Quantum annealing for neural network optimization problems: A new approach via tensor network simulations

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