Resource frugal optimizer for quantum machine learning

Quantum-enhanced data science, also known as quantum machine learning (QML), is of growing interest as an application of near-term quantum computers. Variational QML algorithms have the potential to solve practical problems on real hardware, particularly when involving quantum data. However, training these algorithms can be challenging and calls for tailored optimization procedures. Specifically, QML applications can require a large shot-count overhead due to the large datasets involved. In this work, we advocate for simultaneous random sampling over both the dataset as well as the measurement operators that define the loss function. We consider a highly general loss function that encompasses many QML applications, and we show how to construct an unbiased estimator of its gradient. This allows us to propose a shot-frugal gradient descent optimizer called Refoqus (REsource Frugal Optimizer for QUantum Stochastic gradient descent). Our numerics indicate that Refoqus can save several orders of magnitude in shot cost, even relative to optimizers that sample over measurement operators alone.

Hyperparameter Importance of Quantum Neural Networks Across Small Datasets

As restricted quantum computers are slowly becoming a reality, the search for meaningful first applications intensifies. In this domain, one of the more investigated approaches is the use of a special type of quantum circuit - a so-called quantum neural network -- to serve as a basis for a machine learning model. Roughly speaking, as the name suggests, a quantum neural network can play a similar role to a neural network. However, specifically for applications in machine learning contexts, very little is known about suitable circuit architectures, or model hyperparameters one should use to achieve good learning performance. In this work, we apply the functional ANOVA framework to quantum neural networks to analyze which of the hyperparameters were most influential for their predictive performance. We analyze one of the most typically used quantum neural network architectures. We then apply this to $7$ open-source datasets from the OpenML-CC18 classification benchmark whose number of features is small enough to fit on quantum hardware with less than $20$ qubits. Three main levels of importance were detected from the ranking of hyperparameters obtained with functional ANOVA. Our experiment both confirmed expected patterns and revealed new insights. For instance, setting well the learning rate is deemed the most critical hyperparameter in terms of marginal contribution on all datasets, whereas the particular choice of entangling gates used is considered the least important except on one dataset. This work introduces new methodologies to study quantum machine learning models and provides new insights toward quantum model selection.