Jacobi-Anger Density Estimation for Energy Distribution of Quantum States

TL;DR

This paper introduces JADE, a quantum-inspired method that reconstructs energy distributions of quantum states from limited moments, enabling more efficient ground state energy estimation in quantum computing.

Contribution

JADE is a novel non-parametric technique using Jacobi-Anger expansion to accurately estimate quantum energy distributions from few moments.

Findings

JADE accurately recovers energy distributions in molecular systems.

JADE is applicable to complex probability density estimation in various fields.

The method enhances quantum ground state energy estimation efficiency.

Abstract

The energy distribution of a quantum state is essential for accurately estimating a molecule's ground state energy in quantum computing. Directly obtaining this distribution requires full Hamiltonian diagonalization, which is computationally prohibitive for large-scale systems. A more practical strategy is to approximate the distribution from a finite set of Hamiltonian moments. However, reconstructing an accurate distribution from only a limited number of moments remains a significant challenge. In this work, we introduce Jacobi-Anger Density Estimation (JADE), a non-parametric, quantum-inspired method designed to overcome this difficulty. JADE reconstructs the characteristic function from a finite set of moments using the Jacobi-Anger expansion and then estimates the underlying distribution via an inverse Fourier transform. We demonstrate that JADE can accurately recover the energy distribution of a quantum state for a molecular system. Beyond quantum chemistry, we also show that JADE is broadly applicable to the estimation of complicated probability density functions in various other scientific and engineering fields. Our results highlight JADE as a powerful and versatile tool for practical quantum systems, with the potential to significantly enhance ground state energy estimation and related applications.