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.
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Authors / Affiliations: mappings to Contributors and OrganizationsSee all Organizations.
- 1 Scuola Internazionale Superiore di Studi Avanzati / International School for Advanced Studies [SISSA]
- 2 Centro Internazionale di Fisica Teorica Abdus Salam / Abdus Salam International Centre for Theoretical Physics [ICTP]
- 3 Istituto Officina dei Materiali / Materials Foundry Institute [IOM]
- 4 INFN Sezione di Trieste / INFN Trieste
- Horizon 2020 (through Organization: European Commission [EC])