Optimal quantum circuits for general two-qubit gates
Open accessAbstract
In order to demonstrate nontrivial quantum computations experimentally, such as the synthesis of arbitrary entangled states, it will be useful to understand how to decompose a desired quantum computation into the shortest possible sequence of one-qubit and two-qubit gates. We contribute to this effort by providing a method to construct an optimal quantum circuit for a general two-qubit gate that requires at most 3 controlled-NOT (CNOT) gates and 15 elementary one-qubit gates. Moreover, if the desired two-qubit gate corresponds to a purely real unitary transformation, we provide a construction that requries at most 2 CNOT and 12 one-qubit gates. We then prove that these constructions are optimal with respect to the family of CNOT, $y$-rotation, $z$-rotation, and phase gates.
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A general process on a closed system can be described in terms of reversible channels on larger open systems for both quantum and classical theory.
“It is possible to describe a general process on a closed system in terms of reversible channels on (larger) open systems for both quantum and classical theory [52,53].”
From Simple formulation of no-cloning and no-hiding that admits efficient and robust verification (2024) · cites this paper as [52]
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“3: Sufficient circuit decomposition for 2 qubit isometry V(α, β) For dX = dA = dB = 2, the above isometry is sufficient to generate all points of the CUP-set (u, ū) with 0 ≤ α, β ≤ π [60].”
Influential
- Authors
- Vatan, F., & Williams, C.
- Affiliations
- California Institute of Technology (US)
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2004-03-22
- Volume
- 69
- Issue
- 3
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W2003656163
- Cited by
- 443
- References
- 4
- Citations by year
- 2026: 28 · 2025: 59 · 2024: 62 · 2023: 57 · 2022: 46 · 2021: 36 · 2020: 23 · 2019: 21 · 2018: 6 · 2017: 7 · 2016: 5 · 2015: 9 · 2014: 6 · 2013: 5 · 2012: 5
- FWCI
- 8.79
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review A (publishedVersion)
- arXiv (Cornell University) (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 circuit optimization, CNOT gate, one-qubit gates, phase gate
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