Quantum Universality from Magic States Distillation Applied to CSS Codes

Quantum Universality from Magic States Distillation Applied to CSS Codes Given Clifford group operations and the ability to repeatedly prepare a single-qubit mixed state ρ, can one do universal quantum computation? We show a sharp threshold in the Hadamard “magic” direction of the Bloch sphere between those ρ allowing universal quantum computation, and those for which any calculation can be efficiently classically simulated. As a corollary, the ability to repeatedly prepare any pure state which is not a stabilizer state (e.g., any single-qubit pure state which is not a Pauli eigenstate), together with Clifford group operations, gives quantum universality. As motivation for this question, “magic state” distillation procedures can reduce the general fault-tolerance problem to that of performing fault-tolerant Clifford group circuits. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

Quantum Universality from Magic States Distillation Applied to CSS Codes

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Publisher
Kluwer Academic Publishers-Plenum Publishers
Copyright
Copyright © 2005 by Springer Science+Business Media, Inc.
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-005-7654-8
Publisher site
See Article on Publisher Site

Abstract

Given Clifford group operations and the ability to repeatedly prepare a single-qubit mixed state ρ, can one do universal quantum computation? We show a sharp threshold in the Hadamard “magic” direction of the Bloch sphere between those ρ allowing universal quantum computation, and those for which any calculation can be efficiently classically simulated. As a corollary, the ability to repeatedly prepare any pure state which is not a stabilizer state (e.g., any single-qubit pure state which is not a Pauli eigenstate), together with Clifford group operations, gives quantum universality. As motivation for this question, “magic state” distillation procedures can reduce the general fault-tolerance problem to that of performing fault-tolerant Clifford group circuits.

Journal

Quantum Information ProcessingSpringer Journals

Published: May 23, 2005

References

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