A report discusses an algorithm for a new kind of dynamics based on a quantum-classical hybrid-quantum-inspired maximizer. The model is represented by a modified Madelung equation in which the quantum potential is replaced by different, specially chosen "computational" potential. As a result, the dynamics attains both quantum and classical properties: it preserves superposition and entanglement of random solutions, while allowing one to measure its state variables, using classical methods. Such optimal combination of characteristics is a perfect match for quantum-inspired computing. As an application, an algorithm for global maximum of an arbitrary integrable function is proposed. The idea of the proposed algorithm is very simple: based upon the Quantum-inspired Maximizer (QIM), introduce a positive function to be maximized as the probability density to which the solution is attracted. Then the larger value of this function will have the higher probability to appear.
Special attention is paid to simulation of integer programming and NP- complete problems. It is demonstrated that the problem of global maximum of an integrable function can be found in polynomial time by using the proposed quantum-classical hybrid. The result is extended to a constrained maximum with applications to integer programming and TSP (Traveling Salesman Problem).
This work was done by Michail Zak of Caltech for NASA's Jet Propulsion Laboratory.
NPO-45458
This Brief includes a Technical Support Package (TSP).
Quantum-Inspired Maximizer
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Overview
The document is a Technical Support Package from NASA's Jet Propulsion Laboratory (JPL) detailing a Quantum-Inspired Maximizer, identified by the reference NPO-45458. It discusses a novel algorithm aimed at solving complex optimization problems, particularly those that are traditionally intractable due to their exponential growth in computational time with increasing dimensionality.
The core focus of the document is on the challenges associated with finding global maxima of multi-dimensional functions, a problem that has persisted in computational theory. The proposed maximizer addresses the limitations of classical optimization methods, which often struggle with local maxima. By leveraging principles from quantum information theory, the algorithm is designed to enhance the efficiency of finding solutions to these hard problems.
The document outlines the mathematical framework underpinning the maximizer, including equations that describe the system's dynamics. It highlights the significance of the quantum potential, which differentiates the proposed model from classical mechanics. The model maintains the topology of the Madelung equation, linking the flow of probability density to the action of particles, while introducing a computational potential that facilitates efficient information processing.
The document emphasizes the importance of analog computing in overcoming the "curse" of combinatorial explosion, suggesting that direct simulation of physical phenomena can significantly reduce computational complexity. This approach contrasts with traditional digital computing, which relies on symbolic manipulation of numbers.
In addition to the theoretical aspects, the document serves as a resource for further research and technology development in the field of optimization. It provides contact information for the Innovative Technology Assets Management at JPL for those interested in exploring the implications of this research further.
Overall, the Technical Support Package presents a significant advancement in the quest to solve complex optimization problems, showcasing the potential of quantum-inspired algorithms to revolutionize computational methods in various scientific and engineering applications. The insights provided could have broader implications beyond aerospace, influencing fields that require efficient problem-solving techniques.
