Improving the trainability of VQE on NISQ computers for solving portfolio optimization using convex interpolation

TL;DR

This paper enhances the trainability of VQE for portfolio optimization on NISQ devices by using convex interpolation, enabling larger problem solving and demonstrating successful experiments with fewer qubits, and combining VQE with greedy algorithms.

Contribution

Introduces convex interpolation techniques to improve VQE trainability, along with strategies for initialization and ansatz optimization, validated through experiments and simulations.

Findings

Successful 40-qubit experiment with 10 superconducting qubits

Hybrid VQE and greedy algorithms outperform individual methods

Proposals extend to other large-scale combinatorial problems

Abstract

Solving combinatorial optimization problems using variational quantum algorithms (VQAs) might be a promise application in the NISQ era. However, the limited trainability of VQAs could hinder their scalability to large problem sizes. In this paper, we improve the trainability of variational quantum eigensolver (VQE) by utilizing convex interpolation to solve portfolio optimization. Based on convex interpolation, the location of the ground state can be evaluated by learning the property of a small subset of basis states in the Hilbert space. This enlightens naturally the proposals of the strategies of close-to-solution initialization, regular cost function landscape, and recursive ansatz equilibrium partition. The successfully implementation of a $40$-qubit experiment using only $10$ superconducting qubits demonstrates the effectiveness of our proposals. Furthermore, the quantum inspiration has also spurred the development of a prototype greedy algorithm. Extensive numerical simulations indicate that the hybridization of VQE and greedy algorithms achieves a mutual complementarity, combining the advantages of both global and local optimization methods. Our proposals can be extended to improve the trainability for solving other large-scale combinatorial optimization problems that are widely used in real applications, paving the way to unleash quantum advantages of NISQ computers in the near future.