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arXiv:2510.15340 · npj Quantum Information

Singularity-free dynamical invariants-based quantum control

Ritik Sareen, Akram Youssry, Alberto Peruzzo

Published Aug 5, 2026• 0 citations

Abstract

Abstract State preparation is a cornerstone of quantum technologies, underpinning applications in computation, communication, and sensing. Its importance becomes even more pronounced in non-Markovian open quantum systems, where environmental memory and model uncertainties pose significant challenges to achieving high-fidelity control. Invariant-based inverse engineering provides a principled framework for synthesizing analytic control fields, yet existing parameterizations often lead to experimentally infeasible, singular pulses and are limited to simplified noise models such as those of Lindblad form. Here, we introduce a generalized invariant-based protocol for finite-dimensional state preparation under arbitrary noise conditions. We transform the finite-dimensional control problem into the equivalent problem for a single-qubit, by restricting the dynamics to a designed SU(2) subspace. The control protocol then proceeds in two-stages: first, we construct a family of bounded pulses that achieve perfect state preparation in a closed system; second, we identify the optimal member of this family that minimizes the effect of noise. The framework accommodates both (i) characterized noise, enabling noise-aware control synthesis, and (ii) uncharacterized noise, where a noise-agnostic variant preserves robustness without requiring a master-equation description. Numerical simulations demonstrate high-fidelity state preparation across diverse targets while producing smooth, hardware-feasible control fields. This singularity-free framework extends invariant-based control to realistic open-system regimes, providing a versatile route toward robust quantum state engineering on NISQ hardware and other platforms exhibiting non-Markovian dynamics.

DOI: 10.1038/s41534-026-01343-7

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Abstract State preparation is a cornerstone of quantum technologies, underpinning applications in computation, communication, and sensing. Its importance becomes even more pronounced in non-Markovian open quantum systems, where environmental memory and model uncertainties pose significant challenges to achieving high-fidelity control. Invariant-based inverse engineering provides a principled framework for synthesizing analytic control fields, yet existing parameterizations often lead to experimentally infeasible, singular pulses and are limited to simplified noise models such as those of Lindblad form. Here, we introduce a generalized invariant-based protocol for finite-dimensional state preparation under arbitrary noise conditions. We transform the finite-dimensional control problem into the equivalent problem for a single-qubit, by restricting the dynamics to a designed SU(2) subspace. The control protocol then proceeds in two-stages: first, we construct a family of bounded pulses that achieve perfect state preparation in a closed system; second, we identify the optimal member of this family that minimizes the effect of noise. The framework accommodates both (i) characterized noise, enabling noise-aware control synthesis, and (ii) uncharacterized noise, where a noise-agnostic variant preserves robustness without requiring a master-equation description. Numerical simulations demonstrate high-fidelity state preparation across diverse targets while producing smooth, hardware-feasible control fields. This singularity-free framework extends invariant-based control to realistic open-system regimes, providing a versatile route toward robust quantum state engineering on NISQ hardware and other platforms exhibiting non-Markovian dynamics.

Mitigating noise-induced decoherence is the central challenge in controlling open quantum systems. While existing robust protocols often require precise noise models, we introduce a universal framework for noise-agnostic quantum control that achieves high-fidelity operations without prior environmental noise characterization. This framework capitalizes on the dynamical modification of the system-environment coupling through control drives, an effect rigorously encoded in the dynamical equation. Since the derived noise sensitivity metric remains independent of the coupling details between the system and the environment, our protocol demonstrates robustness against arbitrary Markovian noises within the first-order weak coupling approximation. Numerical validation through quantum state transfer and gate operations reveals near-unity fidelity across diverse noise regimes, achieving orders-of-magnitude error suppression compared to target-only approaches. This framework bridges critical gaps between theoretical control design and experimental constraints, establishing a broadly applicable strategy for high-fidelity quantum information processing across platforms such as superconducting circuits, trapped ions, and solid-state qubits.

