Quantum Computation Over Continuous Variables
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This paper provides necessary and sufficient conditions for constructing a universal quantum computer over continuous variables. As an example, it is shown how a universal quantum computer for the amplitudes of the electromagnetic field might be constructed using simple linear devices such as beam splitters and phase shifters, together with squeezers and nonlinear devices such as Kerr-effect fibers and atoms in optical cavities. Such a device could in principle perform ``quantum floating point'' computations. Problems involving noise, finite precision, and error correction are discussed.
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A universal gate set for CV quantum computing consists of all Gaussian transformations combined with any single non-Gaussian transformation, which corresponds to a nonlinear function on phase space variables.
“In fact, a universal gate set for CV quantum computing consists of the following ingredients: all the Gaussian transformations from Eqs. (3)-(6), combined with any single non-Gaussian transformation, which corresponds to a nonlinear function on the phase space variables (x, p).”
From Continuous-variable quantum neural networks (2019) · cites this paper as [91]
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“…position and momentum operators ˆ x and ˆ p , and we can generate any Hermitian polynomial in ˆ x and ˆ p by using the following set of operators (Lloyd and Braunstein 1999): 1. simple linear operations, {± ˆ x, ± ˆ p } , and quadratic, e.g., ˆ x 2 + ˆ p 2 , 2. a non-linear operation at least…”
MethodInfluentialTwo-Qubit Operations for Finite-Energy Gottesman-Kitaev-Preskill Encodings
Rojkov, I., Röggla, P. M., Wagener, M., Fontboté-Schmidt, M., Welte, S., Home, J., & Reiter, F. (2024) · Physical Review Letters · doi:10.1103/physrevlett.133.100601 · Cited by 12 · see citing works
Propagation of entangled light pulses through dispersing and absorbing channels
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- Authors
- Lloyd, S., & Braunstein, S. L.
- Affiliations
- Massachusetts Institute of Technology (US)
- Bangor University (GB)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 1999-02-22
- Volume
- 82
- Issue
- 8
- Pages
- 1784-1787
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2014704465
- Cited by
- 1,145
- References
- 4
- Citations by year
- 2026: 75 · 2025: 88 · 2024: 68 · 2023: 64 · 2022: 63 · 2021: 77 · 2020: 53 · 2019: 67 · 2018: 52 · 2017: 59 · 2016: 44 · 2015: 25 · 2014: 34 · 2013: 27 · 2012: 36
- FWCI
- 27.32
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review Letters (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- 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 computing, universal quantum computer, squeezed light, beam splitter, phase shifters, Kerr effect, optical resonators, quantum noise, finite precision, quantum error correction
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