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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
Quantum Computation and Quantum Information
Nielsen, M. A., Chuang, I., & Grover, L. K. (2002) · American Journal of Physics · doi:10.1119/1.1463744 · Cited by 21,895
Quantum computation and quantum information
Law, J. (2001) · ACM SIGSOFT Software Engineering Notes · doi:10.1145/505482.505499 · Cited by 20,450
Elementary gates for quantum computation
Barenco, A., Bennett, C. H., Cleve, R., DiVincenzo, D. P., Margolus, N., Shor, P., Sleator, T., Smolin, J. A., & Weinfurter, H. (1995) · Physical Review A · doi:10.1103/physreva.52.3457 · Cited by 4,311 · cited 1×
“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
Devoret, M., & Schoelkopf, R. J. (2013) · Science · doi:10.1126/science.1231930 · Cited by 2,197 · cited 1×
“-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…”
BackgroundUniversal quantum computation with ideal Clifford gates and noisy ancillas
Bravyi, S., & Kitaev, A. (2005) · Physical Review A · doi:10.1103/physreva.71.022316 · Cited by 1,525 · cited 1×
“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].”
BackgroundQuantum Computation with Ions in Thermal Motion
Sørensen, A. S., & Mølmer, K. (1999) · Physical Review Letters · doi:10.1103/physrevlett.82.1971 · Cited by 1,088 · cited 1×
“Indeed, trapped ions with Molmer-Sorenson gate [10] operate in the weak coupling regime (two-qubit gates take roughly 20 fold effort to implement compared to arbitrary single-qubit gates), and Molmer-Sorenson gate itself is equivalent to the CNOT up to a conjugation by a pair of RZ(a) and RZ(−a) gates on both qubits,…”
MethodScaling the Ion Trap Quantum Processor
Monroe, C., & Kim, J. (2013) · Science · doi:10.1126/science.1231298 · Cited by 786 · cited 1×
“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
Amy, M., Maslov, D. A., & Mosca, M. (2014) · IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems · doi:10.1109/tcad.2014.2341953 · Cited by 319 · cited 9×
“We can furthermore explain how to obtain the solution with 12k − 20 T gates to implement a kcontrolled Toffoli gate using k−2 unrestricted ancilla featured in [1] without resorting to a computer optimization.”
BackgroundMethodInfluentialSelf-citationQuantum circuits of T-depth one
Selinger, P. (2012) · arXiv.org · doi:10.1103/physreva.87.042302 · Cited by 252 · cited 10×
“b • • c Z H T T † T T † H Figure 2: Toffoli gate implemented up to a relative phase: gates 1-10 implement a type-{c} special relative phase Toffoli gate, known as the controlled-controlled-iX in [12], whereas circuit with gates 2-10 implements some generic relative phase Toffoli gate.”
BackgroundMethodInfluentialQuantum Circuit Simplification and Level Compaction
Maslov, D. A., Dueck, G. W., Miller, D. M., & Negrevergne, C. (2008) · IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems · doi:10.1109/tcad.2007.911334 · Cited by 248 · cited 4×
“The optimization in [6] is motivated by a computational model where the two-qubit interaction given by diag{I,X±t}, where t ∈ R[0, 1] and X is Pauli-X , is tunable and parametrized by time.”
BackgroundMethodInfluentialSelf-citation
Flagged first, then by citations
Research works printed but not linked: 3
- A. M. Childs, 2003, Proceedings of the thirty-fifth annual ACM symposium on Theory of computing STOC '03
- G. Song, 2004, Quantum Inf. Comput., 4, 361
- V. V. Shende, 2009, Quantum Inf. Comput., 9, 461
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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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