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Annals of Physics

Probabilistic pathways: New frontiers in quantum ensemble control

Abdessamad Belfakir, Randa Herzallah

Published Jul 29, 2025• 0 citations
Publisher

Abstract

In this paper, we propose a novel probabilistic control framework for efficiently controlling an ensemble of quantum systems that can also compensate for the interaction of the systems with the external environment. The main challenge in this problem is to simultaneously steer an ensemble of systems with variation in their internal parameters from an initial state to a desired final state. The minimisation of the discrepancy between the probabilistic description of the dynamics of a quantum ensemble and a predefined desired probabilistic description is the key step in the proposed framework. With this objective, the derived solution will not only allow the transitioning of the ensemble from one state to another, but will generally allow steering an initial distribution of the ensemble to a final distribution. Numerical results are presented, demonstrating the effectiveness of the proposed probabilistic control framework.

DOI
10.1016/j.aop.2025.170158

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In this paper, we propose a novel probabilistic control framework for efficiently controlling an ensemble of quantum systems that can also compensate for the interaction of the systems with the external environment. The main challenge in this problem is to simultaneously steer an ensemble of systems with variation in their internal parameters from an initial state to a desired final state. The minimisation of the discrepancy between the probabilistic description of the dynamics of a quantum ensemble and a predefined desired probabilistic description is the key step in the proposed framework. With this objective, the derived solution will not only allow the transitioning of the ensemble from one state to another, but will generally allow steering an initial distribution of the ensemble to a final distribution. Numerical results are presented, demonstrating the effectiveness of the proposed probabilistic control framework.
In this paper, we propose a novel probabilistic control framework for efficiently controlling an ensemble of quantum systems that can also compensate for the interaction of the systems with the external environment. The main challenge in this problem is to simultaneously steer an ensemble of systems with variation in their internal parameters from an initial state to a desired final state. The minimisation of the discrepancy between the probabilistic description of the dynamics of a quantum ensemble and a predefined desired probabilistic description is the key step in the proposed framework. With this objective, the derived solution will not only allow the transitioning of the ensemble from one state to another, but will generally allow steering an initial distribution of the ensemble to a final distribution. Numerical results are presented, demonstrating the effectiveness of the proposed probabilistic control framework.
A new control method that considers all sources of uncertainty and noises that might affect the time evolutions of quantum physical systems is introduced. Under the proposed approach, the dynamics of quantum systems are characterised by probability density functions (pdfs), thus providing a complete description of their time evolution. Using this probabilistic description, the proposed method suggests the minimisation of the distance between the actual pdf that describes the joint distribution of the time evolution of the quantum system and the external electric field, and the desired pdf that describes the system target outcome. We start by providing the control solution for quantum systems that are characterised by arbitrary pdfs. The obtained solution is then applied to quantum physical systems characterised by Gaussian pdfs and the form of the optimised controller is elaborated. Finally, the proposed approach is demonstrated on a real molecular system and two spin systems showing the effectiveness and simplicity of the method.
A new control method that considers all sources of uncertainty and noises that might affect the time evolutions of quantum physical systems is introduced. Under the proposed approach, the dynamics of quantum systems are characterised by probability density functions (pdfs), thus providing a complete description of their time evolution. Using this probabilistic description, the proposed method suggests the minimisation of the distance between the actual pdf that describes the joint distribution of the time evolution of the quantum system and the external electric field, and the desired pdf that describes the system target outcome. We start by providing the control solution for quantum systems that are characterised by arbitrary pdfs. The obtained solution is then applied to quantum physical systems characterised by Gaussian pdfs and the form of the optimised controller is elaborated. Finally, the proposed approach is demonstrated on a real molecular system and two spin systems showing the effectiveness and simplicity of the method.
A new control method that considers all sources of uncertainty and noises that might affect the time evolutions of quantum physical systems is introduced. Under the proposed approach, the dynamics of quantum systems are characterised by probability density functions (pdfs), thus providing a complete description of their time evolution. Using this probabilistic description, the proposed method suggests the minimisation of the distance between the actual pdf that describes the joint distribution of the time evolution of the quantum system and the external electric field, and the desired pdf that describes the system target outcome. We start by providing the control solution for quantum systems that are characterised by arbitrary pdfs. The obtained solution is then applied to quantum physical systems characterised by Gaussian pdfs and the form of the optimised controller is elaborated. Finally, the proposed approach is demonstrated on a real molecular system and two spin systems showing the effectiveness and simplicity of the method.
Abstract This study introduces an innovative control methodology designed specifically for quantum physical systems. It bridges a critical gap by accounting for the full spectrum of uncertainties and noise that could affect the time evolution of these systems. In contrast to conventional methods, our pioneering approach utilizes probability density functions (pdfs) to characterize quantum dynamics, providing a more detailed and accurate description of their temporal behavior. We propose a strategy that seeks to minimize the discrepancy between the actual pdf, which encapsulates the combined dynamics of the quantum system and an external electric field, and a desired pdf that aligns with the system’s intended outcomes. This strategy marks a significant shift from traditional quantum control techniques. Initially, we present a solution for controlling quantum systems defined by general pdfs. This solution is then demonstrated on quantum systems described by Gaussian pdfs, with an in-depth account of the resulting optimized controller’s structure. The study culminates with practical demonstrations, showcasing the approach’s efficacy and practicality, thus endorsing its potential as a formidable instrument in quantum control. Graphical abstract
This paper considers the optimal control of quantum systems. The controlled quantum systems are described by the probability-density-matrix-based Liouville–von Neumann equation. Using projection operators, the states of the quantum system are decomposed into two sub-spaces, namely the 'main state' space and the 'remaining state' space. Since the control energy is limited, a solution for optimizing the external control force is proposed in which the main state is brought to the desired main state at a certain target time, while the population of the remaining state is simultaneously suppressed in order to diminish its effects on the final population of the main state. The optimization problem is formulated by maximizing a general cost functional of states and control force. An efficient algorithm is developed to solve the optimization problem. Finally, using the hydrogen fluoride (HF) molecular population transfer problem as an illustrative example, the effectiveness of the proposed scheme for a quantum system initially in a mixed state or in a pure state is investigated through numerical simulations.