Sequential Core-wise Structure Search for Quantum Tensor Networks

Keywords: Tensor networks, quantum tensor network, quantum tensor network structure search

TL;DR: SCoSS efficiently searches quantum tensor network core placements with far fewer evaluations while maintaining competitive reconstruction accuracy.

Abstract: Quantum tensor networks (QTNs) represent high-order tensors through contracted circuit-style local cores, offering a clear way to model multilinear interactions across ordered qubits. However, tensor network structure search on QTNs is computationally challenging because it requires selecting core placements while preserving reconstruction accuracy. We propose sequential core-wise structure search (SCoSS), a simple alternating local search framework for QTN structure search (QTN-SS). SCoSS updates one core at a time: for each core, it enumerates feasible local placements, trains the corresponding candidate networks, and selects the candidate minimizing a selection score that balances reconstruction loss and structural complexity. Inspired by TnALE, SCoSS applies alternating local enumeration to QTN core-placement selection. In two controlled experiments that vary the number of qubits and the number of tensor cores, SCoSS evaluates significantly fewer candidate structures than permutation brute-force search while achieving competitive reconstruction accuracy in terms of mean absolute percentage error (MAPE). Under the same evaluation budget, SCoSS also generally yields lower MAPE than permutation random search. These results show that simple core-wise alternating updates provide an efficient route to QTN-SS.

Submission Number: 55