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arXiv:1611.04815 · Physical Review Applied

Restless Tuneup of High-Fidelity Qubit Gates

Michiel Adriaan Rol, Cornelis Christiaan Bultink, T. E. O’Brien, S. R. de Jong, L. S. Theis, Xiang Fu, F. Luthi, R. F. L. Vermeulen, J. C. de Sterke, Alessandro Bruno, D. Deurloo, Raymond N. Schouten, Frank K. Wilhelm, L. DiCarlo

Published Apr 24, 2017• 78 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevapplied.7.041001

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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.
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.
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.
As quantum devices make steady progress towards intermediate scale and fault-tolerant quantum computing, it is essential to develop rigorous and efficient measurement protocols that account for known sources of noise. Most existing quantum characterization protocols such as gate-set tomography and randomized benchmarking assume the noise acting on the qubits is Markovian. However, this assumption is often not valid, as for the case of 1/f charge noise or hyperfine nuclear spin noise. Here, we present a general framework for quantum process tomography (QPT) in the presence of time-correlated noise. We further introduce fidelity benchmarks that quantify the relative strength of different sources of Markovian and non-Markovian noise. As an application of our method, we perform a comparative theoretical and experimental analysis of silicon spin qubits. We first develop a detailed noise model that accounts for the dominant sources of noise and validate the model against experimental data. Applying our framework for time-correlated QPT, we find that the number of independent parameters needed to characterize one- and two-qubit gates can be compressed by 10× and 100× , respectively, when compared to the fully generic case. These compressions reduce the amount of tomographic measurements needed in experiment, while also significantly speeding up numerical simulations of noisy quantum circuit dynamics compared to time-dependent Hamiltonian simulation. Using this compressed noise model, we find good agreement between our theoretically predicted process fidelities and two-qubit interleaved randomized benchmarking fidelities of 99.8% measured in recent experiments on silicon spin qubits. More broadly, our formalism can be directly extended to develop efficient and scalable tuning protocols for high-fidelity control of large arrays of quantum devices with non-Markovian noise. Published by the American Physical Society 2024
As the size and complexity of a quantum computer increases, quantum bit (qubit) characterization and gate optimization become complex and time-consuming tasks. Current calibration techniques require complicated and verbose measurements to tune up qubits and gates, which cannot easily expand to the large-scale quantum systems. We develop a concise and automatic calibration protocol to characterize qubits and optimize gates using QubiC, which is an open source FPGA (field-programmable gate array) based control and measurement system for superconducting quantum information processors. We propose mutli-dimensional loss-based optimization of single-qubit gates and full XY-plane measurement method for the two-qubit CNOT gate calibration. We demonstrate the QubiC automatic calibration protocols are capable of delivering high-fidelity gates on the state-of-the-art transmon-type processor operating at the Advanced Quantum Testbed at Lawrence Berkeley National Laboratory. The single-qubit and two-qubit Clifford gate infidelities measured by randomized benchmarking are of 4.9(1.1)×10−44.9(1.1) \times 10^{-4}4.9(1.1)×10−4 and 1.4(3)×10−21.4(3) \times 10^{-2}1.4(3)×10−2, respectively.