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arXiv:2202.06981 · Physical Review Applied

Minimum Quantum Run-Time Characterization and Calibration via Restless Measurements with Dynamic Repetition Rates

Caroline Tornow, Naoki Kanazawa, Will Shanks, Daniel J. Egger

Published Jun 29, 2022• 27 citations
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Abstract

Qubit calibration and characterization are important for attaining high-fidelity gates in quantum computing, but require a significant amount of time, which limits a device's ability to run useful quantum circuits. This study uses restless measurement, in which the qubits are never reset, to speed up characterization and calibration tasks. The authors also show how quantum process tomography may be performed in a restless setting. This approach reduces the footprint of characterization and calibration on quantum processors by quickly and faithfully executing the corresponding circuits.

DOI
10.1103/physrevapplied.17.064061

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Qubit calibration and characterization are important for attaining high-fidelity gates in quantum computing, but require a significant amount of time, which limits a device's ability to run useful quantum circuits. This study uses restless measurement, in which the qubits are never reset, to speed up characterization and calibration tasks. The authors also show how quantum process tomography may be performed in a restless setting. This approach reduces the footprint of characterization and calibration on quantum processors by quickly and faithfully executing the corresponding circuits.
In order to characterize and calibrate quantum processing devices, a large amount of measurement data has to be collected.Active qubit reset increases the speed at which data can be gathered but requires additional hardware and/or calibration.The experimental apparatus can, however, be operated at elevated repetition rates without reset.In this case, the outcome of a first measurement serves as the initial state for the next experiment.Rol et al. have used this restless operation mode to accelerate the calibration of a single-qubit gate by measuring fixed-length sequences of Clifford gates that compose to X gates [Phys.Rev. Appl.7, 041001 (2017)].However, we find that when measuring pulse sequences that compose to arbitrary operations, distortion appears in the measured data.Here, we extend the restless methodology by showing how to efficiently analyze restless measurements and correct distortions to achieve an identical outcome and accuracy as compared to measurements in which the superconducting qubits are reset.This allows us to rapidly characterize and calibrate qubits.We illustrate this bias-corrected restless measurements method by measuring a Rabi oscillation at a 250 kHz repetition rate without any reset, for a qubit with a decay rate of 1/2π T 1 = 3 kHz.We also show that we can measure a single-and a two-qubit average gate fidelity using randomized benchmarking 20 and 8 times faster, respectively, than measurements that reset the qubits through T 1 decay.
Quantum computers require high fidelity quantum gates. These gates are obtained by routine calibration tasks that eat into the availability of cloud-based devices. Restless circuit execution speeds-up characterization and calibration by foregoing qubit reset in between circuits. Post-processing the measured data recovers the desired signal. However, since the qubits are not reset, leakage -- typically present at the beginning of the calibration -- may cause issues. Here, we develop a simulator of restless circuit execution based on a Markov Chain to study the effect of leakage. In the context of error amplifying single-qubit gates sequences, we show that restless calibration tolerates up to 0.5% of leakage which is large compared to the 10−410^{-4}10−4 gate fidelity of modern single-qubit gates. Furthermore, we show that restless circuit execution with leaky gates reduces by 33% the sensitivity of the ORBIT cost function developed by J. Kelly et al. which is typically used in closed-loop optimal control~[Phys. Rev. Lett. 112, 240504 (2014)]. Our results are obtained with standard qubit state discrimination showing that restless circuit execution is resilient against misclassified non-computational states. In summary, the restless method is sufficiently robust against leakage in both standard and closed-loop optimal control gate calibration to provided accurate results.
Quantum computers require high-fidelity quantum gates. These gates are obtained by routine calibration tasks that eat into the availability of cloud-based devices. Restless circuit execution speeds up characterization and calibration by foregoing qubit reset between circuits. Postprocessing the measured data recovers the desired signal. However, since the qubits are not reset, leakage---typically present at the beginning of the calibration---may cause issues. Here we develop a simulator of restless circuit execution based on a Markov chain to study the effect of leakage. In the context of error-amplifying single-qubit gates sequences, we show that restless calibration tolerates up to 0.5% of leakage, which is large compared to the ${10}^{\ensuremath{-}4}$ gate fidelity of modern single-qubit gates. Furthermore, we show that restless circuit execution with leaky gates reduces by 33% the sensitivity of the ORBIT cost function developed by J. Kelly et al. which is typically used in closed-loop optimal control [Phys. Rev. Lett. 112, 240504 (2014)]. Our results are obtained with standard qubit state discrimination showing that restless circuit execution is resilient against misclassified noncomputational states. In summary, the restless method is sufficiently robust against leakage in both standard and closed-loop optimal control gate calibration to provided accurate results.
In state-of-the-art quantum processors, the time spent tuning gates is a significant portion of experimental run time, and could continue to grow, as number of qubits and achievable fidelities both rise. The authors devise a tune-up protocol that realizes a tenfold speed-up over traditional methods, by constructing a cost function using real-time correlations of the outcomes of nondemolition measurements. This method can be readily generalized to other tune-up problems, including two-qubit gates and measurement operations, and can be parallelized for multi-qubit settings.
Near-term quantum computations are limited by high error rates, the scarcity of qubits and low qubit connectivity. Increasing support for mid-circuit measurements and qubit reset in near-term quantum computers enables qubit reuse that may yield quantum computations with fewer qubits and lower errors. In this work, we introduce a formal model for qubit reuse optimization that delivers provably optimal solutions with respect to quantum circuit depth, number of qubits, or number of swap gates for the first time. This is in contrast to related work where qubit reuse is used heuristically or optimally but without consideration of the mapping effort. We further investigate reset errors on near-term quantum computers by performing reset error characterization experiments. Using the hereby obtained reset error characterization and calibration data of a near-term quantum computer, we then determine a qubit assignment that is optimal with respect to a given cost function. We define this cost function to include gate errors and decoherence as well as the individual reset error of each qubit. We found the reset fidelity to be state-dependent and to range, depending on the reset qubit, from 67.5% to 100% in a near-term quantum computer. We demonstrate the applicability of the developed method to a number of quantum circuits and show improvements in the number of qubits and swap gate insertions, estimated success probability, and Hellinger fidelity of the investigated quantum circuits.
As quantum systems expand in size and complexity, manual qubit characterization and gate optimization will be a non-scalable and time-consuming venture. Physical qubits have to be carefully calibrated because quantum processors are very sensitive to the external environment, with control hardware parameters slowly drifting during operation, affecting gate fidelity. Currently, existing calibration techniques require complex and lengthy measurements to independently control the different parameters of each gate and are unscalable to large quantum systems. Therefore, fully automated protocols with the desired functionalities are required to speed up the calibration process. This paper aims to propose single-qubit calibration of superconducting qubits under continuous weak measurements from a real physical experimental settings point of view. We propose a real-time optimal estimator of qubit states, which utilizes weak measurements and Bayesian optimization to find the optimal control pulses for gate design. Our numerical results demonstrate a significant reduction in the calibration process, obtaining a high gate fidelity. Using the proposed estimator we estimated the qubit state with and without measurement noise and the estimation error between the qubit state and the estimator state is less than 0.02. With this setup, we drive an approximated pi pulse with final fidelity of 0.9928. This shows that our proposed strategy is robust against the presence of measurement and environmental noise and can also be applicable for the calibration of many other quantum computation technologies.