Compact wavefunctions from compressed imaginary time evolution

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.

References in corpus (4)

• Quantum simulation of time-dependent Hamiltonians and the convenient illusion of Hilbert space
• Compressed Modes for Variational Problems in Mathematics and Physics
• Truncated Configuration Interaction expansions as solvers for correlated quantum impurity models and dynamical mean field theory
• Multi-component symmetry-projected approach for molecular ground state correlations

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• Generalising quantum imaginary time evolution to solve linear partial differential equations
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• A Quantum Algorithmic Approach to Multiconfigurational Valence Bond Theory: Insights from Interpretable Circuit Design