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arXiv:2311.13164 · Advanced Quantum Technologies

Control of Open Quantum Systems via Dynamical Invariants

Loris Maria Cangemi, Hilario Espinós, Ricardo Puebla, E. Torrontegui, Amikam Levy

Published Feb 1, 2026• 2 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1002/qute.202500798

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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.
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Quantum systems are inherently sensitive to environmental noise and imperfections in external control fields, which pose a significant challenge for the practical implementation of quantum technologies. These noise sources degrade the fidelity of quantum gates, making their mitigation a key requirement for realizing reliable quantum computing. In this study, we apply Optimal Control Theory (OCT) within a thermodynamically consistent Markovian framework to design high-fidelity quantum gates in the presence of thermal relaxation. Such a description is essential for realistic modeling and optimization of noisy quantum gates in near-term quantum technologies, where strong control fields and thermal environments act simultaneously. Our approach combines OCT with a control-dependent dissipative generator derived from the non-adiabatic master equation framework based on time-dependent invariants of the free evolution. As a result, the driving fields modify both the unitary and dissipative parts of the evolution. We implement the scheme for one- and two-qubit gates embedded in larger Hilbert spaces and compare direct-control and ancilla-assisted architectures. Using logical-subspace-resolved diagnostics, we quantify how the optimized dynamics redistributes the dissipative action between logical and ancillary sectors in the model systems studied here. In particular, we show that ancilla-assisted control can reduce the effective thermal-noise burden on the logical subspace in the relevant parameter regime, while direct control remains the most effective route when available. High-precision propagation of the full open-system dynamics reveals substantial fidelity improvements, in some cases by orders of magnitude, while clarifying the limits of mitigation at large relaxation rates and temperatures.
We develop a novel framework to engineer persistent oscillatory modes in Markovian open quantum systems governed by a time-independent Lindblad master equation. We show that oscillatory modes can be created when the Hamiltonian and jump operator can be expressed in the same block-diagonal form. A key feature of the framework is that the dissipator of the Lindblad master equation are generally non-zero. We identify the weak and strong conditions, where the onset of the oscillatory modes is dependent and independent of the parameters of the system, respectively. Our method extends beyond the typical decoherence-free subspace approach, in which the dissipator is zero. We demonstrate the applicability of this framework using various models, showing how carefully tailored system-environment interactions can produce sustained coherent oscillations.
An important issue in developing quantum technology is that quantum states are so sensitive to noise. We propose a protocol that introduces reverse dynamics, in order to precisely control quantum systems against noise described by the Lindblad master equation. The reverse dynamics can be obtained by constructing the Petz recovery map in continuous time. By providing the exact form of the Hamiltonian and jump operators for the reverse dynamics, we explore the potential of utilizing the near-optimal recovery of the Petz map in controlling noisy quantum dynamics. While time-dependent dissipation engineering enables us to fully recover a single quantum trajectory, we also design a time-independent recovery protocol to protect encoded quantum information against decoherence. Our protocol can efficiently suppress only the noise part of dynamics thereby providing an effective unitary evolution of the quantum system.
Abstract We propose using the dynamical invariants, also known as the Lewis–Riesenfeld invariants, to speed-up the equilibration of a driven open quantum system. This allows us to reverse engineer the time-dependent master equation that describes the dynamics of the open quantum system and systematically derive a protocol that realizes a shortcut to equilibration. The method does not require additional constraints on the timescale of the dynamics beside the Born–Markov approximation and can be generically applied to boost single particle quantum engines significantly. We demonstrate this with the damped harmonic oscillator, and show that our protocol can achieve high-fidelity control on shorter timescales than simple non-optimized protocols. We find that the system is heated during the dynamics to speed-up the equilibration, which can be considered as an analogue of the Mpemba effect in quantum control.
Fast and reliable manipulation with qubits is fundamental for any quantum technology. The implementation of these manipulations in physical systems is the focus of studies involving optimal control theory. Realistic physical devices are open quantum systems. So far, studies in optimal control theory have primarily utilized the Redfield/Lindblad quantum master equation to simulate the dynamics of such systems. However, this Markov description is not always sufficient. Here, we present a study of qubit control utilizing the nonequilibrium Green's function method. We compare the traditional master equation with more general Green's function results and demonstrate that even in the parameter regime suitable for the application of the Redfield/Lindblad approach, the two methods yield drastically different results when addressing evolution involving mixed states. In particular, we find that, in addition to predicting different optimal driving profiles, a more accurate description of system evolution enables the system to reach the desired final state much more quickly. We argue that the primary reason for this is the significance of the non-Markov description of driven system dynamics due to the effect of time-dependent driving on dissipation.