Tractable simulation of error correction with honest approximations to realistic fault models

Puzzuoli, Daniel; Granade, Christopher; Haas, Holger; Criger, Ben; Magesan, Easwar; Cory, David G.

doi:10.1103/physreva.89.022306

Cited by 34 publications

(52 citation statements)

References 49 publications

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“…However, at the logical level, they become completely eclipsed by the high accuracy of the PCa. This characteristic of the PCa has been observed previously [17][18][19].…”

Section: Channelsupporting

confidence: 84%

Errors and pseudothresholds for incoherent and coherent noise

et al. 2016

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We compare the effect of single qubit incoherent and coherent errors on the logical error rate of the Steane [[7,1,3]] quantum error correction code by performing an exact full-density-matrix simulation of an error correction step. We find that the effective 1-qubit process matrix at the logical level reveals the key differences between the error models and provides insight into why the Pauli twirling approximation is a good approximation for incoherent errors and a poor approximation for coherent ones. Approximate channels composed of Clifford operations and Pauli measurement operators that are pessimistic at the physical level result in pessimistic error rates at the logical level. In addition, we observe that the pseudo-threshold can differ by a factor of five depending on whether the error is calculated using the fidelity or the distance.

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“…However, at the logical level, they become completely eclipsed by the high accuracy of the PCa. This characteristic of the PCa has been observed previously [17][18][19].…”

Section: Channelsupporting

confidence: 84%

Errors and pseudothresholds for incoherent and coherent noise

et al. 2016

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“…Conceptually, these errors originate from entanglement between the computational states and the noncomputational states in the transmons and the resonator. Such errors cause most of the mismatch between the ideal gates and the implemented pulses (see also [7,11,33,[47][48][49]). …”

Section: Discussionmentioning

confidence: 99%

“…For this reason, the underlying architecture and its operation call for a deeper analysis, one that goes beyond perturbation theory, rotating wave approximations, and assumptions about Lindblad forms and Markovian dynamics [7].…”

Section: Introductionmentioning

confidence: 99%

Gate-error analysis in simulations of quantum computers with transmon qubits

et al. 2017

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In the model of gate-based quantum computation, the qubits are controlled by a sequence of quantum gates. In superconducting qubit systems, these gates can be implemented by voltage pulses. The success of implementing a particular gate can be expressed by various metrics such as the average gate fidelity, the diamond distance, and the unitarity. We analyze these metrics of gate pulses for a system of two superconducting transmon qubits coupled by a resonator, a system inspired by the architecture of the IBM Quantum Experience. The metrics are obtained by numerical solution of the time-dependent Schrödinger equation of the transmon system. We find that the metrics reflect systematic errors that are most pronounced for echoed cross-resonance gates, but that none of the studied metrics can reliably predict the performance of a gate when used repeatedly in a quantum algorithm.

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“…Only when the bath state, entangled with a given error, is orthogonal to all other bath states is the stochastic error model truly appropriate [5,14]. Despite these fairly well-known results from the early literature on quantum error correction, the use of stochastic error models is still widely used in numerical simulations to calculate thresholds, including many results that have examined the accuracy of approximating various error channels by stochastic errors [18][19][20][21][22][23]. Of course, a significant reason for using this error model this is that these types of errors can be efficiently simulated classically via the Gottesman-Knill theorem [24,25] if one restricts the set of gates to the Clifford group or a subset (often just Pauli operators are used).…”

Section: Introductionmentioning

confidence: 99%

Quantum error-correction failure distributions: Comparison of coherent and stochastic error models

et al. 2017

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We compare failure distributions of quantum error correction circuits for stochastic errors and coherent errors. We utilize a fully coherent simulation of a fault tolerant quantum error correcting circuit for a d = 3 Steane and surface code. We find that the output distributions are markedly different for the two error models, showing that no simple mapping between the two error models exists. Coherent errors create very broad and heavy-tailed failure distributions. This suggests that they are susceptible to outlier events and that mean statistics, such as pseudo-threshold estimates, may not provide the key figure of merit. This provides further statistical insight into why coherent errors can be so harmful for quantum error correction. These output probability distributions may also provide a useful metric that can be utilized when optimizing quantum error correcting codes and decoding procedures for purely coherent errors.

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Tractable simulation of error correction with honest approximations to realistic fault models

Cited by 34 publications

References 49 publications

Errors and pseudothresholds for incoherent and coherent noise

Errors and pseudothresholds for incoherent and coherent noise

Gate-error analysis in simulations of quantum computers with transmon qubits

Quantum error-correction failure distributions: Comparison of coherent and stochastic error models

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