Compact wavefunctions from compressed imaginary time evolution

TL;DR

This paper introduces a black box, compressed sensing-based method called MAGIC for efficiently finding compact wavefunctions of many-body quantum systems without detailed prior knowledge, enabling accurate simulations.

Contribution

The paper presents MAGIC, a novel general method that compresses quantum wavefunctions efficiently, applicable to various systems, without requiring system-specific information.

Findings

Recovered 98% of correlation energy for HF

Achieved 99.996% of total energy with 50 configurations

Applied to dissociation of HF and helium dimer

Abstract

Simulation of quantum systems promises to deliver physical and chemical predictions for the frontiers of technology. Unfortunately, the exact representation of these systems is plagued by the exponential growth of dimension with the number of particles, or colloquially, the curse of dimensionality. The success of approximation methods has hinged on the relative simplicity of physical systems with respect to the exponentially complex worst case. Exploiting this relative simplicity has required detailed knowledge of the physical system under study. In this work, we introduce a general and efficient black box method for many-body quantum systems that utilizes technology from compressed sensing to find the most compact wavefunction possible without detailed knowledge of the system. It is a Multicomponent Adaptive Greedy Iterative Compression (MAGIC) scheme. No knowledge is assumed in the structure of the problem other than correct particle statistics. This method can be applied to many quantum systems such as spins, qubits, oscillators, or electronic systems. As an application, we use this technique to compute ground state electronic wavefunctions of hydrogen fluoride and recover 98% of the basis set correlation energy or equivalently 99.996% of the total energy with $50$ configurations out of a possible $10^7$. Building from this compactness, we introduce the idea of nuclear union configuration interaction for improving the description of reaction coordinates and use it to study the dissociation of hydrogen fluoride and the helium dimer.