Arbitrary two-qubit computation in 23 elementary gates
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We address the problem of constructing quantum circuits to implement an arbitrary two-qubit quantum computation. We pursue circuits without ancilla qubits and as small a number of elementary quantum gates as possible. Our lower bound for worst-case optimal two-qubit circuits calls for at least $17$ gates: $15$ one-qubit rotations and $2$ controlled-NOT (CNOT) gates. We also constructively prove a worst-case upper bound of $23$ elementary gates, of which at most four (CNOT gates) entail multiqubit interactions. Our analysis shows that synthesis algorithms suggested in previous work, although more general, entail larger quantum circuits than ours in the special case of two qubits. One such algorithm has a worst case of $61$ gates, of which $18$ may be CNOT gates.
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Clever partitioning of circuits can achieve good parallelism and efficient use of distributed memory resources for particular supercomputer architectures.
“Clever partitioning of circuits can achieve good parallelism and efficient use of distributed memory resources for particular supercomputer architectures [21-27].”
From Validating quantum computers using randomized model circuits (2019) · cites this paper as [21]
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References 21 · Cited by 59
- Authors
- Bullock, S. S., & Markov, I. L.
- Affiliations
- National Institute of Standards and Technology (US)
- University of Michigan (US)
- ORCID
- Markov, Igor L.
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2003-07-22
- Volume
- 68
- Issue
- 1
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W2143862628
- Cited by
- 59
- References
- 21
- Citations by year
- 2026: 1 · 2025: 1 · 2024: 2 · 2023: 3 · 2022: 3 · 2021: 4 · 2019: 2 · 2017: 1 · 2016: 3 · 2015: 1 · 2014: 1 · 2012: 1
- FWCI
- 8.17
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review A (publishedVersion)
- arXiv (Cornell University) (publishedVersion)
- 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
- quantum gate synthesis, CNOT gate, circuit lower bounds
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