Single-step Quantum Simulation of Two Nucleons

TL;DR

This paper introduces a quantum simulation method combining SSVQE and ADAPT ansatz to efficiently compute low-lying nuclear states, demonstrated on a two-nucleon system with promising accuracy for future quantum nuclear physics applications.

Contribution

The work presents a novel single-step quantum algorithm for nuclear state calculations using an adaptive, symmetry-preserving ansatz, enabling efficient excited state convergence.

Findings

Accurately benchmarks against exact diagonalization.

Successfully converges multiple states simultaneously.

Demonstrates potential for near-term quantum nuclear simulations.

Abstract

Quantum computing offers a scalable approach to solving the nuclear shell model, a highly complex and exponentially scaled many-body problem. This work presents a numerical simulation of the subspace search variational quantum eigensolver (SSVQE) combined with an adaptive derivative-assembles pseudo-trotter (ADAPT) ansatz to obtain the low-lying states of any nuclear system in a single optimization run. As an example, we apply this method in this work to a trivial identical nucleon system, two nucleons in the $0p_{3/2}$ orbital, mapped to 4 qubits depicting m-scheme single-particle states including a surface delta effective interaction using the Jordan-Wigner transformation. The ADAPT-SSVQE algorithm, by utilizing a symmetry-preserving double-excitation ADAPT operator pool, uniquely optimizes a weighted energy sum, forcing the simultaneous convergence of two lowest states within the total angular momentum $M_J=0$ subspace. We demonstrate the accuracy of the method by benchmarking against the exact diagonalization, confirming its potential for probing nuclear structure and pairing phenomena on current and near-future quantum devices without requiring multi-step procedure for excited states.