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Advanced Science Letters

A Quantum Optimization Algorithm Based on Membrane Structure

Zhong Yanhua, Nie Shuzhi

Published Mar 15, 2012• 0 citations
Publisher
DOI
10.1166/asl.2012.2221

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This paper investigates the transformative potential of membrane quantum information theory, proposing a novel approach to quantum information storage and transmission leveraging the inherent self-organization properties of membranes. Traditional quantum information processing relies heavily on qubit manipulation, while membrane-based systems offer a fundamentally different paradigm. We explore a simulation-driven methodology to optimize the arrangement of quantum states within these membranes, revealing promising strategies for enhanced storage density and efficient information transfer. Furthermore, we delve into the potential applications of this architecture, extending beyond simple qubit storage to encompass complex quantum algorithms and data processing. The core claim centers around the demonstration of efficient quantum information manipulation within a membrane structure, highlighting a significant departure from existing approaches.
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We present a variational quantum algorithm that solves the one-dimensional diffusion problem with a space-dependent diffusion constant D(x)D(x)D(x). This problem is relevant for the exchange of hydroxide ions across a two-layer membrane in an alkaline electrolyzer, where the concentration of OH−^-− ion determines the chemical stability for longer time periods. We use 161616 to 646464 grid points across the membrane, resulting from n=4n=4n=4 to 666 data qubits for the ideal statevector and shot-based quantum simulations implemented using Qiskit. For these qubit numbers, the depth of the parametric quantum circuit has been chosen to ensure sufficient expressibility. The state preparation requires particular attention since the diffusivity DDD is piecewise constant in the different layers with discontinuities at the interface. Furthermore, we compare different classical optimization schemes with respect to their convergence in the VQA method. We demonstrate the applicability of the quantum algorithm to a problem with non-trivial boundary conditions and jump conditions of the diffusion constant and outline possible extensions of the proof-of-concept application case of quantum computing. Our simulations show that pronounced hydroxide ion concentration gradients, and thus chemical instabilities, can occur only when the ratio of diffusivity in both layers of the membrane exceeds approximately 50.