Abstract Characterization and calibration of quantum devices are necessary steps to achieve fault-tolerant quantum computing. As quantum devices become more sophisticated, it is increasingly essential to rely not only on physics-based models but also on machine learning models with open-loop optimization. The Graybox approach is a recently proposed platform-agnostic method offering flexibility in modeling the implicit noise. Despite promising results in photonic qubits, its suitability for other platforms is still unknown. We investigate its performance and limitations under realistic conditions, both numerically and experimentally, for the characterization and calibration of gates on superconducting-qubit devices. We find that the Graybox approach performs well on the devices’ pulse-level controls and is able to search for pulse shapes of high-fidelity gates. However, an important limiting factor of the model’s ability to reduce the training errors is the finite number of measurement shots. We therefore derive analytical bounds to explain this limitation, and use them to indicate users whether the characterization performance is optimized. Furthermore, the model’s predictability also depends on other factors such as parameter drift that may occur between the characterization and calibration processes. Our results provide insights into quantum device characterization and gate optimization on superconducting qubits under realistic scenarios using the Graybox approach.
Abstract Characterization and calibration of quantum devices are necessary steps to achieve fault-tolerant quantum computing. As quantum devices become more sophisticated, it is increasingly essential to rely not only on physics-based models but also on machine learning models with open-loop optimization. The Graybox approach is a recently proposed platform-agnostic method offering flexibility in modeling the implicit noise. Despite promising results in photonic qubits, its suitability for other platforms is still unknown. We investigate its performance and limitations under realistic conditions, both numerically and experimentally, for the characterization and calibration of gates on superconducting-qubit devices. We find that the Graybox approach performs well on the devices’ pulse-level controls and is able to search for pulse shapes of high-fidelity gates. However, an important limiting factor of the model’s ability to reduce the training errors is the finite number of measurement shots. We therefore derive analytical bounds to explain this limitation, and use them to indicate users whether the characterization performance is optimized. Furthermore, the model’s predictability also depends on other factors such as parameter drift that may occur between the characterization and calibration processes. Our results provide insights into quantum device characterization and gate optimization on superconducting qubits under realistic scenarios using the Graybox approach.
While the Graybox characterization method allows for implicit noise models and is platform-agnostic, the method lacks uncertainty quantification. Characterization of quantum devices is a crucial process that enables researchers to gain insight from experimental settings. Graybox characterization combines known system dynamics with unknown transformations, where the latter is modeled using machine learning. Prediction uncertainty helps researchers make informed decisions. It allows valuable insights from the devices without overconfidence. We therefore develop a probabilistic Graybox characterization model using probabilistic machine learning, specifically Bayesian Neural Networks, and utilize binary measurement outcomes directly for inference. With stochastic noise in a quantum device, we analyze statistical properties of the measurement data. Our results show that the model's prediction performance solely depends on its ability to capture the expected value of the true expectation value. Our proposed probabilistic Graybox model outperforms the original model by up to 1.9 times in capturing the distribution of observed data. We expect that our results will serve as an additional tool for characterizing quantum devices with uncertainty estimation, as they provide a flexible choice that can be utilized even without extensive prior knowledge of the noise model of the devices.
Efforts to scale-up quantum computation have reached a point where the principal limiting factor is not the number of qubits, but the entangling gate infidelity. However, the highly detailed system characterization required to understand the underlying error sources is an arduous process and impractical with increasing chip size. Open-loop optimal control techniques allow for the improvement of gates but are limited by the models they are based on. To rectify the situation, we provide an integrated open-source tool set for control, calibration, and characterization (C3), capable of open-loop pulse optimization, model-free calibration, model fitting, and refinement. We present a methodology to combine these tools to find a quantitatively accurate system model, high-fidelity gates, and an approximate error budget, all based on a high-performance, feature-rich simulator. We illustrate our methods using simulated fixed-frequency superconducting qubits for which we learn model parameters with less than $1\mathrm{%}$ error and derive a coherence-limited cross-resonance gate that achieves $99.6\mathrm{%}$ fidelity without the need for calibration.
Implementing fast and high-fidelity quantum operations using open-loop quantum optimal control relies on having an accurate model of the quantum dynamics. Any deviations between this model and the complete dynamics of the device, such as the presence of spurious modes or pulse distortions, can degrade the performance of optimal controls in practice. Here, we propose an experimentally simple approach to realize optimal quantum controls tailored to the device parameters and environment while specifically characterizing this quantum system. Concretely, we use physics-inspired machine learning to infer an accurate model of the dynamics from experimentally available data and then optimize our experimental controls on this trained model. We show the power and feasibility of this approach by optimizing arbitrary single-qubit operations on a superconducting transmon qubit, using detailed numerical simulations. We demonstrate that this framework produces an accurate description of the device dynamics under arbitrary controls, together with the precise pulses achieving arbitrary single-qubit gates with a high fidelity of about 99.99%.
Quantum sensors offer significant advantages over classical devices in spatial resolution and sensitivity, enabling transformative applications across materials science, healthcare, and beyond. Their practical performance, however, is often constrained by unmodelled effects, including noise, imperfect state preparation, and non-ideal control fields. In this work, we report the first experimental implementation of a graybox modelling strategy for a solid-state open quantum system. The graybox framework integrates a physics-based system model with a data-driven description of experimental imperfections, achieving higher fidelity than purely analytical (whitebox) approaches while requiring fewer training resources than fully deep-learning blackbox models. We experimentally validate the method on the task of estimating a static magnetic field using a single-spin quantum sensor, performing Bayesian inference with a graybox model trained on prior experimental data. Using roughly 10,000 training datapoints, the graybox model yields several orders of magnitude improvement in mean squared error over the corresponding physics-only model, as well as significant improvement over a blackbox model with comparable size. These results are broadly applicable to a wide range of quantum sensing platforms, not limited to single-spin systems, and are particularly valuable for real-time adaptive protocols, where model inaccuracies can otherwise lead to suboptimal control and degraded performance.
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.
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.