Collective optimization for variational quantum eigensolvers

A variational quantum eigensolver (VQE) optimizes parametrized eigenstates of a Hamiltonian on a quantum processor by updating parameters with a classical computer. Such a hybrid quantum-classical optimization serves as a practical way to leverage classical algorithms in exploiting the power of near-term quantum devices. Here, aiming to solve a group of Hamiltonians more efficiently, we develop an extension of the conventional VQE. A snake algorithm is incorporated to couple optimizing processes for VQEs of different Hamiltonians by gradient descent. Such a so-called collective VQE (CVQE) is applied to simulate molecules with varied bond lengths for demonstration. Numeral simulations show that the CVQE exhibits clear collective behavior in the optimization process of updating parameters. Remarkably, the CVQE tends to avoid a single VQE task to be trapped in the local minimum. The collective optimization utilizes intrinsic relations between related tasks and may inspire advanced hybrid quantum-classical algorithms for solving practical problems with current quantum technologies.