High-fidelity control of qubits requires precisely tuned control parameters. Typically, these parameters are found through a series of bootstrapped calibration experiments which successively acquire more accurate information about a physical qubit. However, optimal parameters are typically different between devices and can also drift in time, which begets the need for an efficient calibration strategy. Here, we introduce a framework to understand the relationship between calibrations as a directed graph. With this approach, calibration is reduced to a graph traversal problem that is automatable and extensible.
High-fidelity control of qubits requires precisely tuned control parameters. Typically, these parameters are found through a series of bootstrapped calibration experiments which successively acquire more accurate information about a physical qubit. However, optimal parameters are typically different between devices and can also drift in time, which begets the need for an efficient calibration strategy. Here, we introduce a framework to understand the relationship between calibrations as a directed graph. With this approach, calibration is reduced to a graph traversal problem that is automatable and extensible.
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 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.
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.
Calibration of a quantum computer is the process of optimizing its control parameters to ensure the accurate implementation of quantum gates.It remains a critical challenge in scaling quantum computers.Existing calibration methods take a generalized approach that focuses on the trade-off between calibration time and fidelity.However, these methods lack the awareness of hardware differences among physical qubits and an elaborate design of parallel calibration.In this paper, we introduce a fine-grained calibration protocol that contains three calibration policies for hardware differences and a method to enable parallel calibration.We begin by profiling qubit pairs to evaluate their responses to different waveform candidates.Based on profiling results, we determine the best calibration policy for the quantum computer, which is the first part of the calibration protocol.The second part of our protocol is to use graph traverse to enable parallel calibration by identifying compatible calibration operations.We validate our protocol through intensive experiments on real quantum machines with up to 127 qubits.Our experimental results demonstrate a 1.84× reduction in terms of the medium of the two-qubit gate error rate, 1.26× reduction in pulse duration, an 8× to 25× reduction in total calibration overhead compared with sequential calibration, an average of 2.12× further reduction in total calibration overhead owing to profiling policy, double of the quantum volume, and a 2.0× to 2.3× reduction in error per layered gate.The proposed protocol emphasizes the importance of hardware-aware and parallel calibration and advances current quantum computers towards fault-tolerant quantum computing.
This work presents a structural critique of calibration-based control frameworks for superconducting quantum computing systems, with particular focus on architectures relying on recursive calibration loops and dependency graph formalism. It is shown that the current paradigm does not resolve the fundamental problem of physical instability, but instead formalizes it as an operational requirement. Continuous recalibration, parameter drift, and dependency-driven control structures indicate the absence of stable, reproducible computational states. The analysis demonstrates that the system does not admit a stationary operational regime, and that control is effectively shifted from physical determinacy to procedural scheduling. Directed acyclic graphs and calibration routines are shown to reorganize instability rather than eliminate it. Furthermore, the framework lacks invariant quantities, external validation criteria, and any demonstrated convergence toward stable configurations. Validation remains internal and self-referential, preventing the establishment of physically meaningful computational states. Scalability is assumed through automation, but no structural argument is provided to ensure bounded error propagation or stability under system growth. As a result, increasing system size amplifies the instability it attempts to manage. The work concludes that the calibration-based paradigm represents a systematic redefinition of instability as workflow. The resulting architecture does not achieve control of a quantum system, but continuous management of its failure modes.
Model-based quantum optimal control promises to solve a wide range of critical quantum technology problems within a single, flexible framework. The catch is that highly-accurate models are needed if the optimized controls are to meet the exacting demands set by quantum engineers. A practical alternative is to directly calibrate control parameters by taking device data and tuning until success is achieved. In quantum computing, gate errors due to inaccurate models can be efficiently polished if the control is limited to a few (usually hand-designed) parameters; however, an alternative tool set is required to enable efficient calibration of the complicated waveforms potentially returned by optimal control. We propose an automated model-based framework for calibrating quantum optimal controls called Learning Iteratively for Feasible Tracking (LIFT). LIFT achieves high-fidelity controls despite parasitic model discrepancies by precisely tracking feasible trajectories of quantum observables. Feasible trajectories are set by combining black-box optimal control and the bilinear dynamic mode decomposition, a physics-informed regression framework for discovering effective Hamiltonian models directly from rollout data. Any remaining tracking errors are eliminated in a non-causal way by applying model-based, norm-optimal iterative learning control to subsequent rollout data. We use numerical experiments of qubit gate synthesis to demonstrate how LIFT enables calibration of high-fidelity optimal control waveforms in spite of model discrepancies.