Collective optimization for variational quantum eigensolvers

Abstract

Variational quantum eigensolver (VQE) optimizes parameterized 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 up classical algorithms to exploit the power of near-term quantum computing. Here, we develop a hybrid algorithm for VQE, emphasizing the classical side, that can solve a group of related Hamiltonians simultaneously. The algorithm incorporates a snake algorithm into many VQE tasks to collectively optimize variational parameters of different Hamiltonians. Such so-called collective VQEs~(cVQEs) is applied for solving molecules with varied bond length, which is a standard problem in quantum chemistry. Numeral simulations show that cVQE is not only more efficient in convergence, but also trends to avoid single VQE task to be trapped in local minimums. The collective optimization utilizes intrinsic relations between related tasks and may inspire advanced hybrid quantum-classical algorithms for solving practical problems.

arXiv comment9 pages, 5 figures. Comments are welcome

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• The Meta-Variational Quantum Eigensolver (Meta-VQE): Learning energy profiles of parameterized Hamiltonians for quantum simulation
• Variational quantum algorithm with information sharing
• Operator Sampling for Shot-frugal Optimization in Variational Algorithms
• Selected topics of quantum computing for nuclear physics
• Molecular Quantum Circuit Design: A Graph-Based Approach
• Quantum Gaussian filter for exploring ground-state properties
• Hybrid quantum-classical algorithms for solving quantum chemistry in Hamiltonian-wavefunction space
• Inverse iteration quantum eigensolvers assisted with a continuous variable
• The impacts of optimization algorithm and basis size on the accuracy and efficiency of variational quantum eigensolver
• Variational quantum simulation of the quantum critical regime
• Velocity Verlet-based optimization for variational quantum eigensolvers