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
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
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.
Quantum mechanics, though a probabilistic theory, gives a 'deterministic' answer to the question of how the present determines the future. In essence, in order to predict future probabilities, we need to (numerically) propagate the time-dependent Schrödinger equation from the present to the future. It is interesting to note that classical mechanics of macroscopic bodies, though reputed to be a deterministic theory, does not allow, due to chaos (which unfortunately is more prevalent than integrability), such clear insights into the future. In contrast, small (e.g., atomic, molecular and photonic) systems which are best understood using the tools of quantum mechanics, do not suffer from chaos, rendering the prediction of the probability-distributions of future events possible. The field of quantum control deals with an important modification of this task, namely, it asks: given a wave function in the present, what dynamics, i.e. what Hamiltonian, guarantees a desired outcome or 'objective' in the future? In practice one may achieve this goal of modifying and finding the desired Hamiltonian by introducing external fields, e.g. laser light. It is then possible to reach the objective in a 'trial-and-error' fashion, performed either numerically or in the laboratory. We can guess or build a Hamiltonian, do an experiment, or propagate the initial wave function to the future, compare the result with the desirable objective, and correct the guess for the Hamiltonian until satisfactory agreement with the objective is reached. A systematic way of executing this procedure is the sub-field called 'optimal control'. The trial-and-error method is often very time consuming and rarely provides mechanistic insight. There are situations where analytical solutions exist, rendering the control strategies more transparent. This is especially so when one can identify quantum interferences as the heart of quantum control, the essence of the field called 'coherent control'. The experience accumulated so far by many groups is that quantum interferences are the mechanism underlying most successful control scenarios and control experiments. The identification of the control mechanism is especially facile when the time-dependence of the Hamiltonian merely serves to prepare a state which then evolves in the absence of external fields. Analytical theories also exist when the explicit time dependence of the Hamiltonian can be treated adiabatically. Under these circumstances one can identify the quantum interfering pathways that lead to control, allowing for the simultaneous exploration of entire 'landscapes' (and not just a single 'desirable' objective) resulting from varying all the experimental 'knobs' at our disposal, e.g., relative- and envelope-phases, intensities, polarizations, and pulse-sequencing. Such 'pulse-shaping' knobs are now available down to the sub-femtosecond regime in broad spectral regions ranging from the UV to the IR. We expect that comprehensive investigations of the quantum interference required to control dynamical processes will result in a more detailed understanding of the dynamics themselves. Together with experimental progress---the stage is now set for many exciting applications in fundamental and applied sciences by 'tailoring' light--matter interactions essentially at will.
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.