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Level reduction and the quantum threshold theorem
 PH.D. THESIS, CALTECH, 2007, EPRINT ARXIV:QUANTPH/0703230
, 2007
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Errordetectionbased quantum fault tolerance against discrete Pauli noise
, 2006
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ACCURACY THRESHOLD FOR POSTSELECTED QUANTUM COMPUTATION
, 2008
"... We prove an accuracy threshold theorem for faulttolerant quantum computation based on error detection and postselection. Our proof provides a rigorous foundation for the scheme suggested by Knill, in which preparation circuits for ancilla states are protected by a concatenated errordetecting code ..."
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Cited by 14 (2 self)
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We prove an accuracy threshold theorem for faulttolerant quantum computation based on error detection and postselection. Our proof provides a rigorous foundation for the scheme suggested by Knill, in which preparation circuits for ancilla states are protected by a concatenated errordetecting code and the preparation is aborted if an error is detected. The proof applies to independent stochastic noise but (in contrast to proofs of the quantum accuracy threshold theorem based on concatenated errorcorrecting codes) not to stronglycorrelated adversarial noise. Our rigorously established lower bound on the accuracy threshold, 1.04 × 10 −3, is well below Knill’s numerical estimates.
Postselection threshold against biased noise,” arXiv:quantph/0608018
, 2006
"... Abstract. The highest current estimates for the amount of noise a quantum computer can tolerate are based on faulttolerance schemes relying heavily on postselecting on no detected errors. However, there has been no proof that these schemes give even a positive tolerable noise threshold. A technique ..."
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Cited by 2 (0 self)
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Abstract. The highest current estimates for the amount of noise a quantum computer can tolerate are based on faulttolerance schemes relying heavily on postselecting on no detected errors. However, there has been no proof that these schemes give even a positive tolerable noise threshold. A technique to prove a positive threshold, for probabilistic noise models, is presented. The main idea is to maintain strong control over the distribution of errors in the quantum state at all times. This distribution has correlations which conceivably could grow out of control with postselection. But in fact, the error distribution can be written as a mixture of nearby distributions each satisfying strong independence properties, so there are no correlations for postselection to amplify. 1.
Accuracy threshold for postselected quantum computation
 Quantum Information and Computation
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Leakage Suppression in the Toric Code
"... Abstract—Quantum codes excel at correcting local noise but fail to correct leakage faults that excite qubits to states outside the computational space. Aliferis and Terhal have shown that an accuracy threshold exists for leakage faults using gadgets called leakage reduction units (LRUs). However, th ..."
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Abstract—Quantum codes excel at correcting local noise but fail to correct leakage faults that excite qubits to states outside the computational space. Aliferis and Terhal have shown that an accuracy threshold exists for leakage faults using gadgets called leakage reduction units (LRUs). However, these gadgets reduce the threshold and increase experimental complexity, and the costs have not been thoroughly understood. We explore a variety of techniques for leakage resilience in topological codes. Our contributions are threefold. First, we develop a leakage model that is physically motivated and efficient to simulate. Second, we use MonteCarlo simulations to survey several syndrome extraction circuits. Third, given the capability to perform 3outcome measurements, we present a dramatically improved syndrome processing algorithm. Our simulations show that simple circuits with one extra CNOT per qubit reduce the accuracy threshold by less than a factor of 4 when leakage and depolarizing noise rates are comparable compared to a scenario without leakage. This becomes a factor of 2 when the decoder uses 3outcome measurements. Finally, we make the surprising observation that for physical error rates less than 2 × 10−4, placing LRUs after every gate may achieve the lowest logical error rate. We expect that the ideas may generalize to other topological codes. I.
LEAKAGE SUPPRESSION IN THE TORIC CODE
"... Quantum codes excel at correcting local noise but fail to correct leakage faults that excite qubits to states outside the computational space. Aliferis and Terhal [1] have shown that an accuracy threshold exists for leakage faults using gadgets called leakage reduction units (LRUs). However, these ..."
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Quantum codes excel at correcting local noise but fail to correct leakage faults that excite qubits to states outside the computational space. Aliferis and Terhal [1] have shown that an accuracy threshold exists for leakage faults using gadgets called leakage reduction units (LRUs). However, these gadgets reduce the accuracy threshold and can increase overhead and experimental complexity, and these costs have not been thoroughly understood. Our work explores a variety of techniques for leakageresilient, faulttolerant error correction in the context of topological codes. Our contributions are threefold. First, we develop a leakage model that differs in critical details from earlier models. Second, we use MonteCarlo simulations to survey several syndrome extraction circuits. Third, given the capability to perform threeoutcome measurements, we present a dramatically improved syndrome processing algorithm. Our simulation results show that simple circuits with one extra CNOT per qubit and no additional ancillas reduce the accuracy threshold by less than a factor of 4 when leakage and depolarizing noise rates are comparable. This becomes a factor of 2 when the decoder uses 3outcome measurements. Finally, when the physical error rate is less than 2×10−4, placing LRUs after every gate may achieve the lowest logical error rates of all of the circuits we considered. We expect the closely related planar and rotated codes to exhibit the same accuracy thresholds and that the ideas may generalize naturally to other topological codes.
Holonomic quantum computing in symmetryprotected ground states of spin chains
"... Abstract. While solidstate devices offer naturally reliable hardware for modern classical computers, thus far quantum information processors resemble vacuum tube computers in being neither reliable nor scalable. Strongly correlated many body states stabilized in topologically ordered matter offer t ..."
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Abstract. While solidstate devices offer naturally reliable hardware for modern classical computers, thus far quantum information processors resemble vacuum tube computers in being neither reliable nor scalable. Strongly correlated many body states stabilized in topologically ordered matter offer the possibility of naturally fault tolerant computing, but are both challenging to engineer and coherently control and cannot be easily adapted to different physical platforms. We propose an architecture which achieves some of the robustness properties of topological models but with a drastically simpler construction. Quantum information is stored in the symmetryprotected degenerate ground states of spin1 chains, while quantum gates are performed by adiabatic nonAbelian holonomies using only singlesite fields and nearestneighbor couplings. Gate operations respect the symmetry, and so inherit some protection from noise and disorder from the symmetryprotected ground states. ar X iv