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arXiv:2603.13020

Constraint-native quantum control for fidelity--complexity trade-offs with inexact proximal ADMM

Ziwen Song

quant-phphysics.atom-phSubmitted Mar 13, 2026• Announced Mar 16, 2026• 0 citations• Revised Jul 11, 2026 (v2)
v1 · Mar 13, 2026v2 · Jul 11, 2026
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Abstract

Quantum-control pulses are often optimised for nominal fidelity before waveform constraints are imposed. This sequence can conceal the fidelity cost of producing smooth, band-limited, and amplitude-admissible controls. Here, we evaluate a constraint-native alternative based on inexact proximal alternating-direction updates. The formulation combines gate-infidelity minimisation with amplitude bounds, Fourier-domain bandwidth projection, amplitude sparsity, and total-variation regularisation. We compare it with GRAPE, standard Krotov optimisation, and L-BFGS-B on a single-qubit gate, a leakage-prone qutrit gate, and a two-qubit entangler without a directly controlled target generator. Random seeds are paired across methods, and qutrit computational-subspace fidelity is reported alongside leakage. PADMM-Warm reached mean qutrit and two-qubit fidelities of $0.6363$ and $0.9541$, respectively, while reducing total variation by factors of $13.2$ and $10.7$ relative to L-BFGS-B. These results define a reproducible fidelity--complexity trade-off, not a universal fidelity advantage. The method is therefore a numerical tool for exploring low-complexity control frontiers rather than a replacement for unconstrained high-fidelity solvers.

