Publications

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An introduction to large deviations with applications in physics

Ivan N. Burenev, Daniël W. H. Cloete, Vansh Kharbanda, Hugo Touchette

SciPost Phys. Lect. Notes 104 (2025) · published 23 October 2025 | · pdf

These notes are based on the lectures that one of us (HT) gave at the Summer School on the "Theory of Large Deviations and Applications," held in July 2024 at Les Houches in France. They present the basic definitions and mathematical results that form the theory of large deviations, as well as many simple motivating examples of applications in statistical physics, which serve as a basis for the many other lectures given at the school that covered more specific applications in biophysics, random matrix theory, nonequilibrium systems, geophysics, and the simulation of rare events, among other topics. These notes extend the lectures, which can be accessed online, by presenting exercises and pointer references for further reading.

1 citation
Stochastic resetting and large deviations

Martin R. Evans, John C. Sunil

SciPost Phys. Lect. Notes 103 (2025) · published 16 October 2025 | · pdf

Stochastic resetting has been a subject of considerable interest within statistical physics, both as means of improving completion times of complex processes such as searches and as a paradigm for generating nonequilibrium stationary states. In these lecture notes we give a self-contained introduction to the toy model of diffusion with stochastic resetting. We also discuss large deviation properties of additive functionals of the process such as the cost of resetting. Finally, we consider the generalisation from Poissonian resetting, where the resetting process occurs with a constant rate, to non-Poissonian resetting.
High-dimensional random landscapes: From typical to large deviations

Valentina Ros

SciPost Phys. Lect. Notes 102 (2025) · published 13 October 2025 | · pdf

We discuss tools and concepts that emerge when studying high-dimensional random landscapes, i.e., random functions on high-dimensional spaces. As an illustrative example, we consider an inference problem in two forms: low-rank matrix estimation (case 1) and low-rank tensor estimation (case 2). We show how to map the inference problem onto the optimization problem of a high-dimensional landscape, which exhibits distinct geometrical properties in the two cases. We discuss methods for characterizing typical realizations of these landscapes and their optimization through local dynamics. We conclude by highlighting connections between the landscape problem and large deviation theory.

1 citation
Les Houches lectures on flow networks in biology

Swarnavo Basu, Karen Alim

SciPost Phys. Lect. Notes 101 (2025) · published 10 October 2025 | · pdf

Flows are essential to transport resources over large distances. As soon as diffusion becomes time-limiting, flows are needed. Flows are key for the function of multiple human organs, from the blood vasculature to the lungs, the digestive tract, the lymphatic system, and many more. While physics governs the flow dynamics, biology's response to flows governs the flow network architecture. We start with the fluid physics of Stokes flow, the prerequisite to describe the flows in biological flow networks. Then we explore how the network adaptation dynamics of biological flow networks reorganize network architecture to minimize flow dissipation or homogenize transport, storing memories of past flows along the way.
Numerical aspects of large deviations

Alexander K. Hartmann

SciPost Phys. Lect. Notes 100 (2025) · published 30 September 2025 | · pdf

An introduction to numerical large-deviation sampling is provided. First, direct biasing with a known distribution is explained. As simple example, the Bernoulli process is used throughout the text. Next, Markov chain Monte Carlo (MCMC) simulations are introduced. In particular, the Metropolis-Hastings algorithm is explained. As first implementation of MCMC, sampling of the plain Bernoulli model is shown. Next, an exponential bias is used for the same model, which allows one to obtain the tails of the distribution of a measurable quantity. This approach is generalized to MCMC simulations, where the states are vectors of $U(0,1)$ random entries. This allows one to use the exponential or any other bias to access the large-deviation properties of rather arbitrary random processes. Finally, some recent research applications to study more complex models are discussed.
Many-body open quantum systems

Rosario Fazio, Jonathan Keeling, Leonardo Mazza, Marco Schirò

SciPost Phys. Lect. Notes 99 (2025) · published 14 August 2025 | · pdf

These lecture notes discuss the recent theoretical advances in the understanding of open quantum many-body physics in platforms where both dissipative and coherent processes can be tuned and controlled to a high degree. We start by reviewing the theoretical frameworks and methods used to describe and tackle open quantum many-body systems. We then discuss the use of dissipative processes to engineer many-body stationary states with desired properties and the emergence of dissipative phase transitions arising out of the competition between coherent evolution and dissipation. We review the dynamics of open quantum many body systems in the presence of correlated many-body dissipative processes, such as heating and many-body losses. Finally we provide a different perspective on open quantum many-body systems by looking at stochastic quantum trajectories, relevant for the case in which the environment represents a monitoring device, and the associated measurement-induced phase transitions.

