An inductive bias from quantum mechanics: learning order effects with non-commuting measurements

There are two major approaches to building good machine learning algorithms: feeding lots of data into large models, or picking a model class with an "inductive bias" that suits the structure of the data. When taking the second approach as a starting point to design quantum algorithms for machine learning, it is important to understand how mathematical structures in quantum mechanics can lead to useful inductive biases in quantum models. In this work, we bring a collection of theoretical evidence from the Quantum Cognition literature to the field of Quantum Machine Learning to investigate how non-commutativity of quantum observables can help to learn data with "order effects", such as the changes in human answering patterns when swapping the order of questions in a survey. We design a multi-task learning setting in which a generative quantum model consisting of sequential learnable measurements can be adapted to a given task - or question order - by changing the order of observables, and we provide artificial datasets inspired by human psychology to carry out our investigation. Our first experimental simulations show that in some cases the quantum model learns more non-commutativity as the amount of order effect present in the data is increased, and that the quantum model can learn to generate better samples for unseen question orders when trained on others - both signs that the model architecture suits the task.