2 November 2025 List of Tutorials

Pauli Propagation: A Framework For Simulating Quantum Systems

In this tutorial, we present the framework of Pauli propagation for simulating quantum systems and quantum circuits. This new framework is particularly suited for quickly estimating expectation values and surrogating parametrized quantum circuits, thus making it a natural candidate for emulating quantum machine learning algorithms and enabling hybrid quantum-classical approaches at scale. Pauli propagation has been shown to efficiently simulate generic noisy and noise-free quantum circuits, as well as variational quantum algorithms that do not suffer from barren plateaus. Beyond its direct applications, the framework offers an alternative perspective on quantum computations and what makes them hard to simulate classically. We will first cover the foundations of Pauli propagation, including common gates and approximations. Everything will be accompanied by pedagogical code examples using the "PauliPropagation.jl" library. Then, we will move on to our theoretical results proving polynomial runtime for classical simulations of certain families of quantum circuits, including a case study on simulating quantum convolutional neural networks in practice. Finally, we will discuss a possible future of Pauli propagation, from its algorithmic manifestations to how it can assist quantum computers at scale.