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arXiv:1907.03864 · npj Quantum Information

Real-time calibration with spectator qubits

Swarnadeep Majumder, Leonardo Andreta de Castro, Kenneth R. Brown

Published Feb 7, 2020• 42 citations
arXivHTMLPDF

Abstract

Abstract Accurate control of quantum systems requires a precise measurement of the parameters that govern the dynamics, including control fields and interactions with the environment. Parameters will drift in time and experiments interleave protocols that perform parameter estimation, with protocols that measure the dynamics of interest. Here we specialize to a system made of qubits where the dynamics correspond to a quantum computation. We propose setting aside some qubits, which we call spectator qubits, to be measured periodically during the computation, to act as probes of the changing experimental and environmental parameters. By using control strategies that minimize the sensitivity of the qubits involved in the computation, we can acquire sufficient information from the spectator qubits to update our estimates of the parameters and improve our control. As a result, we can increase the length of experiments where the dynamics of the data qubits are highly reliable. In particular, we simulate how spectator qubits can keep the error level of operations on data qubits below a 10 −4 threshold in two scenarios involving coherent errors: a classical magnetic field gradient dynamically decoupled with sequences of two or four π -pulses, and laser beam instability detected via crosstalk with neighboring atoms in an ion trap.

DOI
10.1038/s41534-020-0251-y

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Abstract Accurate control of quantum systems requires a precise measurement of the parameters that govern the dynamics, including control fields and interactions with the environment. Parameters will drift in time and experiments interleave protocols that perform parameter estimation, with protocols that measure the dynamics of interest. Here we specialize to a system made of qubits where the dynamics correspond to a quantum computation. We propose setting aside some qubits, which we call spectator qubits, to be measured periodically during the computation, to act as probes of the changing experimental and environmental parameters. By using control strategies that minimize the sensitivity of the qubits involved in the computation, we can acquire sufficient information from the spectator qubits to update our estimates of the parameters and improve our control. As a result, we can increase the length of experiments where the dynamics of the data qubits are highly reliable. In particular, we simulate how spectator qubits can keep the error level of operations on data qubits below a 10 −4 threshold in two scenarios involving coherent errors: a classical magnetic field gradient dynamically decoupled with sequences of two or four π -pulses, and laser beam instability detected via crosstalk with neighboring atoms in an ion trap.
We demonstrate a trapped-ion protocol in which a nearby, dedicated "monitor" qubit tracks magnetic-field drifts in real time without interrupting data-qubit operations. Using two 40Ca+^{40}\mathrm{Ca}^+40Ca+ ions and the optical--metastable--ground architecture, we encode the data qubit in the ground-state manifold and the monitor qubit in a metastable-state manifold to achieve spectral separation. The monitor qubit senses common magnetic fluctuations during data-qubit experiments, enabling feedforward corrections to the qubit-control drives. Under applied magnetic noise with a realistic spectrum (1/f21/f^{2}1/f2), the protocol maintains coherence and, when compared with interleaved calibration, it extends usable data-qubit probe times by up to a factor of ∼2{\sim}\sqrt{2}∼2​ and doubles the experimental duty cycle. These results establish monitor qubits as a scalable tool for real-time recalibration in quantum information processors.
We introduce two classes of lightweight, adaptive calibration protocols for quantum computers that leverage fast feedback. The first enables shot-by-shot updates to device parameters using measurement outcomes from simple, indefinite-outcome quantum circuits. This low-latency approach supports rapid tuning of one or more parameters in real time to mitigate drift. The second protocol updates parameters after collecting measurements from definite-outcome circuits (e.g.~syndrome extraction circuits for quantum error correction), balancing efficiency with classical control overheads. We use numerical simulations to demonstrate that both methods can calibrate 1- and 2-qubit gates rapidly and accurately even in the presence of decoherence, state preparation and measurement (SPAM) errors, and parameter drift. We propose and demonstrate effective adaptive strategies for tuning the hyperparameters of both protocols. Finally, we demonstrate the feasibility of real-time in-situ calibration of qubits performing quantum error correction, using only syndrome data, via numerical simulations of syndrome extraction in the [[5,1,3]] code.
We demonstrate a trapped-ion protocol in which a nearby, dedicated monitor qubit tracks magnetic field drifts in real time without interrupting data-qubit operations. Using two 40Ca+^{40}\mathrm{Ca}^{+}40Ca+ ions and the optical-metastable-ground architecture, we encode the data qubit in the ground-state manifold and the monitor qubit in a metastable-state manifold to achieve spectral separation. The monitor qubit senses common magnetic fluctuations during data-qubit experiments, enabling feedforward corrections to the qubit-control drives. Under applied magnetic noise with a realistic spectrum (1/f21/{f}^{2}1/f2), the protocol maintains coherence and, when compared with interleaved calibration, it extends usable data-qubit probe times by up to a factor of approximately 2\sqrt{2}2​ and doubles the experimental duty cycle. These results establish monitor qubits as a scalable tool for real-time recalibration in quantum information processors.
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.
State-of-the-art two-qubit gates with trapped ions employ open-loop control that rely on simplified models to precompute control sequences. Our aim is to introduce closed-loop control for two-qubit gates to correct disturbances as they occur during the gate implementation. We introduce a spectator ion into the ion chain used for quantum logic processing, where it couples with the other ions through collective motional modes. The spectator ion's position is continuously monitored by driving dipole transitions and detecting the resultant fluorescence. We show that incorporating a spectator ion is feasible for linear Paul trap implementations and is expected to reduce the two-qubit gate Bell-state preparation infidelity by an order of magnitude with the deleterious effects of position monitoring being negligible compared to the thermal effects that exist in the system, even in the absence of the spectator ions. Mathematically, we describe driven ion-trap dynamics, including the spectator ion, by a stochastic quantum master equation involving the amplitude-modulation multimode-motional coupling gate, motional drift, thermal effects, recoil from photon scattering, spontaneous decay, and light shift. Our on-the-fly control method employs reinforcement learning with the reward function based on the actual geometric phase of the spectator ion. A key advantage of our approach is that we introduce a control method that involves `learning' and correcting disturbances happening in the trap on-the-fly, thus achieving high-fidelity gates. Our approach will lead to a significantly higher two-qubit gate fidelity at a reduced calibration overhead owing to the small parameter drift in the control system.
We present and experimentally implement a real-time protocol for calibrating the frequency of a resonantly driven qubit, achieving exponential scaling in calibration precision with the number of measurements, up to the limit imposed by decoherence. The real-time processing capabilities of a classical controller dynamically generate adaptive probing sequences for qubit-frequency estimation. Each probing evolution time and drive frequency are calculated to divide the prior probability distribution into two branches, following a locally optimal strategy that mimics a conventional binary search. The scheme does not require repeated measurements at the same setting, as it accounts for state preparation and measurement errors. Its use of a parametrized probability distribution favors numerical accuracy and computational speed. We show the efficacy of the algorithm by stabilizing a flux-tunable transmon qubit, leading to improved coherence and gate fidelity. As benchmarked by gate-set tomography, the field-programmable gate array (FPGA) powered control electronics partially mitigates non-Markovian noise, which is detrimental to quantum error correction. The mitigation is achieved by dynamically updating and feeding forward the qubit frequency. Our protocol highlights the importance of feedback in improving the calibration and stability of qubits subject to drift and can be readily applied to other qubit platforms.