Fourier space readout method for efficiently recovering functions encoded in quantum states

TL;DR

This paper introduces a hybrid Fourier space readout method that efficiently extracts function values from quantum states, maintaining quantum speedups in computer-aided engineering applications.

Contribution

It presents a novel quantum-classical hybrid approach with explicit circuits and analyzes its complexity, showing preserved quantum advantages during readout.

Findings

Quantum complexity scales logarithmically with grid size.

Classical complexity scales linearly with target points.

Quantum speedups are maintained during solution readout.

Abstract

Applying quantum computing in the computer-aided engineering (CAE) problems are highly expected since quantum computers yield potential exponential speedups for the operations between extremely large matrices and vectors. Although efficient quantum algorithms for the above problems have been intensively investigated, it remains a crucial task to extract all the grid-point values encoded in the prepared quantum states, which was believed to eliminate the achieved quantum advantage. In this paper, we propose a quantum-classical hybrid Fourier space readout (FSR) method to efficiently recover the underlying function from its corresponding quantum state. We provide explicit quantum circuits, followed by theoretical and numerical discussions on its complexity. In particular, the complexity on quantum computers has only a logarithmic dependence on the grid number, while the complexity on classical computers has a linear dependence on the number of target points instead of the grid number. Our result implies that the achieved quantum speedups are not necessarily ruined when we read out the solutions to the CAE problems.