Seddon, J.R. and Campbell, E.T. (2019) Quantifying magic for multi-qubit operations. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 475 (2227). ISSN 1364-5021
Abstract
The development of a framework for quantifying ‘non-stabilizerness’ of quantum operations is motivated by the magic state model of fault-tolerant quantum computation and by the need to estimate classical simulation cost for noisy intermediate-scale quantum (NISQ) devices. The robustness of magic was recently proposed as a well-behaved magic monotone for multi-qubit states and quantifies the simulation overhead of circuits composed of Clifford + T gates, or circuits using other gates from the Clifford hierarchy. Here we present a general theory of the ‘non-stabilizerness’ of quantum operations rather than states, which are useful for classical simulation of more general circuits. We introduce two magic monotones, called channel robustness and magic capacity, which are well-defined for general n-qubit channels and treat all stabilizer-preserving CPTP maps as free operations. We present two complementary Monte Carlo-type classical simulation algorithms with sample complexity given by these quantities and provide examples of channels where the complexity of our algorithms is exponentially better than previously known simulators. We present additional techniques that ease the difficulty of calculating our monotones for special classes of channels.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2019 The Authors. This is an author-produced version of a paper subsequently published in Proc. of the Royal Society A: Mathematical, Physical and Engineering Sciences. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | stabilizer states; resource theories; classical simulation; clifford gates; magic states; quantum channels |
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: | 20 Aug 2019 07:53 |
Last Modified: | 20 Aug 2019 08:05 |
Status: | Published |
Publisher: | The Royal Society |
Refereed: | Yes |
Identification Number: | 10.1098/rspa.2019.0251 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:149861 |