- PubMed (publishedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- 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 information, Gottesman-Knill theorem, Gaussian states, harmonic oscillator, quadratic Hamiltonians, quantum measurement, quantum advantage
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