S&W: International Workshop “Basic Principles of Quantum Computational Mechanics”
Fehmi Cirak, h 11:00-12-00:
Design and modeling of shape-programmable structures – 2/2
This second lecture illustrates a quantum RVE solver that combines conventional algorithms such as a fixed-point iteration for a homogeneous reference material and the Fast Fourier Transform (FFT). However, the quantum computing reformulation of these algorithms requires a fundamental paradigm shift and a complete rethinking and overhaul of the classical implementation. We employ or develop several techniques, including the Quantum Fourier Transform (QFT), quantum encoding of polynomials, classical piecewise Chebyshev approximation of functions and an auxiliary algorithm for implementing the fixed-point iteration and show that, indeed, an efficient implementation of RVE solvers on quantum computers is possible. We additionally provide theoretical proofs and numerical evidence confirming the anticipated O(log N)c complexity of the proposed solver
