The DOI matches its Crossref record; 11 of the 11 references it cites were found in a registry or an index.
Advantages of using relative-phase Toffoli gates with an application to multiple control Toffoli optimization
Open accessAbstract
Various implementations of the Toffoli gate up to a relative phase have been known for years. The advantage over the regular Toffoli gate is its smaller circuit size. However, its use has been often limited to a demonstration of quantum control in designs such as those where the Toffoli gate is being applied last or otherwise for some specific reasons the relative phase does not matter. It was commonly believed that the relative-phase deviations would prevent the relative-phase Toffoli gates from being very helpful in practical large-scale designs. In this paper, we report three circuit identities that provide the means for replacing certain configurations of the multiple control Toffoli gates with their simpler relative-phase implementations, up to a selectable unitary on certain qubits, and without changing the overall functionality. We illustrate the advantage via applying those identities to the optimization of the known circuits implementing multiple control Toffoli gates, and report the reductions in the controlled-not count, $T$count, as well as the number of ancillae used. We suggest that a further study of the relative-phase Toffoli implementations and their use may yield other optimizations.
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“The AND can be implemented with only 3 CNOTs using a relative phase Toffoli implementation [36], [54] given by Qiskit's Margolus gate RCCX and a consecutive S † .”
From High-Round QAOA for MAX $k$-SAT on Trapped Ion NISQ Devices (2023) · cites this paper as [36]
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Cites
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“We illustrate the advantage via applying those identities to the optimization of the known circuits implementing multiple control Toffoli gates, and report the reductions in the CNOT-count, T - count, as well as the number of ancillae used.”
MethodSuperconducting Circuits for Quantum Information: An Outlook
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“-level implementations, and fault-tolerant gates on the logical level. Given the limitations of the current quantum control even in the most promising and developed ions traps [7] and superconducting [4] quantum information processing approaches, coupled with an observation that even the smallest of non-linear (consid…”
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“The known approaches employ state purification and gate teleportation as a means of generating the T gate, that can get quite costly in the realistic systems [3].”
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MethodScaling the Ion Trap Quantum Processor
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“sformations for physical-level implementations, and fault-tolerant gates on the logical level. Given the limitations of the current quantum control even in the most promising and developed ions traps [7] and superconducting [4] quantum information processing approaches, coupled with an observation that even the smalle…”
BackgroundPolynomial-Time T-Depth Optimization of Clifford+T Circuits Via Matroid Partitioning
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BackgroundMethodInfluentialQuantum Circuit Simplification and Level Compaction
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BackgroundMethodInfluentialSelf-citation
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Toward the first quantum simulation with quantum speedup
Childs, A. M., Maslov, D., Nam, Y., Ross, N. J., & Su, Y. (2018) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1801723115 · Cited by 551
“The reflection about |0〉 is implemented as a multiply-controlled Z gate, following the construction in [55] that uses ancillas in the state |0〉.”
BackgroundMethodInfluentialSelf-citationApplying Grover’s Algorithm to AES: Quantum Resource Estimates
Grassl, M., Langenberg, B., Roetteler, M., & Steinwandt, R. (2016) · Lecture Notes in Computer Science · doi:10.1007/978-3-319-29360-8_3 · Cited by 299
Quantum Computer Systems for Scientific Discovery
Alexeev, Y., Bacon, D., Brown, K. R., Calderbank, R., Carr, L. D., Chong, F. T., DeMarco, B., Englund, D. R., Farhi, E., Fefferman, B., et al. (2021) · PRX Quantum · doi:10.1103/prxquantum.2.017001 · Cited by 339
“125,126], multiple-control gates [127,128], libraries for integer arithmetic and finite fields, and many domain-”
BackgroundSelf-citationQuantum Computer Systems for Scientific Discovery
Alexeev, Y., Bacon, D., Brown, K. R., Calderbank, R., Carr, L. D., Chong, F. T., DeMarco, B., Englund, D., Farhi, E., Fefferman, B., et al. (2021) · DSpace@MIT (Massachusetts Institute of Technology) · doi:10.6082/h7fqg-6vt65 · Cited by 257
Self-citationAccelerated Variational Quantum Eigensolver
Wang, D., Higgott, O., & Brierley, S. (2019) · Physical Review Letters · doi:10.1103/physrevlett.122.140504 · Cited by 241
Metadata
- Authors
- Maslov, D.
- Affiliations
- U.S. National Science Foundation (US)
- Corresponding author
- Maslov, Dmitri
- ORCID
- Maslov, Dmitri
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2016-02-10
- Volume
- 93
- Issue
- 2
- ISSN
- 0556-2791 (ISSN-L)
- 2469-9926
- 2469-9934
- OpenAlex
- W1749786511
- Cited by
- 193
- References
- 11
- Citations by year
- 2026: 17 · 2025: 19 · 2024: 28 · 2023: 23 · 2022: 30 · 2021: 23 · 2020: 17 · 2019: 12 · 2018: 8 · 2017: 10 · 2016: 5
- FWCI
- 9.61
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Licence
- Locations
- Physical Review A (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- National Science Foundation
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Information and Cryptography
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Quantum-Dot Cellular Automata
- Keywords
- quantum circuit synthesis
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