Abstract 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.
Abstract 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.
This thesis investigates how principles from physics can serve as inductive biases that make learning and optimization more tractable in machine learning and quantum computing. Physical structure - encoded in Hamiltonians, physics-inspired dynamics, circuit architectures, and measurement protocols - constrains the hypothesis class, enabling learning under limited computational and data budgets in high-dimensional settings. The thesis presents four case studies showing how these physics-inspired inductive biases can be incorporated into both classical and quantum models. First, quantum diffusion models are introduced as generative models for quantum states. A Markovian noising process, motivated by statistical physics, defines the forward dynamics, while parameterized quantum circuits implement the reverse dynamics. Second, a Potts-model Hamiltonian is used to formulate a graph-coloring objective, leading to a physics-informed neural architecture that generalizes beyond the training distribution. Third, parameterized quantum circuits and hybrid classical-quantum models are evaluated for an anomaly detection task in highly imbalanced classical transaction data, using circuit structure as an additional inductive bias. Fourth, a data-driven classical-shadow method is developed, in which a neural network maps shadow snapshots to observable expectation values. This work fits into the broader effort of quantum device certification. Overall, the results show that physics-inspired inductive biases are a robust lever for resource-efficient learning, while NISQ-era quantum resources provide modest task- and metric-dependent benefits rather than a consistent advantage over classical baselines.
Generalisation in machine learning often relies on the ability to encode structures present in data into an inductive bias of the model class. To understand the power of quantum machine learning, it is therefore crucial to identify the types of data structures that lend themselves naturally to quantum models. In this work we look to quantum contextuality -- a form of nonclassicality with links to computational advantage -- for answers to this question. We introduce a framework for studying contextuality in machine learning, which leads us to a definition of what it means for a learning model to be contextual. From this, we connect a central concept of contextuality, called operational equivalence, to the ability of a model to encode a linearly conserved quantity in its label space. A consequence of this connection is that contextuality is tied to expressivity: contextual model classes that encode the inductive bias are generally more expressive than their noncontextual counterparts. To demonstrate this, we construct an explicit toy learning problem -- based on learning the payoff behaviour of a zero-sum game -- for which this is the case. By leveraging tools from geometric quantum machine learning, we then describe how to construct quantum learning models with the associated inductive bias, and show through our toy problem that they outperform their corresponding classical surrogate models. This suggests that understanding learning problems of this form may lead to useful insights about the power of quantum machine learning.
Quantum machine learning is an emergent field that continues to draw significant interest for its potential to offer improvements over classical algorithms in certain areas. However, training quantum models remains a challenging task, largely because of the difficulty in establishing an effective inductive bias when solving high-dimensional problems. In this work, we propose a training framework that prioritizes informative data points over the entire training set. This approach draws inspiration from classical techniques such as and to introduce an additional inductive bias through the training data itself. By selectively focusing on informative samples, we aim to steer the optimization process toward more favorable regions of the parameter space. This data-centric approach complements existing strategies such as warm-start initialization methods, providing an additional pathway to address performance challenges in quantum machine learning. We provide theoretical insights into the benefits of prioritizing informative data for quantum models, and we validate our methodology with numerical experiments on selected recognition tasks of quantum phases of matter. Our findings indicate that this strategy could be a valuable approach for improving the performance of quantum machine learning models.
Quantum machine learning is an emergent field that continues to draw significant interest for its potential to offer improvements over classical algorithms in certain areas. However, training quantum models remains a challenging task, largely because of the difficulty in establishing an effective inductive bias when solving high-dimensional problems. In this work, we propose a training framework that prioritizes informative data points over the entire training set. This approach draws inspiration from classical techniques such as curriculum learning and hard example mining to introduce an additional inductive bias through the training data itself. By selectively focusing on informative samples, we aim to steer the optimization process toward more favorable regions of the parameter space. This data-centric approach complements existing strategies such as warm-start initialization methods, providing an additional pathway to address performance challenges in quantum machine learning. We provide theoretical insights into the benefits of prioritizing informative data for quantum models, and we validate our methodology with numerical experiments on selected recognition tasks of quantum phases of matter. Our findings indicate that this strategy could be a valuable approach for improving the performance of quantum machine learning models.
Generative quantum machine learning models are trained to deduce the probability distribution underlying a given dataset, and to produce new, synthetic samples from it. The majority of such models proposed in the literature, like the Quantum Circuit Born Machine (QCBM), fundamentally work on a binary level. Real-world data, however, is often numeric, requiring the models to translate between binary and continuous representations. We analyze how this transition influences the performance of quantum models and show that it requires the models to learn correlations that are solely an artifact of the way the data is encoded, and not related to the data itself. At the same time, structure of the original data, like continuity, can be obscured in the binary representation, hindering generalization. To mitigate these effects, we propose a strategy based on Gray-codes that can be implemented with essentially no overhead, conserves structures in the data, and avoids artificial correlations in situations in which the standard approach creates them. Considering datasets drawn from various low-dimensional probability distributions, we verify that, in most cases, QCBMs using the reflected Gray code learn faster and more accurately than those with standard binary code. This shows that, as complement to specifically tailored circuit ansätze or data pre-processing, binary encodings can be used to introduce inductive biases into generative machine learning models.
The rapidly emerging paradigms of quantum machine learning (QML) and variational quantum computing (VQC) promise to combine quantum computational advantages with the powerful capabilities of machine learning and optimization. However, early attempts to naively translate classical machine learning techniques into the quantum domain have encountered severe scalability bottlenecks, both practical and theoretical. This dissertation posits that overcoming these limitations requires a fundamental shift in model and algorithm design: the deliberate integration of inductive bias. By embedding task-specific prior knowledge into quantum models and optimization strategies, this research demonstrates how to achieve the scalability required for near-term real-world applications and long-term success towards quantum advantage. This dissertation demonstrates the power of inductive bias across four methodological contributions. First, fast, gradient-free parameter and ansatz optimizers are developed to bypass costly gradient estimation on quantum computers. By explicitly embedding restriction and implicit biases into the quantum circuit ansatz and optimization method, these algorithms drastically improve resource efficiency, scaling variational quantum eigensolvers for molecular chemistry and quantum feature-map learning for classical data. Second, building on this scalable processing of high-dimensional classical data for discriminative tasks, the dissertation advances generative QML. To achieve high-quality, diverse real-world image generation, a quantum generator is designed with a strong, explicit inductive bias toward visual data, structurally reflecting both spatial image features and distribution characteristics. Third, complementary to learning from classical data, the dissertation advances QML for quantum data, processing inputs directly as quantum states rather than classical vectors. Here, a quantum Gaussian process paradigm is established, deriving a physics-informed inductive bias by encoding quantum information-theoretic assumptions. This bias guarantees provable model faithfulness and theoretical scalability. Finally, to ground this theoretical framework in physical reality, it is demonstrated on regression, classification, and optimization tasks, particularly for physical models. These physical applications close the loop to the initial quantum chemistry research, reinforcing both the overarching necessity and the natural presence of domain-specific inductive bias. Overall, the dissertation delivers timely and relevant findings that advance QML and VQC for near-term practical applications, while laying a foundation for the long-term perspective of quantum computing at scale.