Solving Quantum Ground-State Problems with Nuclear Magnetic Resonance

TL;DR

This paper demonstrates using an NMR quantum simulator with a variational approach to accurately find the ground state of a Heisenberg spin model, showcasing quantum advantage in leveraging trial wavefunctions.

Contribution

First experimental implementation of a variational-wavefunction approach with phase estimation on an NMR quantum simulator for a many-body ground-state problem.

Findings

Achieved high-precision eigenenergies to 10^-5 decimal digit

Ground-state fidelity exceeded 80%

Successfully captured singlet-to-triplet transition near critical field

Abstract

Quantum ground-state problems are computationally hard problems; for general many-body Hamiltonians, there is no classical or quantum algorithm known to be able to solve them efficiently. Nevertheless, if a trial wavefunction approximating the ground state is available, as often happens for many problems in physics and chemistry, a quantum computer could employ this trial wavefunction to project the ground state by means of the phase estimation algorithm (PEA). We performed an experimental realization of this idea by implementing a variational-wavefunction approach to solve the ground-state problem of the Heisenberg spin model with an NMR quantum simulator. Our iterative phase estimation procedure yields a high accuracy for the eigenenergies (to the 10^-5 decimal digit). The ground-state fidelity was distilled to be more than 80%, and the singlet-to-triplet switching near the critical field is reliably captured. This result shows that quantum simulators can better leverage classical trial wavefunctions than classical computers.