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Weinstein Y.S.,Quantum Information Science Group
Quantum Information Processing | Year: 2015

In this work, we explore the accuracy of quantum error correction depending of the order of the implemented syndrome measurements. CSS codes require that bit-flip and phase-flip syndromes be measured separately. To comply with fault-tolerant demands and to maximize accuracy, this set of syndrome measurements should be repeated allowing for flexibility in the order of their implementation. We examine different possible orders of Shor-state and Steane-state syndrome measurements for the [[7,1,3]] quantum error correction code. We find that the best choice of syndrome order, determined by the fidelity of the state after noisy error correction, will depend on the error environment. We also compare the fidelity when syndrome measurements are done with Shor states versus Steane states and find that Steane states generally, but not always, lead to final states with higher fidelity. Together, these results allow a quantum computer programmer to choose the optimal syndrome measurement scheme based on the system’s error environment. © 2015 Springer Science+Business Media New York Source

Weinstein Y.S.,Quantum Information Science Group
Physical Review A - Atomic, Molecular, and Optical Physics | Year: 2011

I calculate the fidelity of a [7,1,3] Calderbank-Shor-Steane quantum error correction code logical zero state constructed in a nonequiprobable Pauli operator error environment for two methods of encoding. The first method is to apply fault-tolerant error correction to an arbitrary state of seven qubits utilizing Shor states for syndrome measurement. The Shor states are themselves constructed in the nonequiprobable Pauli operator error environment, and their fidelity depends on the number of verifications done to ensure multiple errors will not propagate into the encoded quantum information. Surprisingly, performing these verifications may lower the fidelity of the constructed Shor states. The second encoding method is to simply implement the [7,1,3] encoding gate sequence also in the nonequiprobable Pauli operator error environment. Perfect error correction is applied after both methods to determine the correctability of the implemented errors. I find that which method attains higher fidelity depends on which of the Pauli operators errors is dominant. Nevertheless, perfect error correction applied after the encoding suppresses errors to at least first order for both methods. © 2011 American Physical Society. Source

Weinstein Y.S.,Quantum Information Science Group
Physical Review A - Atomic, Molecular, and Optical Physics | Year: 2013

Correcting errors is a vital but expensive component of fault-tolerant quantum computation. Standard fault-tolerant protocol assumes the implementation of error correction, via syndrome measurements and possible recovery operations, after every quantum gate. In fact, this is not necessary. Here we demonstrate that error correction should be applied more sparingly. We simulate encoded single-qubit rotations within the [7,1,3] code and show via fidelity measures that applying error correction after every gate is not desirable. © 2013 American Physical Society. Source

Weinstein Y.S.,Quantum Information Science Group | Chai D.,Quantum Information Science Group | Xie N.,Quantum Information Science Group
Quantum Information Processing | Year: 2016

We analyze the improvement in output state fidelity upon improving the construction accuracy of ancilla states. Specifically, we simulate gates and syndrome measurements on a single qubit of information encoded into the [[7,1,3]] quantum error correction code and determine the output state fidelity as a function of the accuracy with which Shor states (for syndrome measurements) and magic states (to implement T-gates) are constructed. When no syndrome measurements are applied during the gate sequence, we observe that the fidelity increases after performance of a T-gate and improving magic states construction slows the fidelity decay rate. In contrast, when syndrome measurements are applied, loss of fidelity occurs primarily after the syndrome measurements taken after a T-gate. Improving magic state construction slows the fidelity decay rate, and improving Shor state construction raises the initial fidelity but does not slow the fidelity decay rate. Along the way, we show that applying syndrome measurements after every gate does not maximize the output state fidelity. Rather, syndrome measurements should be applied sparingly. © 2015 Springer Science+Business Media New York Source

Aggarwal V.,Princeton University | Calderbank A.R.,Princeton University | Gilbert G.,Quantum Information Science Group | Weinstein Y.S.,Quantum Information Science Group
Quantum Information Processing | Year: 2010

We introduce finite-level concatenation threshold regions for quantum fault tolerance. These volume thresholds are regions in an error probability manifold that allow for the implemented system dynamics to satisfy a prescribed implementation inaccuracy bound at a given level of quantum error correction concatenation. Satisfying this condition constitutes our fundamental definition of fault tolerance. The prescribed bound provides a halting condition identifying the attainment of fault tolerance that allows for the determination of the optimum choice of quantum error correction code(s) and number of concatenation levels. Our method is constructed to apply to finite levels of concatenation, does not require that error proabilities consistently decrease from one concatenation level to the next, and allows for analysis, without approximations, of physical systems characterized by non-equiprobable distributions of qubit error probabilities. We demonstrate the utility of this method via a general error model. © 2010 Springer Science+Business Media, LLC. Source

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