Efficient quantum circuits for Toeplitz and Hankel matrices

TL;DR

This paper demonstrates that quantum circuits can efficiently implement sparse and Fourier-sparse Toeplitz and Hankel matrices, enabling quantum solutions for physical problems with these symmetries using deterministic queries.

Contribution

It introduces methods for efficient quantum circuit implementation of sparse and Fourier-sparse Toeplitz and Hankel matrices, advancing quantum algorithms for structured matrix problems.

Findings

Quantum circuits can implement sparse Toeplitz matrices efficiently.

Quantum circuits can implement Fourier-sparse Hankel matrices efficiently.

Enables quantum solutions for physical problems with Toeplitz or Hankel symmetry.

Abstract

Toeplitz and Hankel matrices have been a subject of intense interest in a wide range of science and engineering related applications. In this paper, we show that quantum circuits can efficiently implement sparse or Fourier-sparse Toeplitz and Hankel matrices. This provides an essential ingredient for solving many physical problems with Toeplitz or Hankel symmetry in the quantum setting with deterministic queries.