Variational approaches to constructing the many-body nuclear ground state for quantum computing

TL;DR

This paper investigates variational quantum algorithms, specifically the unitary coupled cluster method, to efficiently approximate nuclear ground states on quantum hardware, addressing classical computational limitations.

Contribution

It demonstrates the application of variational approaches to nuclear physics, highlighting their potential to reduce resource requirements compared to classical methods.

Findings

Variational methods can approximate nuclear ground states with fewer qubits and shallower circuits.

Large parameter spaces and entanglement pose challenges for current hardware implementation.

Prospects for hardware improvements could enable practical quantum simulations of complex nuclei.

Abstract

We explore the preparation of specific nuclear states on gate-based quantum hardware using variational algorithms. Large scale classical diagonalization of the nuclear shell model have reached sizes of $10^9 - 10^{10}$ basis states, but are still severely limited by computational resources. Quantum computing can, in principle, solve such systems exactly with exponentially fewer resources than classical computing. Exact solutions for large systems require many qubits and large gate depth, but variational approaches can effectively limit the required gate depth. We use the unitary coupled cluster approach to construct approximations of the ground-state vectors, later to be used in dynamics calculations. The testing ground is the phenomenological shell model space, which allows us to mimic the complexity of the inter-nucleon interactions. We find that often one needs to minimize over a large number of parameters, using a large number of entanglements that makes challenging the application on existing hardware. Prospects for rapid improvements with more capable hardware are, however, very encouraging.