Efficacious qubit mappings for quantum simulations of the $^{12}$C rotational band

TL;DR

This paper demonstrates quantum simulations of the $^{12}$C nucleus using variational quantum eigensolvers, leveraging symmetry and Gray encoding to reduce resource demands and achieve acceptable energies despite noise.

Contribution

It introduces a symmetry-adapted basis and Gray encoding for efficient quantum simulation of atomic nuclei, specifically applied to $^{12}$C.

Findings

Achieved acceptable bound-state energies with noisy quantum hardware.

Reduced model space size using symmetry-adapted basis.

Demonstrated resource efficiency with Gray encoding.

Abstract

Solving atomic nuclei from first principles places enormous demands on computational resources, which grow exponentially with increasing number of particles and the size of the space they occupy. We present first quantum simulations based on the variational quantum eigensolver for the low-lying structure of the $^{12}$C nucleus that provide acceptable bound-state energies even in the presence of noise. We achieve this by taking advantage of two critical developments. First, we utilize an almost perfect symmetry of atomic nuclei that, in a complete symmetry-adapted basis, drastically reduces the size of the model space. Second, we use the efficacious Gray encoding, for which it has been recently shown that it is resource efficient, especially when coupled with a near band-diagonal structure of the nuclear Hamiltonian.