Bloch oscillation with a diatomic tight-binding model on quantum computers

We aim to explore a more efficient way to simulate few-body dynamics on quantum computers. Instead of mapping the second quantization of the system Hamiltonian to qubit Pauli gate representation via the Jordan-Wigner transform, we propose to use the few-body Hamiltonian matrix under the state-vector basis representation, which is more economical on the required number of quantum registers. For a single-particle excitation state on a one-dimensional chain, Γ qubits can simulate N=2Γ number of sites, in comparison to N qubits for N sites via the Jordan-Wigner approach. A two-band diatomic tight-binding model is used to demonstrate the effectiveness of the state-vector basis representation. Both one-particle and two-particle quantum circuits are constructed, and some numerical tests on IBM hardware are presented.