Digital quantum simulations of the SSH model on a parameterized quantum circuit

Quantum computing holds immense potential to revolutionize many fields, including cryptography, material science, drug discovery, and artificial intelligence. Currently, we are in the NISQ era, where quantum devices up to a few hundred noisy qubits are available. We carry out digital quantum simulations of the non-interacting SSH model on a parameterized quantum circuit. The circuit is composed of two parts: the first part is used to prepare the initial bonding state from the product state |00....0>. The second part consists of M-layer composite quantum gates that process the quantum state. The rotation angles of the single-qubit gates are treated as variational parameters which are optimized using classical algorithms. We then study the evolutions of the ground-state energy, entanglement entropy, and mutual information on the circuit for two scenarios where the initial and final states either belong to the same or different topological phases. In the first case, we find that the ground-state energy converges exponentially fast with increasing circuit depth M. The entanglement entropy approaches saturation values after very few layers and the mutual information is nonzero only for a few close neighbor sites. However, in the second case where the initial and final state have different topologies, to prepare the ground state exactly, the minimal circuit depth is a quarter of the system size, consistent with the Lieb-Ronbinson bound for propagating the information. Additionally, the maxima of the entanglement entropy grows with the system size and mutual information propagates throughout the entire system.