Multi-nucleon structure and dynamics via quantum computing*

We propose a method to compute the structure and dynamics for second-quantized many-nucleon Hamiltonians on near-term noisy intermediate scale quantum computers. We develop an oracle-based Hamiltonian input model that computes the many-nucleon states and non-zero Hamiltonian matrix elements of the many-nucleon system. With our Fock-state based input model, we show how to implement the sparse matrix simulation algorithms to calculate the dynamics of the second-quantized many-nucleon Hamiltonian. Based on the dynamics simulation methods, we also present the methodology for structure calculations of the many-nucleon system. In this work, we provide explicit design of our input model of the second-quantized Hamiltonian within a direct encoding scheme that maps the occupation of each available single-particle state in the many-nucleon state to the state of specific qubit in quantum register. We analyze our method and provide the asymptotic cost in computing resources for structure and dynamics calculations of many-nucleon systems. For pedagogical purpose, we demonstrate our method with two model problems in restricted model spaces.