A fast quantum mechanical algorithm for database search
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
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
On the Power of Quantum Computation
SIAM Journal on Computing
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
SIAM Journal on Computing
Fault-tolerant quantum computation
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Quantum Universality from Magic States Distillation Applied to CSS Codes
Quantum Information Processing
New Limits on Fault-Tolerant Quantum Computation
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Error-detection-based quantum fault tolerance against discrete pauli noise
Error-detection-based quantum fault tolerance against discrete pauli noise
An upper bound on the threshold quantum decoherence rate
Quantum Information & Computation
Accuracy threshold for postselected quantum computation
Quantum Information & Computation
Signal propagation and noisy circuits
IEEE Transactions on Information Theory
On the maximum tolerable noise of k-input gates for reliable computation by formulas
IEEE Transactions on Information Theory
Noise Threshold for Universality of Two-Input Gates
IEEE Transactions on Information Theory
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We prove new upper bounds on the tolerable level of noise in a quantum circuit. Weconsider circuits consisting of unitary k-qubit gates each of whose input wires is subject todepolarizing noise of strength p, as well as arbitrary one-qubit gates that are essentiallynoise-free. We assume that the output of the circuit is the result of measuring somedesignated qubit in the final state. Our main result is that for p 1 - Θ(1/√k), theoutput of any such circuit of large enough depth is essentially independent of its input,thereby making the circuit useless. For the important special case of k = 2, our bound isp 35.7%. Moreover, if the only allowed gate on more than one qubit is the two-qubitCNOT gate, then our bound becomes 29.3%. These bounds on p are numerically betterthan previous bounds, yet are incomparable because of the somewhat different circuitmodel that we are using. Our main technique is the use of a Pauli basis decomposition,in which the effects of depolarizing noise are very easy to describe.