Towards Quantum Computational Mechanics

Abstract

The rapid advancements in quantum computing as ushered in a new era for computer simulations, presenting groundbreaking opportunities across diverse disciplines. Central to this revolution is the quantum processor's capacity to entangle qubits, unlocking unprecedented possibilities for addressing computational challenges on an extreme scale, far beyond the reach of classical computing. In this study, we explore how quantum computing can be employed to enhance computational mechanics. Our focus is on the analysis of Representative Volume Element (RVE) within the framework of multiscale solid mechanics. We introduce an innovative quantum algorithm designed to solve the RVE problem. This algorithm is capable of compute RVEs of discretization size N in 𝒪(Poly log(N)) time, thus achieving an exponential speed-up over traditional classical computing approaches that typically scales linearly with N. We validate our approach with case studies including the solution of one and two dimensional Poisson's equation, as well as an RVE of a composite bar with piece-wise constant phases. We provide quantum circuit designs that requires only 𝒪(Poly log(N)) universal quantum gates,underscoring the efficiency of our approach. Our work suggests a major way in which quantum computing can be combined with and brought to bear on computational mechanics.

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