Fast-feedback Protocols Calibrate 1- and 2-qubit Gates in Quantum Computers, Controlling Drift and SPAM Errors

Quantum computers promise revolutionary computational power, but maintaining their delicate quantum states presents a significant challenge, as even slight drifts in device parameters can introduce errors. Alicia B. Magann, Nathan E. Miller, and Robin Blume-Kohout, alongside colleagues at Sandia National Laboratories and other institutions, now demonstrate fast-feedback protocols that actively calibrate quantum computers in real time. Their research introduces two adaptive calibration methods, one updating parameters with each measurement and another balancing efficiency with classical control, both of which rapidly and accurately tune qubits even with inherent errors and drift. This achievement represents a crucial step towards building stable and reliable quantum computers capable of performing complex calculations, and the team validates the approach through simulations of qubits performing error correction using established quantum codes.

This work introduces two classes of lightweight, adaptive calibration protocols for quantum computers that leverage fast feedback. The first protocol 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, such as syndrome extraction circuits for quantum error correction, balancing efficiency with classical control overheads. Numerical simulations were used to evaluate the performance of these protocols.

Iterative Calibration Corrects Quantum System Drift

Quantum systems are susceptible to drift, changes in their optimal parameters caused by environmental factors. Maintaining accurate calibration is therefore crucial for reliable operation. Researchers have developed two methods to address this challenge: Iterative Optimization with Correlation (IOC) and Dynamic Optimization with Constraints (DOC). IOC dynamically adjusts the circuit depth during calibration to balance accuracy and speed. DOC uses a rule-based approach, adjusting circuit depth based on observed error rates and setting minimum and maximum depth limits to prevent over- or under-calibration.

The performance of these methods depends on key parameters, including circuit depth, a gain parameter related to the optimization step size, and constraints defining the minimum and maximum allowable circuit depths. The team investigated these calibration methods under various noise and drift scenarios, including random walk, Ornstein-Uhlenbeck processes, jump processes, and 1/f noise. Results demonstrate that IOC generally converges faster than DOC, particularly in simpler noise environments. However, DOC proves more robust to sudden jumps in the optimal parameter, as its built-in mechanism reduces circuit depth when large errors are detected.

IOC can become stuck in a local minimum after a jump if the maximum circuit depth is too high. Both methods can be adapted to different noise models by adjusting their parameters. The team found that setting an appropriate maximum circuit depth is critical for IOC’s robustness to jump processes. As noise becomes more complex, calibration becomes more challenging for both methods. This research highlights the trade-offs between speed and robustness, providing valuable guidance for choosing the appropriate method and tuning its parameters for different noise environments.

Rapid Calibration Corrects Qubit Drift and Errors

Researchers have developed two novel calibration protocols for quantum computers that rapidly and accurately tune qubit parameters, even with imperfections in the system. These methods address the challenge of maintaining qubit fidelity by adapting to drift and errors in real time. The first protocol operates on a shot-by-shot basis, updating parameters immediately after each quantum measurement. This approach utilizes indefinite-outcome circuits to probe qubit behavior and estimate the magnitude of any calibration error. Experiments demonstrate that this protocol can effectively calibrate a single-qubit rotation gate, achieving convergence of the rotation error with each measurement update.

The team discovered that the rate of convergence is directly controlled by a gain parameter, allowing for precise adjustment of the calibration speed. Analysis reveals that the asymptotic stationary variance of the rotation error is proportional to this gain parameter, providing a clear relationship between calibration speed and stability. Furthermore, the research demonstrates that the convergence rate does not depend on the sensitivity of the probe circuit, offering flexibility in circuit design. The second protocol employs definite-outcome circuits, such as those used for error correction, to collect measurement data before updating parameters.

This balances efficiency with the overhead of classical control. Numerical simulations show that both the indefinite-outcome and definite-outcome protocols significantly outperform traditional batch calibration methods. Specifically, the new protocols achieve faster calibration and maintain higher experiment uptime. The team successfully demonstrated the feasibility of real-time, in-situ calibration of qubits performing error correction, using only syndrome data extracted from the [[5,1,3]] code. This advancement paves the way for more robust and reliable quantum computations by enabling continuous adaptation to changing conditions and minimizing the impact of errors.

Fast Calibration Boosts Quantum Computer Accuracy

Researchers have developed two new methods for calibrating quantum computers, addressing the critical challenge of maintaining accuracy as these systems operate. Both approaches utilize fast feedback to adjust device parameters, mitigating the effects of drift and errors that accumulate during computation. The first method updates parameters after each measurement using simple quantum circuits, enabling rapid, real-time tuning. The second method balances efficiency with control overhead by updating parameters after collecting data from more complex circuits, suitable for error correction protocols.

Demonstrations show that both calibration techniques effectively improve the accuracy of both single- and two-qubit gates, even in the presence of noise and imperfections in state preparation and measurement. Importantly, the team successfully demonstrated in-simulation calibration of qubits performing error correction, using only the data generated by the error correction process itself. This advancement suggests a pathway towards self-correcting quantum computers that can maintain accuracy autonomously.