Solving graph problems using permutation-invariant quantum machine learning

TL;DR

This paper demonstrates that incorporating problem-specific symmetries into quantum machine learning circuits significantly improves graph classification performance, especially when the symmetry is accurately reflected.

Contribution

It introduces a method to embed symmetry into quantum circuits for graph problems, showing substantial performance gains over non-symmetrized approaches.

Findings

Symmetry-aware quantum circuits outperform standard ansatzes on graph classification tasks.

Even approximate symmetry incorporation yields notable performance improvements.

The method provides a straightforward way to include symmetry in quantum circuit design.

Abstract

Many computational problems are unchanged under some symmetry operation. In classical machine learning, this can be reflected with the layer structure of the neural network. In quantum machine learning, the ansatz can be tuned to correspond to the specific symmetry of the problem. We investigate this adaption of the quantum circuit to the problem symmetry on graph classification problems. On random graphs, the quantum machine learning ansatz classifies whether a given random graph is connected, bipartite, contains a Hamiltonian path or cycle, respectively. We find that if the quantum circuit reflects the inherent symmetry of the problem, it vastly outperforms the standard, unsymmetrized ansatzes. Even when the symmetry is only approximative, there is still a significant performance gain over non-symmetrized ansatzes. We show how the symmetry can be included in the quantum circuit in a straightforward constructive method.