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Quantum-control pulses are often optimised for nominal fidelity before waveform constraints are imposed. This sequence can conceal the fidelity cost of producing smooth, band-limited, and amplitude-admissible controls. Here, we evaluate a constraint-native alternative based on inexact proximal alternating-direction updates. The formulation combines gate-infidelity minimisation with amplitude bounds, Fourier-domain bandwidth projection, amplitude sparsity, and total-variation regularisation. We compare it with GRAPE, standard Krotov optimisation, and L-BFGS-B on a single-qubit gate, a leakage-prone qutrit gate, and a two-qubit entangler without a directly controlled target generator. Random seeds are paired across methods, and qutrit computational-subspace fidelity is reported alongside leakage. PADMM-Warm reached mean qutrit and two-qubit fidelities of 0.63630.63630.6363 and 0.95410.95410.9541, respectively, while reducing total variation by factors of 13.213.213.2 and 10.710.710.7 relative to L-BFGS-B. These results define a reproducible fidelity--complexity trade-off, not a universal fidelity advantage. The method is therefore a numerical tool for exploring low-complexity control frontiers rather than a replacement for unconstrained high-fidelity solvers.
We present a variational quantum framework for finite-horizon quantum control based on hardware-efficient ansätze. The objective is to steer a quantum system from a given initial state to a desired target state over a fixed time horizon by minimizing a terminal cost defined in terms of state fidelity. Instead of explicitly synthesizing time-dependent control fields or enforcing Hamiltonian reachability constraints, the proposed method reformulates the control objective as a variational optimization problem in which a hardware-efficient parameterized quantum circuit provides a surrogate parameterization of the terminal evolution. The circuit consists of alternating layers of single-qubit rotations and entangling gates, whose parameters are optimized using classical routines to minimize the terminal infidelity. This formulation avoids reliance on problem-specific or physics-inspired ansätze, providing a flexible and implementation-friendly approach compatible with near-term quantum devices. Numerical experiments on multi-qubit state-transfer benchmarks demonstrate high-fidelity state transfer while highlighting the trade-off between ansatz expressivity, optimization complexity, and scalability with respect to system size and circuit depth.
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Quantum optimal control can produce fast and robust multi-qubit gates, but experimentally calibrating the resulting high-dimensional waveforms remains challenging because direct searches over large parameter spaces converge slowly. Building on the low-rank structure of quantum-control landscapes, we develop and benchmark a Hessian-based calibration method for optimal-control gates. The method identifies the few waveform directions that affect fidelity to leading order, with the number of directions set by the accessible leakage and coherent error channels, and optimizes only within this principal space using closed-loop experimental feedback. We apply this approach to an amplitude-robust controlled-Z gate on metastable-state 171Yb nuclear-spin qubits. Experimentally, we verify the predicted Hessian-sensitive directions and demonstrate rapid convergence of the optimization protocol. The optimized gate reaches a raw fidelity of 0.9959(2), increasing to 0.99902(7) after postselection on no detected loss, and the performance is essentially unchanged under laser-power variations of up to 20%. We further show that the same fidelity Hessian directions can correct certain Hamiltonian parameter errors. These results establish low-rank Hessian optimization as an efficient and physically motivated calibration strategy for high-dimensional optimal-control gates, which is broadly applicable to many qubit types.
Dynamic control via optimized, piecewise-constant pulses is a common paradigm for open-loop control to implement quantum gates. While numerous methods exist for the synthesis of such controls, there are many open questions regarding the robustness of the resulting control schemes in the presence of model uncertainty; unlike in classical control, there are generally no analytical guarantees on the control performance with respect to inexact modeling of the system. In this paper a new robustness measure based on the differential sensitivity of the gate fidelity error to parametric (structured) uncertainties is introduced, and bounds on the differential sensitivity to parametric uncertainties are used to establish performance guarantees for optimal controllers for a variety of quantum gate types, system sizes, and control implementations. Specifically, it is shown how a maximum allowable perturbation over a set of Hamiltonian uncertainties that guarantees a given fidelity error, can be reliably computed. This measure of robustness is inversely proportional to the upper bound on the differential sensitivity of the fidelity error evaluated under nominal operating conditions. Finally, the results show that the nominal fidelity error and differential sensitivity upper bound are positively correlated across a wide range of problems and control implementations, suggesting that in the high-fidelity control regime, rather than there being a trade-off between fidelity and robustness, higher nominal gate fidelities are positively correlated with increased robustness of the controls in the presence of parametric uncertainties.
High-fidelity quantum gates are essential for scalable quantum computation. However, at short durations, short-timescale waveform distortions break the time-reflection symmetry of control pulses, preventing the precise closure of cyclic evolution. This mechanism renders conventional symmetric protocols intrinsically over-constrained. Conventional strategies typically rely on smoothing the pulse envelopes or embedding the interaction pulse within a longer qubit pulse to bypass short-timescale distortions, which inevitably leads to a persistent speed-fidelity trade-off. To overcome this limitation, we introduce a cyclic control strategy based on parameter-space expansion, which restores controllability by incorporating an additional degree of freedom. We experimentally demonstrate this approach in a superconducting controlled-Z gate, achieving robust suppression of coherent errors without increasing gate duration, reducing the average coherent error from 0.27% to 0.12% across multiple two-qubit gates, as validated by cross-entropy benchmarking. Our results establish a general route to fast, high-fidelity cyclic quantum gates beyond the conventional speed-fidelity trade-off.
Achieving fast and high-fidelity qubit operations is crucial for unlocking the potential of quantum computers. In particular, reaching low gate errors in two-qubit gates has been a long-standing challenge in the field of superconducting qubits due to their typically long duration relative to coherence times. To realize fast gates, we use the hybridization between fixed-frequency superconducting qubits with a strongly interacting coupler mode that is tunable in frequency. To reduce population leakage during required adiabatic passages through avoided level crossings, we employ a sensitivity-adaptive closed-loop optimization method to design complex pulse shapes. We compare the performance of Gaussian-square, Fourier-series, and piecewise-constant-slope pulse parametrizations and are able to reach 99.9% controlled- Z -gate fidelity using a 64-ns-long Fourier-series pulse defined by only seven parameters. These high-fidelity values are achieved by analyzing the optimized pulse shapes to identify and systematically mitigate signal-line distortions in the experiment. To improve the convergence speed of the optimization, we implement an adaptive cost function, which continuously maximizes the sensitivity. The demonstrated method can be used for tune-up and recalibration of superconducting quantum processors.