Simple factorization of unitary transformations
Open accessAbstract
We demonstrate a method for general linear optical networks that allows one to factorize any $\mathrm{SU}(n$) matrix in terms of two $\mathrm{SU}(n\ensuremath{-}1)$ blocks coupled by an SU(2) entangling beam splitter. The process can be recursively continued in a straightforward way, ending in a tidy arrangement of SU(2) transformations. The method hinges only on a linear relationship between input and output states, and can thus be applied to a variety of scenarios, such as microwaves, acoustics, and quantum fields.
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Any two-qubit gate can be obtained from single-qubit rotational gates and at least one entangling gate by using circuit decompositions.
“Any two-qubit gate can be obtained from this minimal set by using circuit decompositions (Barenco et al. , 1995; Blaauboer and De Visser, 2008; de Guise et al. , 2018; Peterson et al. , 2020; Watts et al. , 2013).”
From Noisy intermediate-scale quantum algorithms (2022) · cites this paper as de Guise et al., 2018
Cites
A scheme for efficient quantum computation with linear optics
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Elementary gates for quantum computation
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Quantum Walks of Correlated Photons
Peruzzo, A., Lobino, M., Matthews, J. C. F., Matsuda, N., Politi, A., Poulios, K., Zhou, X.-Q., Lahini, Y., Ismail, N., Wörhoff, K., et al. (2010) · Science · doi:10.1126/science.1193515 · Cited by 929 · see citing works
Integrated multimode interferometers with arbitrary designs for photonic boson sampling
Crespi, A., Osellame, R., Ramponi, R., Brod, D. J., Galvão, E. F., Spagnolo, N., Vitelli, C., Maiorino, E., Mataloni, P., & Sciarrino, F. (2013) · Nature Photonics · doi:10.1038/nphoton.2013.112 · Cited by 662 · see citing works
Randomizing Quantum States: Constructions and Applications
Hayden, P., Leung, D., Shor, P. W., & Winter, A. (2004) · Communications in Mathematical Physics · doi:10.1007/s00220-004-1087-6 · Cited by 345 · see citing works
Experimental realization of a quantum quincunx by use of linear optical elements
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Noisy intermediate-scale quantum algorithms
Bharti, K., Cervera-Lierta, A., Kyaw, T. H., Haug, T., Alperin-Lea, S., Anand, A., Degroote, M., Heimonen, H., Kottmann, J. S., Menke, T., et al. (2022) · Reviews of Modern Physics · doi:10.1103/revmodphys.94.015004 · Cited by 1,726 · see citing works
Applications of near-term photonic quantum computers: software and algorithms
Bromley, T. R., Arrazola, J. M., Jahangiri, S., Izaac, J., Quesada, N., Gran, A. D., Schuld, M., Swinarton, J., Zabaneh, Z., & Killoran, N. (2020) · Quantum Science and Technology · doi:10.1088/2058-9565/ab8504 · Cited by 128 · see citing works
- Authors
- de Guise, H., Di Matteo, O., & Sánchez-Soto, L. L.
- Affiliations
- Universidad Complutense de Madrid (ES)
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2018-02-20
- Volume
- 97
- Issue
- 2
- ISSN
- 0556-2791 (ISSN-L)
- 2469-9926
- 2469-9934
- OpenAlex
- W2792521527
- Cited by
- 70
- References
- 6
- Citations by year
- 2026: 6 · 2025: 11 · 2024: 11 · 2023: 4 · 2022: 10 · 2021: 8 · 2020: 11 · 2019: 5 · 2018: 4
- FWCI
- 3.92
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review A (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- Docta Complutense (Universidad Complutense de Madrid) (submittedVersion, other-oa)
- MPG.PuRe (Max Planck Society) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Government of Canada
- Ministerio de Economía y Competitividad (FIS2015-67963-P)
- 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
- linear optical networks, quantum state transformation, microwave photonics, quantum acoustics, quantum field theory
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