Paper ID: 2410.09470 • Published Oct 12, 2024
Exploring Channel Distinguishability in Local Neighborhoods of the Model Space in Quantum Neural Networks
Sabrina Herbst, Sandeep Suresh Cranganore, Vincenzo De Maio, Ivona Brandic
TL;DR
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With the increasing interest in Quantum Machine Learning, Quantum Neural
Networks (QNNs) have emerged and gained significant attention. These models
have, however, been shown to be notoriously difficult to train, which we
hypothesize is partially due to the architectures, called ansatzes, that are
hardly studied at this point. Therefore, in this paper, we take a step back and
analyze ansatzes. We initially consider their expressivity, i.e., the space of
operations they are able to express, and show that the closeness to being a
2-design, the primarily used measure, fails at capturing this property. Hence,
we look for alternative ways to characterize ansatzes by considering the local
neighborhood of the model space, in particular, analyzing model
distinguishability upon small perturbation of parameters. We derive an upper
bound on their distinguishability, showcasing that QNNs with few parameters are
hardly discriminable upon update. Our numerical experiments support our bounds
and further indicate that there is a significant degree of variability, which
stresses the need for warm-starting or clever initialization. Altogether, our
work provides an ansatz-centric perspective on training dynamics and
difficulties in QNNs, ultimately suggesting that iterative training of small
quantum models may not be effective, which contrasts their initial motivation.