Characterizing quantum gates via randomized benchmarking

Magesan, Easwar; Gambetta, Jay; Emerson, Joseph

doi:10.1103/physreva.85.042311

Cited by 410 publications

(586 citation statements)

References 55 publications

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“…We then proceed with a randomized benchmarking 56,57 analysis of these pulse sequences. In such an analysis, one generates random sequences of Clifford gates of a given length and determines the average fidelity of these sequences.…”

Section: Introductionmentioning

confidence: 99%

Fast pulse sequences for dynamically corrected gates in singlet-triplet qubits

et al. 2017

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We present a set of experimentally feasible pulse sequences that implement any single-qubit gate on a singlet-triplet spin qubit and demonstrate that these new sequences are up to three times faster than existing sequences in the literature. We show that these sequences can be extended to incorporate built-in dynamical error correction, yielding gates that are robust to both charge and magnetic field noise and up to twice as fast as previous dynamically corrected gate schemes. We present a thorough comparison of the performance of our new sequences with that of several existing ones using randomized benchmarking, considering both quasistatic and 1/f α noise models. We provide our results both as a function of evolution time and as a function of the number of gates, which respectively yield both an effective coherence time and an estimate of the number of gates that can be performed within this coherence time. We determine which set of pulse sequences gives the best results for a wide range of noise strengths and power spectra. Overall, we find that the traditional, slower sequences perform best when there is no field noise or when the noise contains significant high-frequency components; otherwise, our new, fast sequences exhibit the best performance.

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Section: Introductionmentioning

confidence: 99%

Fast pulse sequences for dynamically corrected gates in singlet-triplet qubits

et al. 2017

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“…To obtain this to a precision of ∼ 10 −3 is challenging in practice. However, if one is willing to sacrifice optimality, a Pauli-or Clifford-twirling [20,21] can be applied that converts any noise channel into a simple mixture of Pauli errors or depolarizing noise, making the characterization task much more manageable. A very recent independent paper by Li and Benjamin [22] discusses similar issues to those addressed here.…”

Section: Probabilistic Error Cancellationmentioning

confidence: 99%

Error Mitigation for Short-Depth Quantum Circuits

Temme¹,

Bravyi²,

Gambetta³

2017

Phys. Rev. Lett.

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1,073

987

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Two schemes are presented that mitigate the effect of errors and decoherence in short-depth quantum circuits. The size of the circuits for which these techniques can be applied is limited by the rate at which the errors in the computation are introduced. Near-term applications of early quantum devices, such as quantum simulations, rely on accurate estimates of expectation values to become relevant. Decoherence and gate errors lead to wrong estimates of the expectation values of observables used to evaluate the noisy circuit. The two schemes we discuss are deliberately simple and don't require additional qubit resources, so to be as practically relevant in current experiments as possible. The first method, extrapolation to the zero noise limit, subsequently cancels powers of the noise perturbations by an application of Richardson's deferred approach to the limit. The second method cancels errors by resampling randomized circuits according to a quasi-probability distribution.From the time quantum computation generated wide spread interest, the strongest objection to its viability was the sensitivity to errors and noise. In an early paper, William Unruh [1] found that the coupling to the environment sets an ultimate time and size limit for any quantum computation. This initially curbed the hopes that the full advantage of quantum computing could be harnessed, since it set limits on the scalability of any algorithm. This problem was, at least in theory, remedied with the advent of quantum error correction [2][3][4]. It was proven that if both the decoherence and the imprecision of gates could be reduced below a finite threshold value, then quantum computation could be performed indefinitely [5,6]. Although it is the ultimate goal to reach this threshold in an experiment that is scalable to larger sizes, the overhead that is needed to implement a fully fault-tolerant gate set with current codes [7] seems prohibitively large [8,9]. In turn, it is expected that in the near term the progress in quantum experiments will lead to devices with dynamics, which are beyond what can be simulated with a conventional computer. This leads to the question: what computational tasks could be accomplished with only limited, or no error correction?The suggestions of near-term applications in such quantum devices mostly center around quantum simulations with short-depth circuit [10][11][12] and approximate optimization algorithms [13]. Furthermore, certain problems in material simulation may be tackled by hybrid quantum-classical algorithms [14]. In most such applications, the task can be abstracted to applying a short-depth quantum circuits to some simple initial state and then estimating the expectation value of some observable after the circuit has been applied. This estimation must be accurate enough to achieve a simulation precision comparable or exceeding that of classical algorithms. Yet, although the quantum system evolves coherently for the most part of the short-depth circuit, the effects of decoherence already become apparent...

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“…In experiments, this number is estimated by a protocol called randomized benchmarking (RB) [36,37]. However, as in our simulation we have access to the error channel given by Eq.…”

Section: A Average Gate Fidelitymentioning

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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Characterizing quantum gates via randomized benchmarking

Cited by 410 publications

References 55 publications

Fast pulse sequences for dynamically corrected gates in singlet-triplet qubits

Fast pulse sequences for dynamically corrected gates in singlet-triplet qubits

Error Mitigation for Short-Depth Quantum Circuits

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

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