Variational Quantum Optimization with Multi-Basis Encodings

TL;DR

This paper introduces a novel variational quantum algorithm that uses multi-basis encodings and nonlinear activations, achieving better optimization performance with fewer resources and shallower circuits, demonstrated on large MaxCut problems.

Contribution

The authors propose a new variational quantum algorithm with multi-basis encodings and nonlinear activations, enabling efficient optimization on large graphs with reduced quantum resources.

Findings

Achieved a twofold increase in effective quantum resources.

Reduced measurement complexity quadratically.

Successfully optimized MaxCut on 512-vertex graphs using a single GPU.

Abstract

Despite extensive research efforts, few quantum algorithms for classical optimization demonstrate realizable quantum advantage. The utility of many quantum algorithms is limited by high requisite circuit depth and nonconvex optimization landscapes. We tackle these challenges by introducing a new variational quantum algorithm that benefits from two innovations: multi-basis graph encodings and nonlinear activation functions. Our technique results in increased optimization performance, a factor of two increase in effective quantum resources, and a quadratic reduction in measurement complexity. While the classical simulation of many qubits with traditional quantum formalism is impossible due to its exponential scaling, we mitigate this limitation with exact circuit representations using factorized tensor rings. In particular, the shallow circuits permitted by our technique, combined with efficient factorized tensor-based simulation, enable us to successfully optimize the MaxCut of the nonlocally connected $512$-vertex DIMACS library graphs on a single GPU. By improving the performance of quantum optimization algorithms while requiring fewer quantum resources and utilizing shallower, more error-resistant circuits, we offer tangible progress for variational quantum optimization.