Quantum simulation of nuclear Hamiltonian with a generalized transformation for Gray code encoding

Abstract

We present the quantum simulation of the deuteron to calculate its binding energy using the variational quantum eigensolver, which is based on a hybrid quantum-classical approach. Apart from a commonly used Hamiltonian derived from pionless effective field theory, we consider the interaction which can be easily studied with conventional classical methods but the corresponding operator leading to nonzero off-tridiagonal matrix elements. To map the many-body basis states on the qubit states, three encodings are explored, namely, one-hot, Bravyi-Kitaev, and the Gray code. We perform a generalized transformation for many-body operators in Gray code encoding, and simulate the Hamiltonians with nonzero off-tridiagonal matrix elements. Furthermore, the analyses of the relative efficiency of all encodings and corresponding transformations are carried out using the noise model of a real IBM quantum device. We demonstrate that the Gray code is more efficient for a large basis, irrespective of the form of potential and the presence of hardware noise.