Version 6.1 presents an integral framework for an enhanced GRAPE algorithm for quantumoptimal control.The architecture combines:1. finite-dimensional Hamiltonian control;2. exact or controlled numerical propagation;3. analytic GRAPE gradients using exact Fréchet derivatives;4. gradient verification by independent numerical differentiation;5. robustness to parameter uncertainty;6. robustness to stochastic and quasistatic noise;7. amplitude and slew-rate constraints;8. spectral regularization;9. train/validation/test separation at the level of individual uncertainty realizations;10. multi-start optimization;11. computational-budget-matched comparison; 12. ablation analysis;13. distribution-shift stress testing;14. preregistered statistical analysis;15. independent reproducibility.The central optimization problem is written as a constrained robust optimization problem:maxϵJ(ϵ) (1)subject to amplitude, slew-rate, bandwidth, and numerical constraints.The robust objective is constructed from an in-sample expectation of gate or state-transferfidelity together with explicit regularization terms.A separate held-out distribution is reserved for validation and a locked test distribution isreserved for final evaluation.The framework distinguishes:training performance ̸= validation performance ̸= test performance. (2)The exact propagator derivative is expressed using the Fréchet derivative of the matrixexponential:∂Un∂ϵk,n= D expAn[︃−iℏHk∆t]︃, (3)whereAn = −iℏHn∆t. (4)This formulation avoids the mathematically invalid simplification ∂eA/∂x = eA ∂A/∂x,which only holds under additional commutation conditions.Version 6.1 additionally introduces formal computational-budget specification, ablationexperiments, paired statistical comparisons, bootstrap confidence intervals, multiple-comparisoncontrol, computational profiling, and independent reproduction.No experimental advantage is claimed.
Version 6.1 presents an integral framework for an enhanced GRAPE algorithm for quantumoptimal control.The architecture combines:1. finite-dimensional Hamiltonian control;2. exact or controlled numerical propagation;3. analytic GRAPE gradients using exact Fréchet derivatives;4. gradient verification by independent numerical differentiation;5. robustness to parameter uncertainty;6. robustness to stochastic and quasistatic noise;7. amplitude and slew-rate constraints;8. spectral regularization;9. train/validation/test separation at the level of individual uncertainty realizations;10. multi-start optimization;11. computational-budget-matched comparison; 12. ablation analysis;13. distribution-shift stress testing;14. preregistered statistical analysis;15. independent reproducibility.The central optimization problem is written as a constrained robust optimization problem:maxϵJ(ϵ) (1)subject to amplitude, slew-rate, bandwidth, and numerical constraints.The robust objective is constructed from an in-sample expectation of gate or state-transferfidelity together with explicit regularization terms.A separate held-out distribution is reserved for validation and a locked test distribution isreserved for final evaluation.The framework distinguishes:training performance ̸= validation performance ̸= test performance. (2)The exact propagator derivative is expressed using the Fréchet derivative of the matrixexponential:∂Un∂ϵk,n= D expAn[︃−iℏHk∆t]︃, (3)whereAn = −iℏHn∆t. (4)This formulation avoids the mathematically invalid simplification ∂eA/∂x = eA ∂A/∂x,which only holds under additional commutation conditions.Version 6.1 additionally introduces formal computational-budget specification, ablationexperiments, paired statistical comparisons, bootstrap confidence intervals, multiple-comparisoncontrol, computational profiling, and independent reproduction.No experimental advantage is claimed.
Version 6.1 develops an integral framework for an analog quantum simulator of spin modelsbased on programmable superconducting-qubit arrays.The principal objective is not merely to construct a quantum device, but to establish atraceable mappingcontrol parameters −→ Hreal −→ quantum evolution −→ observables −→ classical reference.The framework supports transverse-field Ising, XY, XXZ, Heisenberg, long-range, anddisordered spin Hamiltonians.Version 6.1 introduces an explicit Hamiltonian- identification layer between hardwarecalibration and scientific validation.The realized Hamiltonian is decomposed into target terms, static calibration errors, dynamiccontrol errors, crosstalk, leakage, decoherence, and residual unwanted interactions.Validation is organized hierarchically:1. hardware calibration;2. Hamiltonian identification;3. state-preparation validation;4. readout calibration;5. static observable validation;6. dynamical observable validation;7. finite-size benchmarking;8. statistical equivalence testing;9. cross-device reproducibility;10. independent analytical reproduction. The statistical framework replaces the inadequate criterion of “statistical significance ofagreement” with an equivalence framework based on preregistered tolerances.The primary hypothesis is therefore formulated using two one-sided tests (TOST) or anequivalent confidence interval criterion:|∆O| < ϵO.Version 6.1 additionally specifies:• a supplementary Bayesian posterior probability of equivalence as a robustness check;• an explicit distinction between engineering no-go and physical falsification.The framework also specifies negative controls, positive controls, blind analysis, lockedanalysis code, exclusion rules, uncertainty propagation, data provenance, and reproducibilityrequirements.No experimental result or quantum advantage is claimed.
Numerical optimal control (GRAPE) can in principle discover pulse shapes that suppress all coherent gate error to machine precision. But when does that capability actually matter? We present a systematic comparison of Gaussian, DRAG, and GRAPE pulses for single-qubit gates on a three-level transmon model parameterized by IQM Garnet hardware (T1=37μs, T2=9.6μs,α/2π=−200 MHz), with the explicit goal of identifying the regimes where numerical optimization provides genuine practical advantage over analytical methods.
