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 gates representation via the Jordan-Wigner transform, we propose to use the few-body Hamiltonian matrix under the statevector basis representation which is more economical on the required number of quantum registers. For a single-particle excitation state on a one-dimensional chain, $\Gamma$ qubits can simulate $N=2^\Gamma$ 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 statevector basis representation. Both one-particle and two-particle quantum circuits are constructed and some numerical tests on IBM hardware are presented.