Logical error rate in the Pauli twirling approximation

Katabarwa, Amara; Geller, Michael R.

doi:10.1038/srep14670

Cited by 19 publications

(15 citation statements)

References 15 publications

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“…Small incoherent errors can be well approximated by Pauli errors. In turn, these Pauli error models can accurately reproduce the behavior of quantum error-correcting (QEC) protocols in the presence of incoherent channels [17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

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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Section: Introductionmentioning

confidence: 99%

Errors and pseudothresholds for incoherent and coherent noise

et al. 2016

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“…The analysis conducted for the approximated channels will not be precise due to the fact that parts of the evolutions of the density matrices will be lost when operating with the twirled channels instead of the original ones. Nevertheless, work in the literature has shown that the estimations obtained using the twirling methods presented in this paper are accurate [56].…”

Section: B Approximating Quantum Channels With Twirlingmentioning

confidence: 80%

Approximating Decoherence Processes for the Design and Simulation of Quantum Error Correction Codes on Classical Computers

et al. 2020

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Quantum information is prone to suffer from errors caused by the so-called decoherence, which describes the loss in coherence of quantum states associated to their interactions with the surrounding environment. This decoherence phenomenon is present in every quantum information task, be it transmission, processing or even storage of quantum information. Consequently, the protection of quantum information via quantum error correction codes (QECC) is of paramount importance to construct fully operational quantum computers. Understanding environmental decoherence processes and the way they are modeled is fundamental in order to construct effective error correction methods capable of protecting quantum information. Moreover, quantum channel models that are efficiently implementable and manageable on classical computers are required in order to design and simulate such error correction schemes. In this paper, we present a survey of decoherence models, reviewing the manner in which these models can be approximated into quantum Pauli channel models, which can be efficiently implemented on classical computers. We also explain how certain families of quantum error correction codes can be entirely simulated in the classical domain, without the explicit need of a quantum computer. A quantum error correction code for the approximated channel is also a correctable code for the original channel, and its performance can be obtained by Monte Carlo simulations on a classical computer. INDEX TERMS Decoherence, quantum channels, quantum error correction, Gottesman-Knill theorem.

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“…) impact of applying a Pauli twirl approximation converting a general noise channel to a depolarizing noise channel and enabling scalable numerical simulations of Clifford circuits, instead of full-density-matrix simulations, has already been studied in the literature (see, e.g., [56]). Results on small codes suggest that Pauli twirling overestimates the logical error rate, thus providing to some extent an upper bound on the logical error rate [57]. It has also been reported that Pauli twirling is a good approximation for incoherent noise models and worse for coherent errors [58].…”

Section: Coherence Of Noise and Pauli Twirlingmentioning

confidence: 95%

Towards a realistic GaAs-spin qubit device for a classical error-corrected quantum memory

et al. 2020

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Based on numerically optimized real-device gates and parameters we study the performance of the phase-flip (repetition) code on a linear array of gallium arsenide (GaAs) quantum dots hosting singlet-triplet qubits. We first examine the expected performance of the code using simple error models of circuit-level and phenomenological noise, reporting, for example, a circuit-level depolarizing noise threshold of approximately 3%. We then perform density-matrix simulations using a maximum-likelihood and minimum-weight matching decoder to study the effect of real-device dephasing, readout error, and quasistatic as well as fast gate noise. Considering the tradeoff between qubit readout error and dephasing time (T 2) over measurement time, we identify a subthreshold region for the phase-flip code which lies within experimental reach.

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Logical error rate in the Pauli twirling approximation

Cited by 19 publications

References 15 publications

Errors and pseudothresholds for incoherent and coherent noise

Errors and pseudothresholds for incoherent and coherent noise

Approximating Decoherence Processes for the Design and Simulation of Quantum Error Correction Codes on Classical Computers

Towards a realistic GaAs-spin qubit device for a classical error-corrected quantum memory

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