Upper bounds on the noise threshold for fault-tolerant quantum computing
Quantum Information & Computation
Fault-tolerance threshold for a distance-three quantum code
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
On the structure of protocols for magic state distillation
TQC'09 Proceedings of the 4th international conference on Theory of Quantum Computation, Communication, and Cryptography
Systematic distillation of composite Fibonacci anyons using one mobile quasiparticle
Quantum Information & Computation
Magic-state distillation with the four-qubit code
Quantum Information & Computation
The robustness of magic state distillation against errors in Clifford gates
Quantum Information & Computation
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Given Clifford group operations and the ability to repeatedly prepare a single-qubit mixed state 驴, can one do universal quantum computation? We show a sharp threshold in the Hadamard "magic" direction of the Bloch sphere between those 驴 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.