Quantum Annealing for Neural Network optimization problems: a new approach via Tensor Network simulations

TL;DR

This paper introduces a tensor network-based classical simulation method for quantum annealing applied to neural network optimization problems, enabling efficient analysis of larger systems and potential quantum circuit implementations.

Contribution

It presents a novel tensor network approach to simulate quantum annealing for neural network optimization, bridging classical and quantum computation techniques.

Findings

Tensor network representation enables efficient classical simulation of QA.

Optimized states can be transformed into shallow quantum circuits.

Simulation scales favorably with system size and bond dimension.

Abstract

Quantum Annealing (QA) is one of the most promising frameworks for quantum optimization. Here, we focus on the problem of minimizing complex classical cost functions associated with prototypical discrete neural networks, specifically the paradigmatic Hopfield model and binary perceptron. We show that the adiabatic time evolution of QA can be efficiently represented as a suitable Tensor Network. This representation allows for simple classical simulations, well-beyond small sizes amenable to exact diagonalization techniques. We show that the optimized state, expressed as a Matrix Product State (MPS), can be recast into a Quantum Circuit, whose depth scales only linearly with the system size and quadratically with the MPS bond dimension. This may represent a valuable starting point allowing for further circuit optimization on near-term quantum devices.