Robust quantum control requires real-time validation of Hamiltonian perturbations to ensure gate fidelity under drift and noise. We present the first embedded implementation of Hermitian Spectral Bounds (HSB) for quantum systems, achieving $\gamma=1$ exact certification for Hermitian Hamiltonians with $O(n^{3})$ complexity—orders of magnitude faster than LMI-based methods. Through FPGA/SoC integration and experimental validation on superconducting transmons, we demonstrate $<100~\mu s$ verification latency, zero false negatives, and < 0.01% false positive rate. The method enables autonomous recalibration triggers and real-time go/no-go decisions for quantum operations.
Robust quantum control requires real-time validation of Hamiltonian perturbations to ensure gate fidelity under drift and noise. We present the first embedded implementation of Hermitian Spectral Bounds (HSB) for quantum systems, achieving γ=1 exact certification for Hermitian Hamiltonians with O(n3) complexity—orders of magnitude faster than LMI-based methods. Through FPGA/SoC integration and experimental validation on superconducting transmons, we demonstrate <100μs verification latency, zero false negatives, and < 0.01% false positive rate. The method enables autonomous recalibration triggers and real-time go/no-go decisions for quantum operations.
Modern quantum devices require high-precision Hamiltonian dynamics, but environmental noise can cause calibrated Hamiltonian parameters to drift over time, necessitating expensive recalibration. Detecting when recalibration is needed is challenging, especially since the very gates required for sophisticated verification protocols may themselves be miscalibrated. While cloud quantum computing services implement heuristic routines for triggering recalibration, the fundamental limits of optimal recalibration are not yet known. We develop efficient Hamiltonian certification and changepoint detection protocols in the autonomous setting, where we cannot rely on an external noiseless device and use only single-qubit gates and measurements, making the protocols robust to the calibration issues for multi-qubit operations they aim to detect. For unknown n-qubit Hamiltonians H and H0 with operator norm bounded by M, our certification protocol distinguishes whether ∥H−H0∥F≥ε or ∥H−H0∥F≤O(ε/n) with sample complexity O(nM2ln(1/δ)/ε2) and total evolution time O(nMln(1/δ)/ε2). We achieve this by evolving random stabilizer product states and performing adaptive single-qubit measurements based on a classically simulable hypothesis state. Extending this to continuous monitoring, we develop an online changepoint detection algorithm using the CUSUM procedure that achieves a detection delay time bound of O(nMln(ME∞[T])/ε2), matching the known asymptotically optimal scaling with respect to false alarm run time E∞[T]. Our approach enables quantum devices to autonomously monitor their own calibration status without requiring ancillary systems, entangling operations, or a trusted reference device, offering a practical solution for robust quantum computing with contemporary noisy devices.
We develop a structure-specific fidelity-threshold robustness margin for finite-dimensional closed quantum systems under piecewise-constant coherent control. A scalar physical parameter may perturb the drift, a control Hamiltonian, or another declared Hamiltonian component across the control horizon. A differential sensitivity bound for trace-amplitude gate fidelity yields a threshold-dependent Lipschitz constant on the connected safe parameter component and hence a certified finite perturbation radius. Recentering this certificate produces an iterative one-dimensional method that takes certified safe steps toward the first fidelity-threshold boundary in either parameter direction. A three-qubit gate-control example shows that these finite margins vary by up to a factor of three across controllers of comparable nominal fidelity and contain structure-dependent information not captured by nominal differential sensitivity alone.
Can a high-quality quantum gate be certified when uncharacterized state-preparation and measurement errors are dominant? Can this be achieved with low experimental overhead? Here, we introduce a sound black-box certification protocol for a single-qubit gate based on a small set of fixed, deterministic sequences. From the data, the protocol derives finite-sample bounds on the gate's rotation eigenvalue, a gauge-invariant property. Its phase reveals the accuracy of the rotation angle, while its modulus quantifies the loss of coherence under repeated gate applications. We implement the protocol on a 40Ca+ trapped-ion processor and certify the X-gate rotation eigenvalue using 22000 circuit executions, and demonstrate the robustness of certification to state-preparation and measurement errors by deliberately degrading the readout. Finally, we prove that these spectral constraints imply, up to a physically meaningful unitary change of basis, a rigorous average gate-fidelity lower bound for every time-independent qubit model compatible with the data. In both readout settings, the spectral bounds yield the same fidelity certificate of 99.94(3)% with 99% confidence. Our results establish a new standard for quantum-gate certification by combining soundness and experimental efficiency without requiring trusted reference operations, randomized circuits, or model fitting.
Quantum error correction will be essential for quantum computers to realise their full potential. As quantum computers advance towards demonstrating a universal fault-tolerant logical gate set, implementing scalable and low-latency real-time decoding will be crucial to avoid an exponential slowdown and maintain a fast logical clock rate. Here, we demonstrate low-latency feedback with a scalable FPGA decoder integrated into the control system of a superconducting quantum processor. We perform an 8-qubit stability experiment with up to 25 decoding rounds and a sub-microsecond mean decoding time per round, providing strong evidence that the backlog problem will be avoided when the decoder is operated as a streaming decoder on a superconducting hardware with the strictest speed requirements. We observe logical error suppression as the number of decoding rounds is increased. We also implement and time a fast-feedback experiment demonstrating a decoding response time of 9.6 μs for a total of 9 measurement rounds.
For given control channels, quantum control theory determines whether quantum gates can be realized, but not their resilience to errors. We address this problem by establishing existence criteria for robust gate implementation in d-level systems. Our criteria reveal that implementability of all gates is not enough: a universal family of robust gates exists if and only if the driven Hamiltonians share no common symmetry. When these criteria hold, we can make gates resilient to any combination of static perturbations, uniform Hamiltonian rescaling, perturbations at a finite set of selected frequencies, and perturbations with arbitrary selected waveforms. We can impose robustness conditions broadly with limited information about errors, e.g., against any static perturbations; we can also tailor these conditions to the platform, e.g., against environment-induced noise with dominant spectral peaks, requiring no spectral details beyond the peak frequencies. We numerically construct explicit protocols for robust gates, reducing average gate infidelity by approximately two to seven orders of magnitude under Hamiltonian perturbations and environment-induced noise. Together, our existence criteria and numerical constructions provide practical guidance for evaluating the potential of quantum platforms and designing robust quantum gates.
We study the problem of certifying local Hamiltonians from real-time access to their dynamics. Given oracle access to e−itH for an unknown k-local Hamiltonian H and a fully specified target Hamiltonian H0, the goal is to decide whether H is exactly equal to H0 or differs from H0 by at least ε in normalized Frobenius norm, while minimizing the total evolution time. We introduce the first intolerant Hamiltonian certification protocol that achieves optimal performance for all constant-locality Hamiltonians. For general n-qubit, k-local, traceless Hamiltonians, our procedure uses O(ck/ε) total evolution time for a universal constant c, and succeeds with high probability. In particular, for O(1)-local Hamiltonians, the total evolution time becomes Θ(1/ε), matching the known Ω(1/ε) lower bounds and achieving the gold-standard Heisenberg-limit scaling. Prior certification methods either relied on implementing inverse evolution of H, required controlled access to e−itH, or achieved near-optimal guarantees only in restricted settings such as the Ising case (k=2). In contrast, our algorithm requires neither inverse evolution nor controlled operations: it uses only forward real-time dynamics and achieves optimal intolerant certification for all constant-locality Hamiltonians.