Our central finding is that properly calibrated DRAG already operates near the decoherence floor. At 20 ns gate time, GRAPE eliminates all coherent error (1−F<10−15), but DRAG achieves 1−F=4.9×10−4 in coherent error alone,and 8.4×10−4 under full decoherence -- only 1.2× above GRAPE's decoherence-limited performance. More surprisingly,DRAG is \emph{more robust} than GRAPE to qubit frequency detuning (minimum fidelity 0.990 vs.\ 0.931 over ±5 MHz), the dominant calibration uncertainty in charge-noise-limited transmons. GRAPE retains superior amplitude robustness (minimum fidelity 0.994 vs.\ 0.990) and provides the only route to guaranteed zero coherent error, which matters at short gate times (≲15 ns) where perturbative corrections break down.
These results lead to concrete calibration guidance: (1) properly calibrated DRAG is sufficient for gate times ≳20 ns on hardware with T2/T≳500, (2) GRAPE is necessary at short gate times or when targeting error rates well below the decoherence floor, and (3) robust optimal control incorporating frequency uncertainty should be used when detuning is the dominant noise source. We decompose the full error budget (coherent, T1, T2, control noise) and provide the open-source QubitPulseOpt framework for reproducing all results.
Superconducting-qubit control is fundamentally constrained by decoherence, finite bandwidth, and hardware-limited drive amplitudes, making high-fidelity state preparation sensitive to optimizer initialization under non-convex open-system dynamics. We propose a hybrid reinforcement learning (RL)–quantum optimal control (QOC) pipeline in which a lightweight, tabular, model-free RL agent is trained offline in simulation to generate feasible, bounded seed pulses, which are subsequently refined via GRAPE under Lindblad dynamics. Hard amplitude constraints are enforced consistently across both stages, ensuring strict feasibility throughout optimization. Performance is evaluated using a budget-matched protocol based on fidelity evaluations (F-evals), enabling controlled comparison with random-start multi-start GRAPE. On a transmon-like qubit benchmark with relaxation and dephasing, RL warm-starting reduces the median online refinement effort in the adopted finite-difference GRAPE implementation from 7568 to 3543 F-evals (2.14× reduction) while achieving terminal state fidelity ≥0.995 under identical constraints and evaluation budgets. We provide a theoretical interpretation of the improvement in terms of basin-of-attraction probability shaping in constrained control landscapes and an amortized cost analysis showing that the offline RL cost is recovered after a small number of reuse cycles. The results support the view that learning-based initialization can improve warm-start quality relative to uninformed feasible multi-start in constrained open-system quantum-control benchmarks, while broader practical comparison against stronger physics-guided seeds remains for future work.
Highly accurate and robust control of quantum operations is vital for the realization of error-correctible quantum computation. In this paper, we show that the robustness of high-precision controls can be remarkably enhanced through sampling-based stochastic optimization of a risk-sensitive (RS) loss function. Following the stochastic gradient-descent direction of this loss function, the optimization is guided to penalize poor-performance uncertainty samples in a tunable manner. We propose two algorithms, which are termed as the RS GRAPE and the adaptive RS GRAPE. Their effectiveness is demonstrated by numerical simulations, which is shown to be able to achieve high-control robustness while maintaining high fidelity.
We introduce the MAGICARP algorithm, a numerical optimization method for quantum optimal control problems that combines the structure provided by Pontryagin's Maximum Principle (PMP) and the robustness of gradient ascent techniques, such as GRAPE. MAGICARP is formulated as a "shooting technique", aiming to determine the appropriate initial adjoint momentum to realize a target quantum gate. This method naturally incorporates time and energy optimal constraints through a PMP-informed pulse structure. We demonstrate MAGICARP's effectiveness through illustrative numerical examples, comparing its performance to GRAPE and highlighting its advantages in specific scenarios.
Version 6.1 develops an integrated research framework for a modular particle detector usingmultiple quantum correlation resources.The architecture does not posit one universal quantum resource. Instead, it defines a resourcestackH = {C, D, S, V, E}, (1)together with an adaptive controller operating on measured resource estimates, uncertaintyintervals, detector conditions, and environmental covariates.The V6.1 architecture introduces five major extensions: 1. leakage-resistant experimental data partitioning;2. explicit calibration and domain-shift correction;3. uncertainty-aware adaptive resource selection;4. multi-objective classification and energy inference;5. hierarchical reproducibility and falsification criteria.The detector is represented as a conditional measurement system:p(Y | P, Z, Q, Θ), (2)where P denotes particle state, Z environmental conditions, Q the quantum subsystem, andΘ the locked experimental configuration.The adaptive controller selects a resource or resource subset using a preregistered utilityfunction:r⋆ = arg minr∈HLr. (3)Unlike a simple point-estimate controller, V6.1 explicitly propagates uncertainty and allowsan abstention state when the available evidence does not justify a classification.The primary validation framework evaluates classification, energy reconstruction, backgroundrejection, calibration, calibration transfer, robustness, and independent replication.Version 6.1 additionally integrates an explicit sensor platform layer, an event-conditioningchannel, a multi-resource feature vector, and a readout-and-timing block.No experimental result is claimed.