Single-step Quantum Simulation of Two Nucleons

TL;DR

The paper tackles the exponential scaling of the nuclear shell-model Hamiltonian and the challenge of accessing excited states on near-term quantum devices. It combines subspace-search VQE (SSVQE) with an adaptive, symmetry-preserving ADAPT-VQE ansatz built from a double-excitation operator pool to minimize a weighted sum $L( heta)=\sum w_i \langle \phi_i| U^ap H U | \phi_i\rangle$ and converge to the lowest $k$ eigenstates within the $M_J$-conserving subspace in a single optimization. Applied to two identical nucleons in the $0p_{3/2}$ orbital mapped via Jordan-Wigner to a 4-qubit Hamiltonian, the method yields $E_0=-2.0$ MeV and $E_1=-0.4$ MeV, in agreement with exact diagonalization, using a single-parameter ansatz ($ heta_0=0.785$) and a compact circuit. These results demonstrate a scalable, symmetry-aware quantum-classical workflow capable of capturing ground and low-lying excited-state structure in nuclear systems on NISQ devices, with potential extensions to larger spaces and isospin-inclusive configurations.

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.

Figures (2)

• Figure 1: Quantum circuit of the ansatz, $U(\theta)=exp(-i\theta_0A_1)$, in terms of Pauli evolution gate in terms of double-excitation operator $A_1$ (shown here for brevity without coefficients of the involved terms) with $t\equiv \theta_0=0.785$.
• Figure 2: An equivalent representation of the quantum circuit shown in Fig. \ref{['fig:qc']} but in terms of single and double-qubit gates suitable for the real hardware implementation.