A Majorana operator pool for adapt-VQE in nuclear shell model

Abstract

Quantum computers can represent a quantum many-body system in a natural way, but the devices available today are noisy, and that is what motivates the hybrid quantum-classical algorithms known as variational quantum eigensolvers. One of them, ADAPT-VQE, builds the trial state one operator at a time, taking at every step the generator with the largest energy gradient out of a predefined pool. That pool is the central design choice of the algorithm, and in this work we test two ways of changing it within the nuclear shell model, in the p shell with the Cohen–Kurath interaction. The first is to replace the usual fermionic double excitations by quartic products of Majorana operators, which map onto a single Pauli string under Jordan–Wigner instead of a sum of eight. The second is to give up the restriction to the physical sector and let the ansatz move through the whole Fock space, adding a quadratic penalty in the proton and neutron numbers. We run classical simulations of seventeen pshell nuclei and compare the pools in convergence and in number of operations. The results obtained with the projected Majorana pool are equivalent to those obtained for the same nuclei with the fermionic one. If the projection onto the physical sector is dropped and the symmetries are imposed through the penalty instead, the cost in operations grows by up to two orders of magnitude, and no convergence is found within the analyzed values of the penalty for nine of the seventeen nuclei.