Optimal two-qubit circuits for universal fault-tolerant quantum computation

Abstract We study two-qubit circuits over the Clifford+CS gate set, which consists of the Clifford gates together with the controlled-phase gate CS = diag(1, 1, 1, i). The Clifford+CS gate set is universal for quantum computation and its elements can be implemented fault-tolerantly in most error-cor...

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Autores principales:	Andrew N. Glaudell, Neil J. Ross, Jacob M. Taylor
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2021
Materias:	Physics QC1-999 Electronic computers. Computer science QA75.5-76.95
Acceso en línea:	https://doaj.org/article/b87c367ca64743fbbbb519b209473cc6
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spelling	oai:doaj.org-article:b87c367ca64743fbbbb519b209473cc62021-12-02T17:14:31ZOptimal two-qubit circuits for universal fault-tolerant quantum computation10.1038/s41534-021-00424-z2056-6387https://doaj.org/article/b87c367ca64743fbbbb519b209473cc62021-06-01T00:00:00Zhttps://doi.org/10.1038/s41534-021-00424-zhttps://doaj.org/toc/2056-6387Abstract We study two-qubit circuits over the Clifford+CS gate set, which consists of the Clifford gates together with the controlled-phase gate CS = diag(1, 1, 1, i). The Clifford+CS gate set is universal for quantum computation and its elements can be implemented fault-tolerantly in most error-correcting schemes through magic state distillation. Since non-Clifford gates are typically more expensive to perform in a fault-tolerant manner, it is often desirable to construct circuits that use few CS gates. In the present paper, we introduce an efficient and optimal synthesis algorithm for two-qubit Clifford+CS operators. Our algorithm inputs a Clifford+CS operator U and outputs a Clifford+CS circuit for U, which uses the least possible number of CS gates. Because the algorithm is deterministic, the circuit it associates to a Clifford+CS operator can be viewed as a normal form for that operator. We give an explicit description of these normal forms and use this description to derive a worst-case lower bound of $$5{{\rm{log}}}_{2}(\frac{1}{\epsilon })+O(1)$$ 5 log 2 ( 1 ϵ ) + O ( 1 ) on the number of CS gates required to ϵ-approximate elements of SU(4). Our work leverages a wide variety of mathematical tools that may find further applications in the study of fault-tolerant quantum circuits.Andrew N. GlaudellNeil J. RossJacob M. TaylorNature PortfolioarticlePhysicsQC1-999Electronic computers. Computer scienceQA75.5-76.95ENnpj Quantum Information, Vol 7, Iss 1, Pp 1-11 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Physics QC1-999 Electronic computers. Computer science QA75.5-76.95
spellingShingle	Physics QC1-999 Electronic computers. Computer science QA75.5-76.95 Andrew N. Glaudell Neil J. Ross Jacob M. Taylor Optimal two-qubit circuits for universal fault-tolerant quantum computation
description	Abstract We study two-qubit circuits over the Clifford+CS gate set, which consists of the Clifford gates together with the controlled-phase gate CS = diag(1, 1, 1, i). The Clifford+CS gate set is universal for quantum computation and its elements can be implemented fault-tolerantly in most error-correcting schemes through magic state distillation. Since non-Clifford gates are typically more expensive to perform in a fault-tolerant manner, it is often desirable to construct circuits that use few CS gates. In the present paper, we introduce an efficient and optimal synthesis algorithm for two-qubit Clifford+CS operators. Our algorithm inputs a Clifford+CS operator U and outputs a Clifford+CS circuit for U, which uses the least possible number of CS gates. Because the algorithm is deterministic, the circuit it associates to a Clifford+CS operator can be viewed as a normal form for that operator. We give an explicit description of these normal forms and use this description to derive a worst-case lower bound of $$5{{\rm{log}}}_{2}(\frac{1}{\epsilon })+O(1)$$ 5 log 2 ( 1 ϵ ) + O ( 1 ) on the number of CS gates required to ϵ-approximate elements of SU(4). Our work leverages a wide variety of mathematical tools that may find further applications in the study of fault-tolerant quantum circuits.
format	article
author	Andrew N. Glaudell Neil J. Ross Jacob M. Taylor
author_facet	Andrew N. Glaudell Neil J. Ross Jacob M. Taylor
author_sort	Andrew N. Glaudell
title	Optimal two-qubit circuits for universal fault-tolerant quantum computation
title_short	Optimal two-qubit circuits for universal fault-tolerant quantum computation
title_full	Optimal two-qubit circuits for universal fault-tolerant quantum computation
title_fullStr	Optimal two-qubit circuits for universal fault-tolerant quantum computation
title_full_unstemmed	Optimal two-qubit circuits for universal fault-tolerant quantum computation
title_sort	optimal two-qubit circuits for universal fault-tolerant quantum computation
publisher	Nature Portfolio
publishDate	2021
url	https://doaj.org/article/b87c367ca64743fbbbb519b209473cc6
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Optimal two-qubit circuits for universal fault-tolerant quantum computation

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