Noise Resilience and Robust Convergence Guarantees for the Variational Quantum Eigensolver

Variational Quantum Algorithms (VQAs) are a class of hybrid quantum-classical algorithms that leverage on classical optimization tools to find the optimal parameters for a parameterized quantum circuit.

One relevant application of VQAs is the Variational Quantum Eigensolver (VQE), which aims at steering the output of the quantum circuit to the ground state of a certain Hamiltonian.

Recent works have provided global convergence guarantees for VQEs under suitable local surjectivity and smoothness hypotheses, but little has been done in characterizing convergence of these algorithms when the underlying quantum circuit is affected by noise.

In this work, we derive an upper bound on the error on the optimal parameters of a VQE under the effect of different coherent and incoherent noise processes.

We then procced to show robust convergence guarantees of the algorithm to the perturbed optimal parameters.

Our work provides novel theoretical insight into the behavior of VQAs subject to noise.

Furthermore, we accompany our results with numerical simulations implemented via Pennylane.