Clifford Circuit Optimization with Templates and Symbolic Pauli Gates

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 quan...

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Autores principales:	Sergey Bravyi, Ruslan Shaydulin, Shaohan Hu, Dmitri Maslov
Formato:	article
Lenguaje:	EN
Publicado:	Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften 2021
Materias:	Physics QC1-999
Acceso en línea:	https://doaj.org/article/7d0859525d074bea9cde649fb06421fc
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id	oai:doaj.org-article:7d0859525d074bea9cde649fb06421fc
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spelling	oai:doaj.org-article:7d0859525d074bea9cde649fb06421fc2021-11-16T13:17:31ZClifford Circuit Optimization with Templates and Symbolic Pauli Gates2521-327X10.22331/q-2021-11-16-580https://doaj.org/article/7d0859525d074bea9cde649fb06421fc2021-11-01T00:00:00Zhttps://quantum-journal.org/papers/q-2021-11-16-580/pdf/https://doaj.org/toc/2521-327XThe 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.Sergey BravyiRuslan ShaydulinShaohan HuDmitri MaslovVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenarticlePhysicsQC1-999ENQuantum, Vol 5, p 580 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Physics QC1-999
spellingShingle	Physics QC1-999 Sergey Bravyi Ruslan Shaydulin Shaohan Hu Dmitri Maslov Clifford Circuit Optimization with Templates and Symbolic Pauli Gates
description	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.
format	article
author	Sergey Bravyi Ruslan Shaydulin Shaohan Hu Dmitri Maslov
author_facet	Sergey Bravyi Ruslan Shaydulin Shaohan Hu Dmitri Maslov
author_sort	Sergey Bravyi
title	Clifford Circuit Optimization with Templates and Symbolic Pauli Gates
title_short	Clifford Circuit Optimization with Templates and Symbolic Pauli Gates
title_full	Clifford Circuit Optimization with Templates and Symbolic Pauli Gates
title_fullStr	Clifford Circuit Optimization with Templates and Symbolic Pauli Gates
title_full_unstemmed	Clifford Circuit Optimization with Templates and Symbolic Pauli Gates
title_sort	clifford circuit optimization with templates and symbolic pauli gates
publisher	Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
publishDate	2021
url	https://doaj.org/article/7d0859525d074bea9cde649fb06421fc
work_keys_str_mv	AT sergeybravyi cliffordcircuitoptimizationwithtemplatesandsymbolicpauligates AT ruslanshaydulin cliffordcircuitoptimizationwithtemplatesandsymbolicpauligates AT shaohanhu cliffordcircuitoptimizationwithtemplatesandsymbolicpauligates AT dmitrimaslov cliffordcircuitoptimizationwithtemplatesandsymbolicpauligates
_version_	1718426488449007616

Clifford Circuit Optimization with Templates and Symbolic Pauli Gates

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