Quantum Information Processing

, Volume 4, Issue 3, pp 251–264 | Cite as

Quantum Universality from Magic States Distillation Applied to CSS Codes

Article

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.

Keywords

Universal quantam computing protocols stabilizer states 

Pacs

03.67.Lx 03.67.Pp 

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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  1. 1.EECS Department, Computer Science DivisionUniversity of CaliforniaBerkeleyUSA

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