Toward scalable quantum computations of atomic nuclei

TL;DR

This paper demonstrates a scalable quantum simulation approach for nuclear bound states using local Hamiltonians and adaptive ansatz, achieving accurate results with modest circuit depth and favorable resource scaling.

Contribution

It introduces a scalable quantum simulation method for nuclear states employing local Hamiltonians and an adaptive ansatz, with demonstrated accuracy and efficient resource scaling.

Findings

Reproduced exact benchmarks for deuteron and helium-3 within 100 keV.

Achieved modest circuit depths with at most 30 ansatz layers.

Found linear scaling of shots needed with lattice size.

Abstract

We solve the nuclear two-body and three-body bound states via quantum simulations of pionless effective field theory on a lattice in position space. While the employed lattice remains small, the usage of local Hamiltonians including two- and three-body forces ensures that the number of Pauli terms scales linearly with increasing numbers of lattice sites. We use an adaptive ansatz grown from unitary coupled cluster theory to parametrize the ground states of the deuteron and $^3$He, compute their corresponding energies, and analyze the scaling of the required computational resources. Our quantum simulations reproduce exact benchmarks for $^2$H and $^3$He within 100 keV, requiring at most 30 layers in the ansatz and thus resulting in modest circuit depths. Additionally, we find the number of shots required to reach a given precision scales linearly in the lattice size and more mildly in the system size. Based on the agreement with exact benchmarks and mild scaling, we conclude that this can be an efficient, scalable approach for quantum computations of nuclear ground states, particularly to prepare initial states for quantum phase estimation or other filtering algorithms.