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Magic-state distillation with low overhead

Bravyi, Sergey and Haah, Jeongwan (2012) Magic-state distillation with low overhead. Physical Review A, 86 (5). Art. No. 052329. ISSN 1050-2947. doi:10.1103/PhysRevA.86.052329.

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We propose a family of error-detecting stabilizer codes with an encoding rate of 1/3 that permit a transversal implementation of the gate T=exp(−iπZ/8) on all logical qubits. These codes are used to construct protocols for distilling high-quality “magic” states T|+〉 by Clifford group gates and Pauli measurements. The distillation overhead scales as O(logγ(1/ε)), where ε is the output accuracy and γ=log_2(3)≈1.6. To construct the desired family of codes, we introduce the notion of a triorthogonal matrix, a binary matrix in which any pair and any triple of rows have even overlap. Any triorthogonal matrix gives rise to a stabilizer code with a transversal T gate on all logical qubits, possibly augmented by Clifford gates. A powerful numerical method for generating triorthogonal matrices is proposed. Our techniques lead to a twofold overhead reduction for distilling magic states with accuracy ε∼10^(−12) compared with previously known protocols.

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Additional Information:© 2012 American Physical Society. Received 3 October 2012; published 27 November 2012. J.H. is in part supported by the Institute for Quantum Information and Matter (IQIM), an NSF Physics Frontier Center, and by the Korea Foundation for Advanced Studies. J.H. is grateful for the hospitality of the IBM Watson Research Center, in the form of a summer internship while this work is done. S.B. was partially supported by the DARPA QUEST program under Contract No. HR0011-09-C-0047 and by the Intelligence Advanced Research Projects Activity (IARPA) via Department of Interior National Business Center Contract No. D11PC20167.
Group:Institute for Quantum Information and Matter
Funding AgencyGrant Number
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
NSF Physics Frontier CenterUNSPECIFIED
Korea Foundation for Advanced StudiesUNSPECIFIED
IBM Watson Research CenterUNSPECIFIED
DARPA QUEST programHR0011-09-C-0047
Intelligence Advanced Research Projects Activity (IARPA)D11PC20167
Issue or Number:5
Classification Code:PACS: 03.67.Pp
Record Number:CaltechAUTHORS:20130107-153201978
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:36212
Deposited On:08 Jan 2013 00:12
Last Modified:09 Nov 2021 23:20

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