Limits of quantum generative models with classical sampling hardness

Sampling tasks have been successful in establishing quantum advantages both in theory and experiments. This has fueled the use of quantum computers for generative modeling to create samples following the probability distribution underlying a given dataset. In particular, the potential to build generative models on classically hard distributions would immediately preclude classical simulability, due to theoretical separations. In this work, we study quantum generative models from the perspective of output distributions, showing that models that anticoncentrate are not trainable on average, including those exhibiting quantum advantage. In contrast, models outputting data from sparse distributions can be trained. We consider special cases to enhance trainability, and observe that this opens the path for classical algorithms for surrogate sampling. This observed trade-off is linked to verification of quantum processes. We conclude that quantum advantage can still be found in generative models, although its source must be distinct from anticoncentration.

Exploring Channel Distinguishability in Local Neighborhoods of the Model Space in Quantum Neural Networks

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.

On Optimizing Hyperparameters for Quantum Neural Networks

The increasing capabilities of Machine Learning (ML) models go hand in hand with an immense amount of data and computational power required for training. Therefore, training is usually outsourced into HPC facilities, where we have started to experience limits in scaling conventional HPC hardware, as theorized by Moore's law. Despite heavy parallelization and optimization efforts, current state-of-the-art ML models require weeks for training, which is associated with an enormous $CO_2$ footprint. Quantum Computing, and specifically Quantum Machine Learning (QML), can offer significant theoretical speed-ups and enhanced expressive power. However, training QML models requires tuning various hyperparameters, which is a nontrivial task and suboptimal choices can highly affect the trainability and performance of the models. In this study, we identify the most impactful hyperparameters and collect data about the performance of QML models. We compare different configurations and provide researchers with performance data and concrete suggestions for hyperparameter selection.

Streaming IoT Data and the Quantum Edge: A Classic/Quantum Machine Learning Use Case

With the advent of the Post-Moore era, the scientific community is faced with the challenge of addressing the demands of current data-intensive machine learning applications, which are the cornerstone of urgent analytics in distributed computing. Quantum machine learning could be a solution for the increasing demand of urgent analytics, providing potential theoretical speedups and increased space efficiency. However, challenges such as (1) the encoding of data from the classical to the quantum domain, (2) hyperparameter tuning, and (3) the integration of quantum hardware into a distributed computing continuum limit the adoption of quantum machine learning for urgent analytics. In this work, we investigate the use of Edge computing for the integration of quantum machine learning into a distributed computing continuum, identifying the main challenges and possible solutions. Furthermore, exploring the data encoding and hyperparameter tuning challenges, we present preliminary results for quantum machine learning analytics on an IoT scenario.