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Quantum Annealing for Neural Network optimization problems: a new approach via Tensor Network simulations
by Guglielmo Lami, Pietro Torta, Giuseppe E. Santoro, Mario Collura
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Guglielmo Lami |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2208.14468v3 (pdf) |
| Date accepted: | 2023-03-28 |
| Date submitted: | 2023-03-13 14:53 |
| Submitted by: | Lami, Guglielmo |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Computational |
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.
List of changes
-We included a brief introduction to tensor networks, mainly focusing on MPS and bond dimension definitions, now provided in the Introduction.
-We clarified two points raised by the First Referee, concerning the need for trotterization in ED procedures and a comparison of computation times
and maximum system sizes achieved by means of the different numerical techniques.
-We improved the discussion on the Hopfield model, as suggested by the First Referee, in particular concerning Figure 20.
-We verified that our methods prove effective also in the UNSAT regime of the binary perceptron, as suggested by the Referee M.Bukov.
-Also stemming from M. Bukov advice, we tested our results against state-of-the-art classical optimization methods, and we better clarified which sizes we can reach with our code implementation.
-We implemented a list of minor updates, following the comments and suggestions of both Referees.
Published as SciPost Phys. 14, 117 (2023)