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International Journal of Modern Physics B

PROBABILITY DENSITY FUNCTION CONTROL OF QUANTUM SYSTEMS

Yifan Xing, Jun Yong Wu

Published Jun 9, 2011• 2 citations
Publisher

Abstract

This paper proposes a new method of controlling quantum systems via probability density function (PDF) control. Based on the quantum model from the PDF perspective, two specific control algorithms are proposed for the general case and limited input energy, respectively. Unlike traditional quantum control methods, this method directly controls the probability distribution of the quantum state. It provides an alternative method for quantum control engineering.

DOI
10.1142/s0217979211101089

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This paper proposes a new method of controlling quantum systems via probability density function (PDF) control. Based on the quantum model from the PDF perspective, two specific control algorithms are proposed for the general case and limited input energy, respectively. Unlike traditional quantum control methods, this method directly controls the probability distribution of the quantum state. It provides an alternative method for quantum control engineering.
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
Signal processing techniques will lean on blind methods in the near future, where no redundant, resource allocating information will be transmitted through the channel. To achieve a proper decision, however, it is essential to know at least the probability density function (PDF), which to estimate is classically a time consumpting and/or less accurate hard task that may make decisions to fail. This paper describes the design of a quantum assisted PDF estimation method also by way of an example, which promises to achieve the exact PDF by proper setting of parameters in a very rapid way.
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.
This paper explores the potential of quantum computing for probability density estimation (PDE), a crucial component of many machine learning algorithms. Traditional PDE methods often struggle with high-dimensional data, leading to computational bottlenecks and potentially inaccurate estimates. We propose a novel approach leveraging quantum circuits to perform PDE, capitalizing on quantum phenomena like superposition and entanglement to accelerate and potentially enhance the estimation process. Specifically, we outline a quantum algorithm designed to approximate probability density functions (PDFs) directly from data samples. The core of our approach involves encoding data into a quantum state and utilizing quantum gates to perform calculations related to the PDF. Furthermore, we address the challenges of noise inherent in quantum systems through the integration of quantum error correction techniques. This work lays the theoretical groundwork for a quantum-enhanced PDE method, demonstrating the feasibility of significantly improving estimation speed and accuracy for complex datasets. We focus on the conceptual design and potential benefits of this approach, without performing actual experimental validation.