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Physical Review A

Leakage in restless quantum gate calibration

Conrad J. Haupt, Daniel J. Egger

Published Aug 23, 2023• 3 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.108.022614

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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{10}^{\ensuremath{-}4}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.
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.
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.
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.
The ability for users to access quantum computers through the cloud has increased rapidly in recent years. Despite still being Noisy Intermediate-Scale Quantum (NISQ) machines, modern quantum computers are now being actively employed for research and by numerous startups. Quantum algorithms typically produce probabilistic results, necessitating repeated execution to produce the desired outcomes. In order for the execution to begin from the specified ground state each time and for the results of the prior execution not to interfere with the results of the subsequent execution, the reset mechanism must be performed between each iteration to effectively reset the qubits. However, due to noise and errors in quantum computers and specifically these reset mechanisms, a noisy reset operation may lead to systematic errors in the overall computation, as well as potential security and privacy vulnerabilities of information leakage. To counter this issue, we thoroughly examine the state leakage problem in quantum computing, and then propose a solution by employing the classical and quantum one-time pads before the reset mechanism to prevent the state leakage, which works by randomly applying simple gates for each execution of the circuit. In addition, this work explores conditions under which the classical one-time pad, which uses fewer resources, is sufficient to protect state leakage. Finally, we study the role of various errors in state leakage, by evaluating the degrees of leakage under different error levels of gate, measurement, and sampling errors. Our findings offer new perspectives on the design of reset mechanisms and secure quantum computing systems.
ABSTRACT: Recent research has tackled the problem of mitigating noise present in quantum computers in the Noisy Intermediate-Scale Quantum (NISQ) era to enable precise computations and to benefit from the intrinsic properties of quantum mechanics. For this matter, an important task is the characterization of qubits available in quantum devices so as to provide insights on how to reduce noise on the final output of a quantum circuit. Characterization comprises analysis of noise sources and this information can be used to reduce noise with methods such as Cycle Benchmarking, Quantum Error Mitigation, Quantum Error Correction and others. Here, we study optimization of pulses through Quantum Optimal Control (QOC) to obtain higher gate fidelity. We will explore an algorithm that performs calibration on specific quantum gates by implementing optimized pulse schedules to subsequently use the algorithm for analysis of noise sources. Using calibrated gates as input, several benchmarking protocols, including pulse noise extrapolation, leakage analysis from quantum optimal control, and machine learning based classification of qubit readout, will be tested to extract precise information on how noise influences the analyzed qubits. We will explain and discuss different techniques for obtaining properties of qubits and quantum computers. We will implement state discrimination with a Machine Learning (ML) focus to analyze readout errors caused by factors such as cross-talk and leakage into higher quantum states. We will perform noise fitting of optimized pulses and evaluate the effectiveness of important quantum algorithms at the pulse level.
Abstract Reaching high-speed, high-fidelity qubit operations requires precise control over the shape of the underlying pulses. For weakly anharmonic systems, such as superconducting transmon qubits, short gates lead to leakage to states outside of the computational subspace. Control pulses designed with open-loop optimal control may reduce such leakage. However, model inaccuracies can severely limit the usability of such pulses. We implemented a closed-loop optimization that simultaneously adapts all control parameters based on measurements of a cost function built from Clifford gates. We directly optimize the amplitude and phase of each sample point of the digitized control pulse. We thereby fully exploit the capabilities of the pulse generation electronics and create a 4.16 ns single-qubit pulse with 99.76 % fidelity and 0.044 % leakage. This is a sevenfold reduction of the leakage rate and a threefold reduction in standard errors of the best DRAG pulse we have calibrated at such short durations on the same system.