Simulating the Berry Phase Using Quantum Phase Estimation Algorithm

Holonomy describes how the geometric properties of a system change when it evolves along a closed path. The Berry phase is a geometric phase acquired in adiabatic evolution that measures the holonomy of a quantum state. Quantum Phase Estimation (QPE) is a quantum algorithm that estimates properties of quantum systems. Here, we investigate the error sources in quantum simulation induced when computing the Berry phase using QPE. We use QPE to digitally simulate an adiabatic, time-dependent cyclic unitary that evolves around a conical intersection of its excited and ground states. We identify the range of total evolution times, number of time steps, and bits of precision needed to estimate the Berry phase with minimal overall error. These results demonstrate a pathway toward scalable simulation of more complex holonomic quantum systems.