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Conference on Fully Actuated System Theory and Applications (FASTA)

Population Transfer in Quantum Systems Based on Fully Actuated System Approach

Jiaxiang Li, Huilong Xu, Zibo Miao

Published Jul 4, 2025• 0 citations
Publisher

Abstract

Quantum control, an interdisciplinary field combining quantum mechanics and control theory, provides essential tools for manipulating quantum systems in applications such as quantum information, computing, and communication. This paper proposes a novel control strategy for population transfer in quantum systems based on the Fully Actuated Systems (FAS) approach. The study focuses on finite-level open quantum systems, which exhibit intricate behaviors such as dissipation, decoherence, and non-Markovian dynamics due to interactions with their environments. Utilizing the Lindblad equation to describe the time evolution of the system's density matrix, we derive effective control laws for population transfer. Simulation experiments demonstrate the efficacy of the FAS method in achieving desired population transfers in both two-level and threelevel quantum systems, highlighting its potential for advancing quantum control strategies and enabling more precise manipulation of quantum states.

DOI
10.1109/fasta65681.2025.11138628

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Quantum control, an interdisciplinary field combining quantum mechanics and control theory, provides essential tools for manipulating quantum systems in applications such as quantum information, computing, and communication. This paper proposes a novel control strategy for population transfer in quantum systems based on the Fully Actuated Systems (FAS) approach. The study focuses on finite-level open quantum systems, which exhibit intricate behaviors such as dissipation, decoherence, and non-Markovian dynamics due to interactions with their environments. Utilizing the Lindblad equation to describe the time evolution of the system's density matrix, we derive effective control laws for population transfer. Simulation experiments demonstrate the efficacy of the FAS method in achieving desired population transfers in both two-level and threelevel quantum systems, highlighting its potential for advancing quantum control strategies and enabling more precise manipulation of quantum states.
Abstract Quantum control has achieved remarkable success in state transfer, trajectory tracking, and optimal control, yet a fundamental gap remains between trajectory generation and dynamics shaping. Unlike robotic and mechanical systems, where feedback design can directly prescribe transient behaviors such as convergence rates, damping, and robustness, most quantum control methods focus on identifying control fields that achieve a desired evolution without explicitly shaping the dynamics along that evolution. Here we bridge this gap by extending the fully actuated system (FAS) paradigm from classical control to finite-dimensional bilinear quantum systems. We show that controllability does not imply full actuation in quantum dynamics: the Lie-group structure of quantum evolution generally prevents a controllable quantum system from being represented as a FAS. To overcome this limitation, we introduce virtual quantum measurements and construct a local partial FAS representation in the output space, where the highest-order output derivatives are directly assignable by the control Hamiltonians. This representation enables explicit cancellation of nonlinear input–output dynamics and provides a constructive framework for quantum dynamics shaping. The resulting closed-loop behavior can be prescribed through arbitrary pole placement or fixed-time convergence with preassigned settling-time bounds. We further develop an offline closed-loop emulation procedure that converts the feedback law into implementable open-loop control waveforms. Numerical studies on single-qubit and two-qubit systems demonstrate accurate trajectory tracking, fixed-time convergence, prescribed gate-error decay quantified by average gate fidelity, and tunable trade-offs among convergence speed, robustness, and control effort.
There has long been interest to control the transfer of population between specified quantum states. Recent work has optimized the control law for closed system population transfer by using a gradient ascent pulse engineer- ing algorithm [1]. Here, a spin-boson model consisting of two-level atoms which interact with the dissipative environment, is investigated. With opti- mal control, the quantum system can invert the populations of the quantum logic states. The temperature plays an important role in controlling popula- tion transfer. At low temperatures the control has active performance, while at high temperatures it has less erect. We also analyze the decoherence be- havior of open quantum systems with optimal population transfer control, and we find that these controls can prolong the coherence time. We hope that active optimal control can help quantum solid-state-based engineering.
The weak-coupled two-level open quantum system described by non-Markovian time-convolution-less master equation is investigated in this paper. Based on the Lyapunov stability theorem, the system control laws used to transfer state are designed. The characteristics of the purity changes in the non-Markovian open quantum systems are studied. The effectiveness of the control system is ensured by adjusting the parameters of control laws. Three simulation experiments are implemented under the Matlab environment, they are the states transfer from the eigenstate to the superposition state, from the superposition state to the superposition state, and from the mixed state to the superposition state, respectively. Numerical experimental results show that the target state can be reached from different initial states under the action of the control laws designed, and demonstrate the effectiveness of quantum Lyapunov control method proposed.
The weak-coupled two-level open quantum system described by non-Markovian Time-convolution-less master equation is investigated in this paper. The cut-off frequency, coupling constant and transition frequency, which impact on the system's decay rate, coherence factor and purity, are investigated. The appropriate parameters used in system simulation experiments are determined by comparing analysis results of different values of parameters for the effects of system performance. The control laws used to transfer the system states are designed on the basis of the Lyapunov stability theorem. Numerical simulation experiments are implemented under the MATLAB environment. The features of the free evolution trajectory of the non-Markovian systems and the states transfer from a pure state to a desired pure state under the action of the proposed control laws are studied, respectively. By comparing the experimental results, the effectiveness of the proposed quantum Lyapunov control method applied to the state transfer in non-Markovian open quantum systems is verified. Meanwhile, the influences of different control parameters and cut-off frequencies on the system performance are analyzed.
In order to solve the state of an open quantum system with relaxation and dissipation,the dynamical equation of the system in matrix was transformed into vector form in Liouville space. Taking the expectation value for the state under control reaching the target state as performance indicators,an optimal control function was derived for the system transformed. The control a 2-level open quantum system was simulated on in MATLAB. The influence to population transfer probability and control time caused by changing of parameters were analysed contrastively.
Conventional manipulations over quantum systems for, such as coherent population trapping and unidirectional transfer, focus on Hamiltonian engineering while regarding the system's manifold geometry and constraint equation as secondary causes. Here, we treat them on equal footing in controlling a finite-dimensional quantum system under a time-dependent non-Hermitian Hamiltonian, which is inspired by the D'Alembert principle of regarding active force, constraint force, and inertial force in an unbiased way. Under the biorthogonal condition, the non-Hermitian Hamiltonian could be triangularized in a constraint picture spanned by a set of completed and orthonormal basis states, which is found to be a sufficient condition to construct at least one universal nonadiabatic passage in both bra and ket spaces. The passage ends up with a desired target state that is automatically normalized without artificial normalization in the existing treatments for non-Hermitian quantum systems. Moreover, the passage is found to be robust against the parametric deviation when the real part of its global phase is rapidly varying with time. Our protocol is explicitly verified for the perfect population transfer in the two-level system and the chiral population transfer in the three-level system. It generalizes our framework of universal quantum control to the field of the biorthogonal quantum mechanics.