Fault-tolerant quantum computation with constant error
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
SIAM Journal on Computing
Quantum circuits with mixed states
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Quantum computation and quantum information
Quantum computation and quantum information
Classical and Quantum Computation
Classical and Quantum Computation
Fault-tolerant quantum computation
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Polynomial simulations of decohered quantum computers
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Upper bounds on the noise threshold for fault-tolerant quantum computing
Quantum Information & Computation
Quantum universality by state distillation
Quantum Information & Computation
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Let η0 be the supremum of those η for which every poly-size quantum circuit can be simulated by another poly-size quantum circuit with gates of fan-in ≤ 2 that tolorates random noise independently occurring on all wires at the constant rate η. Recent fundamental results showing the principal fact η0 0 give estimates like η0 ≥ 10-6 - 10-4, whereas the only upper bound known before is η0 ≤ 0.74. In this note we improve the latter bound to η0 ≤ 1/2, under the assumption QP ⊆ QNC1. More generally, we show that if the decohereace rate η is greater than 1/2, then we can not even store a single qubit for more than logarithmic time. Our bound also generalizes to the simulating circuits allowing gates of any (constant) fan-in k, in which case we have η0 ≤ 1 - 1/k.