Clifford Circuit Optimization with Templates and Symbolic Pauli Gates

Sergey Bravyi1, Ruslan Shaydulin2, Shaohan Hu3, and Dmitri Maslov1

1IBM Quantum, IBM Thomas J. Watson Research Center, Yorktown Heights, NY 10598
2Mathematics and Computer Science Division, Argonne National Laboratory, Lemont, IL 60439
3JPMorgan Chase & Co., New York, NY 10017

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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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Cited by

[1] Ruslan Shaydulin and Alexey Galda, 2021 IEEE International Conference on Quantum Computing and Engineering (QCE) 291 (2021) ISBN:978-1-6654-1691-7.

[2] Toshinari Itoko and Rudy Raymond, 2021 IEEE International Conference on Quantum Computing and Engineering (QCE) 188 (2021) ISBN:978-1-6654-1691-7.

[3] Giacomo Nannicini, Lev S. Bishop, Oktay Günlük, and Petar Jurcevic, "Optimal qubit assignment and routing via integer programming", arXiv:2106.06446, ACM Transactions on Quantum Computing 3544563 (2022).

[4] Ruslan Shaydulin and Alexey Galda, "Error Mitigation for Deep Quantum Optimization Circuits by Leveraging Problem Symmetries", arXiv:2106.04410.

[5] Kean Chen and Mingsheng Ying, "Automatic Test Pattern Generation for Robust Quantum Circuit Testing", arXiv:2202.10697.

[6] Toshinari Itoko and Rudy Raymond, "Sampling Strategy Optimization for Randomized Benchmarking", arXiv:2109.07653.

[7] Sarah Schneider, Lukas Burgholzer, and Robert Wille, "A SAT Encoding for Optimal Clifford Circuit Synthesis", arXiv:2208.11713.

The above citations are from Crossref's cited-by service (last updated successfully 2022-09-24 16:35:41) and SAO/NASA ADS (last updated successfully 2022-09-24 16:35:42). The list may be incomplete as not all publishers provide suitable and complete citation data.