Quantum computing of the $^6$Li nucleus via ordered unitary coupled clusters

TL;DR

This paper applies the variational quantum eigensolver to the $^6$Li nucleus, demonstrating improved accuracy through operator ordering and error mitigation on a quantum chip, advancing quantum simulations of nuclear systems.

Contribution

It introduces an ordered unitary coupled clusters ansatz for VQE applied to nuclear physics, showing significant accuracy improvements and practical quantum computation on IBM hardware.

Findings

Descending operator order improves convergence by two orders of magnitude.

Error mitigation enables accurate energy estimation with less than 4% error.

Successful demonstration of quantum simulation of $^6$Li on a superconducting quantum chip.

Abstract

The variational quantum eigensolver (VQE) is an algorithm to compute ground and excited state energy of quantum many-body systems. A key component of the algorithm and an active research area is the construction of a parametrized trial wavefunction -- a so called variational ansatz. The wavefunction parametrization should be expressive enough, i.e. represent the true eigenstate of a quantum system for some choice of parameter values. On the other hand, it should be trainable, i.e. the number of parameters should not grow exponentially with the size of the system. Here, we apply VQE to the problem of finding ground and excited state energies of the odd-odd nucleus $^6$Li. We study the effects of ordering fermionic excitation operators in the unitary coupled clusters ansatz on the VQE algorithm convergence by using only operators preserving the $J_z$ quantum number. The accuracy is improved by two order of magnitude in the case of descending order. We first compute optimal ansatz parameter values using a classical state-vector simulator with arbitrary measurement accuracy and then use those values to evaluate energy eigenstates of $^6$Li on a superconducting quantum chip from IBM. We post-process the results by using error mitigation techniques and are able to reproduce the exact energy with an error of 3.8% and 0.1% for the ground state and for the first excited state of $^6$Li, respectively.