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arXiv:2306.03233

Unified Information Dynamic Analysis of Quantum Decision-Making and Search Algorithms: Computational Intelligence Measure

Sergey Victorovich Ulyanov, Fabio Ghisi, I. Kurawaki, V.S. Ulyanov

Published May 30, 2023• 0 citations

Abstract

There are important algorithms built upon a mixture of basic techniques described; for example, the Fast Fourier Transform (FFT) employs both Divide-and-Conquer and Transform-and-Conquer techniques. In this article, the evolution of a quantum algorithm (QA) is examined from an information theory viewpoint. The complex vector entering the quantum algorithmic gate - QAG is considered as an information source both from the classical and the quantum level. The analysis of the classical and quantum information flow in Deutsch-Jozsa, Shor and Grover algorithms is used. It is shown that QAG, based on superposition of states, quantum entanglement and interference, when acting on the input vector, stores information into the system state, minimizing the gap between classical Shannon entropy and quantum von Neumann entropy. Minimizing of the gap between Shannon and von Neumann entropies is considered as a termination criterion of QA computational intelligence measure.

DOI: 10.48550/arxiv.2306.03233

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Shor algorithm dynamics of quantum computation states are analysed from the classical and the quantum information theory points of view. The Shannon entropy is interpreted as the degree of information accessibility through measurement, while the von Neumann entropy is employed to measure the quantum information of entanglement. The intelligence of a state with respect to a subset of qubits is defined. The intelligence of a state is maximal if the gap between the Shannon and the von Neumann entropy for the chosen result qubits is minimal. We prove that the quantum Fourier transform creates maximally intelligent states with respect to the first n qubits for Shor's problem, since it annihilates the gap between the classical and quantum entropies for the first n qubits of every output state.

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