Clifford Circuit Optimization with Templates and Symbolic Pauli Gates Article Swipe
Sergey Bravyi
,
Ruslan Shaydulin
,
Shaohan Hu
,
Dmitri Maslov
·
YOU?
·
· 2021
· Open Access
·
· DOI: https://doi.org/10.22331/q-2021-11-16-580
YOU?
·
· 2021
· Open Access
·
· DOI: https://doi.org/10.22331/q-2021-11-16-580
The Clifford group is a finite subgroup of the unitary group generated by the Hadamard, the CNOT, and the Phase gates. This group plays a prominent role in quantum error correction, randomized benchmarking protocols, and the study of entanglement. Here we consider the problem of finding a short quantum circuit implementing a given Clifford group element. Our methods aim to minimize the entangling gate count assuming all-to-all qubit connectivity. First, we consider circuit optimization based on template matching and design Clifford-specific templates that leverage the ability to factor out Pauli and SWAP gates. Second, we introduce a symbolic peephole optimization method. It works by projecting the full circuit onto a small subset of qubits and optimally recompiling the projected subcircuit via dynamic programming. CNOT gates coupling the chosen subset of qubits with the remaining qubits are expressed using symbolic Pauli gates. Software implementation of these methods finds circuits that are only 0.2% away from optimal for 6 qubits and reduces the two-qubit gate count in circuits with up to 64 qubits by 64.7% on average, compared with the Aaronson-Gottesman canonical form.
Related Topics
Concepts
Controlled NOT gate
Quantum gate
Quantum circuit
Qubit
Quantum computer
Computer science
Quantum Fourier transform
Topology (electrical circuits)
Quantum error correction
Mathematics
Theoretical computer science
Quantum
Quantum mechanics
Physics
Combinatorics
Metadata
- Type
- preprint
- Language
- en
- Landing Page
- https://doi.org/10.22331/q-2021-11-16-580
- https://quantum-journal.org/papers/q-2021-11-16-580/pdf/
- OA Status
- gold
- Cited By
- 6
- References
- 33
- Related Works
- 20
- OpenAlex ID
- https://openalex.org/W3158389508
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
-
https://openalex.org/W3158389508Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.22331/q-2021-11-16-580Digital Object Identifier
- Title
-
Clifford Circuit Optimization with Templates and Symbolic Pauli GatesWork title
- Type
-
preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2021Year of publication
- Publication date
-
2021-11-16Full publication date if available
- Authors
-
Sergey Bravyi, Ruslan Shaydulin, Shaohan Hu, Dmitri MaslovList of authors in order
- Landing page
-
https://doi.org/10.22331/q-2021-11-16-580Publisher landing page
- PDF URL
-
https://quantum-journal.org/papers/q-2021-11-16-580/pdf/Direct link to full text PDF
- Open access
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YesWhether a free full text is available
- OA status
-
goldOpen access status per OpenAlex
- OA URL
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https://quantum-journal.org/papers/q-2021-11-16-580/pdf/Direct OA link when available
- Concepts
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Controlled NOT gate, Quantum gate, Quantum circuit, Qubit, Quantum computer, Computer science, Quantum Fourier transform, Topology (electrical circuits), Quantum error correction, Mathematics, Theoretical computer science, Quantum, Quantum mechanics, Physics, CombinatoricsTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
6Total citation count in OpenAlex
- Citations by year (recent)
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2024: 1, 2023: 1, 2022: 1, 2021: 3Per-year citation counts (last 5 years)
- References (count)
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33Number of works referenced by this work
- Related works (count)
-
20Other works algorithmically related by OpenAlex
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