Clifford Circuit Optimization with Templates and Symbolic Pauli Gates

Bravyi, Sergey; Shaydulin, Ruslan; Hu, Shaohan; Maslov, Dmitri

doi:10.22331/q-2021-11-16-580

Title: Clifford Circuit Optimization with Templates and Symbolic Pauli Gates

Journal Article · Tue Nov 16 00:00:00 EST 2021 · Quantum

DOI:https://doi.org/10.22331/q-2021-11-16-580· OSTI ID:1962607

Bravyi, Sergey ^[1]; Shaydulin, Ruslan ^[2]; Hu, Shaohan ^[3]; Maslov, Dmitri ^[1]

IBM, Yorktown Heights, NY (United States). Thomas J. Watson Research Center
Argonne National Lab. (ANL), Argonne, IL (United States)
JPMorgan Chase & Co., New York, NY (United States)

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.

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Research Organization:: Argonne National Laboratory (ANL), Argonne, IL (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

Grant/Contract Number:: AC02-06CH11357

OSTI ID:: 1962607

Journal Information:: Quantum, Vol. 5; ISSN 2521-327X

Publisher:: Quantum Science Open CommunityCopyright Statement

Country of Publication:: United States

Language:: English

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