Large-Scale VQE Simulations with Tensor-Networks

Approaches in quantum state preparation that include optimizing parameterized quantum circuits can be difficult due to noisy environments and barren plateaus, obscuring their utility as the number of qubits grow. Here, we show that purely classical resources can be used to optimize quantum circuits in an approximate but robust manner. Specifically, we approximate a parameterized circuit with a matrix product state (MPS) of a fixed bond dimension, and we find optimal parameters using classical solvers. We demonstrate this approach by parameterizing circuits representing ground states of the Hubbard model. By initializing parameterized quantum circuits with parameters obtained via classical optimization, we hope to avoid the many problems that occur with quantum algorithms.