Quantum walk of two interacting fermions on a Su–Schrieffer–Heeger (SSH) model via exact and quantum circuit simulations

Abstract

We implemented a continuous-time quantum walk (CTQW) simulation of two spinless, nearest-neighbor-interacting fermions on a one-dimensional Su-Schrieffer-Heeger (SSH) model using numerically exact and quantum gate-based methods. We applied the SSH Hamiltonian with alternating hopping rates and an additional potential energy term to include the Coulomb-like nearest-neighbor interaction between two fermions. To implement the Hamiltonian, we applied the Jordan-Wigner transformation and the Suzuki-Trotter decomposition. The results demonstrate the presence of edge-localized states when the system's intercell hopping strength was sufficiently greater than the intracell hopping strength. Edge localization was strengthened as the intercell hopping rate was increased, and the inclusion of the nearest-neighbor interaction led to the formation of bound states. The gate-based quantum circuit simulation showed qualitative agreement with the exact numerical simulation, with discrepancies that can be attributed to Trotterization and shot-based sampling. This study demonstrates that the CTQW dynamics of the SSH model can be effectively modeled on quantum circuits.