Nuclear shell-model simulation in digital quantum computers

Abstract

The nuclear shell model is one of the prime many-body methods to study the structure of atomic nuclei, but it is hampered by an exponential scaling on the basis size as the number of particles increases. We present a shell-model quantum circuit design strategy to find nuclear ground states by exploiting an adaptive variational quantum eigensolver algorithm. Our circuit implementation is in excellent agreement with classical shell-model simulations for a dozen of light and medium-mass nuclei, including neon and calcium isotopes. We quantify the circuit depth, width and number of gates to encode realistic shell-model wavefunctions. Our strategy also addresses explicitly energy measurements and the required number of circuits to perform them. Our simulated circuits approach the benchmark results exponentially with a polynomial scaling in quantum resources for each nucleus. This work paves the way for quantum computing shell-model studies across the nuclear chart and our quantum resource quantification may be used in configuration-interaction calculations of other fermionic systems.

Shell-model study of58Ni using quantum computing algorithm

“…Table 2 shows a detailed breakdown of the properties associated with each circuit. Through the use of our problem-specific ansatz, the number of gates is kept low compared with more general ansatzes [24]. We have not imposed nearest-neighbour qubit interaction which is a requirement for some quantum computing hardware, and for the J = 2 and J = 4 states, doing this would increase the gate count, though this increase could be minimized with careful re-mapping of single-particle states to qubits.…”

“…Another study presents an excitation-preserving ansatz for VQE, maintaining the correct number of excited orbitals and ensuring efficient quantum circuit implementation to preserve specific proton and neutron numbers [23]. One analysis emphasizes constructing an initial state close to the expected physical state using domain-specific knowledge to reduce local minima and enhance VQE convergence [24]. The Hartree-Fock method has also been used to find occupied and unoccupied states, employing the UCC method to generate correlated states for quantum simulations, including two-particle, two-hole, and higher correlations [10].…”

“…A standard microscopic (treating nucleons as the degree of freedom) method to interpret observed states of nuclei is the configuration interaction nuclear shell model [20][21][22] in which nucleons interact in a defined single-particle basis to produce correlated eigenstates of a model Hamiltonian. Finding the wavefunctions and consequent properties of these eigenstates is the job of a shell model practitioner; a job which has already been explored on real and simulated quantum computers in some of the lightest nuclei [10,23] with various aspects of the specific algorithms needed for quantum computation examined [24,25].…”