Efficient Toffoli gates using qudits
Open accessAbstract
The simplest decomposition of a Toffoli gate acting on 3 qubits requires five 2-qubit gates. If we restrict ourselves to controlled-sign (or controlled-NOT) gates this number climbs to 6. We show that the number of controlled-sign gates required to implement a Toffoli gate can be reduced to just 3 if one of the three quantum systems has a third state that is accessible during the computation---i.e., is actually a qutrit. Such a requirement is not unreasonable or even atypical since we often artificially enforce a qubit structure on multilevel quantums systems (e.g., atoms, photonic polarization plus spatial modes). We explore the implementation of these techniques in optical quantum processing and show that linear optical circuits could operate with much higher probabilities of success.
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Single-photon encoded ququart states could be adopted for the implementation of a quantum key distribution protocol without a reference frame recently proposed in [21,22].
“In particular, single-photon encoded ququart states could be adopted for the implementation of a quantum key distribution protocol without a reference frame recentely proposed [21,22]”
From Experimental generation and characterization of single-photon hybrid ququarts based on polarization and orbital angular momentum encoding (2010) · cites this paper as [22]
In “Heralded Gates” (p. 3), the paper describes an optical target that is effectively a four-level system, using polarization and spatial modes; p. 4 identifies the polarization states as single-photon states. It discusses a Toffoli-gate implementation, however, not the proposed reference-frame-free quantum key distribution protocol or whether these states could implement it. (LLM, conf=0.85)
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Cites
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Adding control to arbitrary unknown quantum operations
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Self-citationCircuit-Based Quantum Random Access Memory for Classical Data
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- Authors
- Ralph, T. C., Resch, K. J., & Gilchrist, A.
- Affiliations
- The University of Queensland (AU)
- University of Waterloo (CA)
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2007-02-16
- Volume
- 75
- Issue
- 2
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W1971820243
- Cited by
- 293
- References
- 3
- Citations by year
- 2026: 13 · 2025: 18 · 2024: 21 · 2023: 32 · 2022: 27 · 2021: 17 · 2020: 16 · 2019: 10 · 2018: 8 · 2017: 11 · 2016: 13 · 2015: 16 · 2014: 15 · 2013: 12 · 2012: 17
- FWCI
- 13.81
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review A (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Queensland Government
- Australian Research Council
- Army Research Office
- 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
- Toffoli gate, qudits, qutrits, gate decomposition, CNOT gate, multilevel quantum systems, linear optical circuits
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