List of Projects
Open Quantum Systems
Tutor: Gabriel Almeida
Abstract
Quantum mechanics is often introduced through the evolution of isolated systems governed by the Schrödinger equation. However, realistic quantum devices are never perfectly isolated: interactions with their environment lead to decoherence, dissipation, and irreversible dynamics. This tutorial provides an introduction to the theoretical and computational tools used to describe such open quantum systems.
What makes quantum circuits hard to simulate?
Tutor: Sagar Pratapsi
Abstract
What makes quantum circuits hard to simulate? Is it the exponential size of the Hilbert space, high entanglement, or something else? In this tutorial, we will answer this question by looking at Clifford circuits: quantum circuits that look hard but are easy to simulate classically using the stabilizer formalism. Then, we will study a special ingredient called "quantum magic" that, when added to Clifford circuits, takes us outside the easy-to-simulate stabilizer world and enables universal quantum computation.
Simulating Many-Body Dynamics with Quantum Computers
Tutor: Rafael Torres
Abstract
Besides serving as tools for quantum algorithms, quantum circuits provide a natural language for describing how quantum systems evolve in time. In this tutorial, we will use quantum circuits to simulate a many-body system, focusing on the paradigmatic transverse-field Ising model of interacting quantum spins. Participants will learn how to construct its time evolution, measure physical observables, and explore the growth of quantum entanglement. We will conclude by running a small spin chain on real quantum hardware and connecting these ideas to broader quantum algorithms.
2D Materials: Twisting Quantum Matter
Tutor: Nicolau Sobrosa
Abstract
Two-dimensional materials have fundamentally rewritten the rules of condensed matter physics. This session bridges foundational concepts in solid-state physics and quantum matter, guiding students from simple tight-binding models to the rich physics of moiré superlattices.
After introducing the tight-binding formalism for describing electrons in solids, we will apply it to graphene, the first stable two-dimensional material, where charge carriers behave as massless Dirac fermions. We will then explore how symmetry breaking and the addition of further layers give rise to new physics, including the opening of a band gap in hexagonal boron nitride (hBN) and the distinctive electronic properties of bilayer graphene.
The session will culminate with twisted bilayer graphene (tBLG). We will see how rotating two graphene layers by a small angle—approximately 1°—creates a moiré pattern and nearly flat electronic bands. Finally, participants will numerically implement a computational method for calculating these bands, a fundamental step towards studying the remarkable quantum phases found in this material, including unconventional superconductivity.
Non-Equilibrium Critical Phenomena
Tutor: Tiago Jorge
Abstract
Equilibrium phase transitions are usually understood through well-defined notions of free energies, order parameters, and symmetry breaking. But many modern quantum systems are intrinsically out of equilibrium: they can be driven in numerous ways, from periodic forces to continuous monitoring.
In this tutorial, we review how symmetry and dimensionality constrain equilibrium ordering, focusing on the Mermin–Wagner theorem and the absence of true continuous symmetry breaking in two-dimensional equilibrium systems. We will then briefly review some examples of genuine out-of-equilibrium phenomena in the context of quantum matter. Finally, students will simulate the Vicsek model, a toy model of locally aligning self-propelled particles that acts as a nonequilibrium “counterexample” to the Mermin–Wagner theorem.
Simulations of Many-Body Quantum Systems
Tutor: Henrique Veiga
Abstract
Interactions are ubiquitous in realistic models of quantum matter. In this tutorial, we will explore the connection between experimentally relevant one-dimensional many-body systems and higher-dimensional classical interacting systems. Using a quantum spin chain, we will examine how inherently quantum properties can be understood by studying the equilibrium properties of a two-dimensional Ising model. Participants will start by studying the ground-state energy of the interacting system via exact diagonalization. After illustrating the scaling limits of this direct approach, we will map the quantum problem onto the Ising model. By doing so, key physical insights become accessible through Monte Carlo simulations. Participants will understand how this mapping bypasses the limitations of exact diagonalization and how statistical sampling converges to physically meaningful results.