Campbell, E. and Howard, M. (2017) Unified framework for magic state distillation and multiqubit gate synthesis with reduced resource cost. Physical Review A, 95. 022316. ISSN 1050-2947
Abstract
The standard approach to fault-tolerant quantum computation is to store information in a quantum error correction code, such as the surface code, and process information using a strategy that can be summarized as distill then synthesize. In the distill step, one performs several rounds of distillation to create high-fidelity logical qubits in a magic state. Each such magic state provides one good T gate. In the synthesize step, one seeks the optimal decomposition of an algorithm into a sequence of many T gates interleaved with Clifford gates. This gate-synthesis problem is well understood for multiqubit gates that do not use any Hadamards. We present an in-depth analysis of a unified framework that realizes one round of distillation and multiqubit gate synthesis in a single step. We call these synthillation protocols, and show they lead to a large reduction in resource overheads. This is because synthillation can implement a general class of circuits using the same number of T states as gate synthesis, yet with the benefit of quadratic error suppression. This general class includes all circuits primarily dominated by control-control-Z gates, such as adders and modular exponentiation routines used in Shor’s algorithm. Therefore, synthillation removes the need for a costly round of magic state distillation. We also present several additional results on the multiqubit gate-synthesis problem. We provide an efficient algorithm for synthesizing unitaries with the same worst-case resource scaling as optimal solutions. For the special case of synthesizing controlled unitaries, our techniques are not just efficient but exactly optimal. We observe that the gate-synthesis cost, measured by T count, is often strictly subadditive. Numerous explicit applications of our techniques are also presented.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2017 American Physical Society. This is an author produced version of a paper subsequently published in Physical Review A. Uploaded in accordance with the publisher's self-archiving policy. |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > Department of Physics and Astronomy (Sheffield) |
Funding Information: | Funder Grant number ENGINEERING AND PHYSICAL SCIENCE RESEARCH COUNCIL (EPSRC) EP/M024261/1 |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 16 Feb 2017 16:30 |
Last Modified: | 01 Jul 2017 17:06 |
Published Version: | http://doi.org/10.1103/PhysRevA.95.022316 |
Status: | Published |
Publisher: | American Physical Society |
Refereed: | Yes |
Identification Number: | 10.1103/PhysRevA.95.022316 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:112413 |