We introduce a method for designing smooth single-qubit control pulses that implement a desired gate while suppressing the effect of unknown static error sources to first order. Unlike dynamically corrected gate constructions that require prior knowledge of the noise model, the present approach is agnostic to the detailed form of the target-bath interaction. The method parametrizes the control propagator through an auxiliary matrix expansion over orthogonal basis functions and enforces decoupling through algebraic orthogonality and equal-norm constraints on the expansion coefficients. These conditions guarantee that the leading Magnus contribution of an arbitrary static interaction reduces to a term proportional to the identity on the target system, thereby cancelling first-order error effects independently of the microscopic origin of the noise. We further show that the same construction suppresses, to first order, mediated couplings between simultaneously controlled qubits when their interaction occurs through intermediate environmental degrees of freedom, yielding effective second-order decoupling of the induced inter-qubit interaction. By using a discrete cosine transform parametrization, the pulse-synthesis problem is cast into a numerically stable constrained optimization with a minimal number of free parameters. Numerical examples for

R_z

rotations and random single-qubit unitaries demonstrate smooth control fields that realize the target gates while remaining robust against arbitrary static single-qubit noise and mediated multi-qubit couplings. These results provide a hardware-friendly route toward noise-agnostic dynamically corrected single-qubit gates.

ABSTRACT Controlling quantum systems in the presence of environmental noise presents significant challenges, primarily because the dissipative dynamics intricately depend on the control fields applied. To address this issue, we introduce a versatile and efficient framework based on dynamical invariants, enabling the analytical design of time‐dependent Hamiltonians tailored for optimal operation in noisy, dissipative environments. By employing a master equation featuring explicitly time‐dependent Lindblad generators, our reverse‐engineering approach allows precise manipulation of state dynamics without expensive iterative state propagation. This method dynamically constructs an effective decoherence‐free subspace, confining the system to a minimally noisy region within the Hilbert space. We illustrate the effectiveness of our technique using two paradigmatic examples: a driven two‐level system and a harmonic oscillator, both coupled to thermal baths. In each case, we achieve substantial fidelity improvements compared to conventional methods, highlighting the robustness and potential of our approach for reliable quantum control in open quantum systems.

Abstract Intrinsic noise in pre-fault-tolerant quantum devices poses a major challenge to the reliable realization of unitary dynamics in quantum algorithms and simulations. To address this, we present a method for simulating open quantum system dynamics on a quantum computer, including negative dissipation rates in the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) master equation. Our approach lies beyond the standard Markovian approximation, enabling the controlled study of non-Markovian processes within a quantum simulation framework. Using this method, we develop a quantum algorithm for calculating ground-state properties that exploits feedback-controlled, noise-assisted dynamics. In this scheme, Lyapunov-based feedback steers the system toward a target virtual state under engineered noise conditions. While noisy simulations typically fail to converge and degrade in performance as noise accumulates over time, our method exhibits improved convergence, albeit with an increased exponential sampling overhead. This framework offers a promising strategy for harnessing current quantum hardware and advancing robust control protocols based on open-system dynamics.

Creating robust quantum operations is a major challenge in the current noisy intermediate-scale quantum computing era. Recently, the importance of noise-resilient control methods has become more pronounced in the field. Ordinarily, noisy quantum systems are described by the Lindblad equation. However, minimizing noise susceptibility using this equation has proven challenging because of its irreversibility. In this study, we propose a method for creating robust pulses based on the stochastic Schr\"odinger equation. This equation describes individual noise realizations under any colored noise process, contrary to the Lindblad equation, which describes mean system behavior under white noise. Using stochastic optimal control techniques, our method, fidelity-enhanced variational quantum optimal control, is able to construct higher-fidelity paths than its nonstochastic counterpart. By accounting for both environmental noise sources as well as noise sources inherent to the control system, highly significant increases in fidelity are noted for both single- and multiple-qubit state preparations.

Dynamically corrected gates are extended to non-Markovian open quantum systems where limitations on the available controls and/or the presence of control noise make existing analytical approaches unfeasible. A computational framework for the synthesis of dynamically corrected gates is formalized that allows sensitivity against non-Markovian decoherence and control errors to be perturbatively minimized via numerical search, resulting in robust gate implementations. Explicit sequences for achieving universal high-fidelity control in a singlet-triplet spin qubit subject to realistic system and control constraint are provided, which simultaneously cancel to the leading order the dephasing due to non-Markovian nuclear-bath dynamics and voltage noise affecting the control fields. Substantially improved gate fidelities are predicted for current laboratory devices.