16 citations
Lectures in quantum gravity

Ivano Basile, Luca Buoninfante, Francesco Di Filippo, Benjamin Knorr, Alessia Platania, Anna Tokareva

SciPost Phys. Lect. Notes 98 (2025) · published 7 August 2025 | · pdf

Formulating a quantum theory of gravity lies at the heart of fundamental theoretical physics. This collection of lecture notes encompasses a selection of topics that were covered in six mini-courses at the Nordita PhD school "Towards Quantum Gravity". The scope was to provide a coherent picture, from its foundation to forefront research, emphasizing connections between different areas. The lectures begin with perturbative quantum gravity and effective field theory. Subsequently, two ultraviolet-complete approaches are presented: Asymptotically safe gravity and string theory. Finally, elements of quantum effects in black hole spacetimes are discussed.

3 citations
Hands-on introduction to randomized benchmarking

Ana Silva, Eliska Greplova

SciPost Phys. Lect. Notes 97 (2025) · published 21 July 2025 | · pdf

Randomized benchmarking techniques have been an essential tool for assessing the performance of contemporary quantum devices. The goal of this tutorial is to provide a pedagogical, self-contained, introduction to randomized benchmarking. With this intention, every chapter is also supplemented with an accompanying Python notebook, illustrating the essential steps of each protocol. In addition, we also introduce more recent trends in the field that bridge shadow tomography with randomized benchmarking, namely through the gate-set shadow protocol.
Introduction to the usage of open data from the Large Hadron Collider for computer scientists in the context of machine learning

Timo Saala, Matthias Schott

SciPost Phys. Lect. Notes 96 (2025) · published 23 June 2025 | · pdf

Deep learning techniques have evolved rapidly in recent years, significantly impacting various scientific fields, including experimental particle physics. To effectively leverage the latest developments in computer science for particle physics, a strengthened collaboration between computer scientists and physicists is essential. As all machine learning techniques depend on the availability and comprehensibility of extensive data, clear data descriptions and commonly used data formats are prerequisites for successful collaboration. In this study, we converted open data from the Large Hadron Collider, recorded in the ROOT data format commonly used in high-energy physics, to pandas DataFrames, a well-known format in computer science. Additionally, we provide a brief introduction to the data's content and interpretation. This paper aims to serve as a starting point for future interdisciplinary collaborations between computer scientists and physicists, fostering closer ties and facilitating efficient knowledge exchange.
Simulation of the 1d XY model on a quantum computer

Marc Farreras, Alba Cervera-Lierta

SciPost Phys. Lect. Notes 95 (2025) · published 11 June 2025 | · pdf

The field of quantum computing has grown fast in recent years, both in theoretical advancements and the practical construction of quantum computers. These computers were initially proposed, among other reasons, to efficiently simulate and comprehend the complexities of quantum physics. In this paper, we present a comprehensive scheme for the exact simulation of the 1-D XY model on a quantum computer. We successfully diagonalize the proposed Hamiltonian, enabling access to the complete energy spectrum. Furthermore, we propose a novel approach to design a quantum circuit to perform exact time evolution. Among all the possibilities this opens, we compute the ground and excited state energies for the symmetric XY model with spin chains of $n=4$ and $n=8$ spins. Further, we calculate the expected value of transverse magnetization for the ground state in the transverse Ising model. Both studies allow the observation of a quantum phase transition from an antiferromagnetic to a paramagnetic state. Additionally, we have simulated the time evolution of the state all spins up in the transverse Ising model. The scalability and high performance of our algorithm make it an ideal candidate for benchmarking purposes, while also laying the foundation for simulating other integrable models on quantum computers.

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