From Quantum Matter to Quantum Computers

Phase diagrams of quantum materials often contain several ordered states, such as magnetism or superconductivity, that are in close proximity to one another as a function of some tuning parameter such as doping, pressure, or magnetic field. From an experimental perspective, it is desirable to have a tuning parameter that can be continuously changed during an experiment. With methods pioneered over the past decade that use piezoelectric actuators to supply forces at low temperatures, elastic tuning, in which one manipulates a crystal by tensioning or compressing it, has become a powerful method for investigating quantum materials. I will introduce some key concepts in elasticity and describe how we can use stress and strain to both tune materials through large regions of their phase diagrams and to probe underlying symmetries.

I will give a broad introduction to quantum simulation using ultracold atoms. I will motivate the enduring interest in this topic, enumerate some major results, and summarize the state of play. I will give some insights on the experimental techniques and the practicalities of operating a quantum gas machine.

The importance of machine learning (ML) in quantum physics has been rising, especially in studies of quantum phases of matter or finding ground states of interacting Hamiltonians. The more widespread its use, the more urgent the critical questions of how to extract meaningful physical insights from ML. I will introduce you to the world of interpreting and explaining neural networks and explain the differences between the two. Drawing on case studies from our research, I will present the limitations of explainability and the advantages of interpretable architectures. I will argue that the most insightful, interpretable models for non-tabular data are largely task-dependent, and I will share our recipe for their design so that you can apply it in your future research!

The practical quantum-computing frontier is now centered on extracting useful results from today’s noisy 50 to 150-qubit devices. Reaching this utility scale—where quantum computations often challenge the classical methods—depends on an often-overlooked software layer that orchestrates error suppression, circuit transpilation, error-mitigation workflows, and results post-processing. This middleware stack is, in itself, an exciting research playground that combines quantum-many-body intuition, advanced numerical methods such as tensor networks, and modern machine-learning tools. In this lecture, I will provide an overview of the quantum middleware landscape, complemented by a hands-on tutorial that demonstrates how its careful application can push many-body simulations to regimes close to the limits of classical simulations, offering students a tangible entry point into state-of-the-art quantum research.

Tensor networks are a powerful tool for compressing high-dimensional mathematical objects. Traditionally their main application has been to quantum wavefunctions in zero or one spatial dimensions. There are sophisticated tensor network methods for two and three dimensions but which can be quite expensive. In recent years, new directions for tensor networks have been expanding their range of applications, building on algorithms from fields such as belief propagation from spin-glass physics and tensor learning algorithms from applied math. I will survey these new algorithms which give a scalable and intellectually interesting route to 2D and 3D physics and which offer methods to perform machine learning using tensor networks.

Quantum observables in the form of few-point correlators are the key to characterizing the dynamics of quantum many-body systems. In dynamics with fast entanglement generation, quantum observables generally become insensitive to the details of the underlying dynamics at long times due to the effects of scrambling. In experimental systems, repeated time-reversal protocols have been successfully implemented to restore sensitivities of quantum observables. Using a 103-qubit superconducting quantum processor, we characterize ergodic dynamics using the second-order out-of-time-order correlators, OTOC$^{(2)}$. In contrast to dynamics without time reversal, OTOC$^{(2)}$ are observed to remain sensitive to the underlying dynamics at long time scales. Furthermore, by inserting Pauli operators during quantum evolution and randomizing the phases of Pauli strings in the Heisenberg picture, we observe substantial changes in OTOC$^{(2)}$ values. This indicates that OTOC$^{(2)}$ is dominated by constructive interference between Pauli strings that form large loops in configuration space. The observed interference mechanism endows OTOC$^{(2)}$ with a high degree of classical simulation complexity, which culminates in a set of large-scale OTOC$^{(2)}$ measurements exceeding the simulation capacity of known classical algorithms. Further supported by an example of Hamiltonian learning through OTOC$^{(2)}$, our results indicate a viable path to practical quantum advantage.

Electrons like photons have a wave-nature and can transmit quantum information. Metallic wires could act as convenient waveguides for such processes. Unlike photons in a waveguide, however, electrons in a metal are interacting Fermions at high density, which strongly decoheres phase information. In effect, semi-classical theories that treat electrons as (quantum-renormalized) billard balls explain conduction processes generally well. A key thrust in quantum materials research is to find materials platforms in which coherence can nonetheless be observed and ideally utilized. Recently, materials based on the structural motif of the Kagome web have attracted significant attention for their tendency to host such strongly coupled phases. In particular, the centro-symmetric layered Kagome metal (K,Rb,Cs)V$_3$Sb$_5$ has entered the focus of experimental and theoretical research. They host a charge-density-wave type transition at elevated temperatures ~100K, followed by a superconducting transition at 3K. Yet there is another type of electronic state which thus far eludes exact microscopic identification. A series of experimental probes detects the onset of anomalous behavior around T’~30-40K, including thermal Hall, $\mu$SR, NMR, magnetic torque, and Kerr rotation. The anomalous low-temperature state carries the characteristics of a chiral, nematic and time-reversal-symmetry breaking fluid (all of which are under most active debate currently). The talk will focus on a recently discovered signature of long range electron coherence within this disordered multi-band semi-metal that evidences quantum coherence over long distances and at high temperatures. While conflicting with single-particle physics, it will likely find its resolution in a complex manybody state with the ability to carry current, akin to that of superconductivity.

A promising near-term application of quantum computers is that of solving combinatorial optimisation problems. This is largely done by encoding hard optimisation problems into Ising spin glass Hamiltonians, whose ground states correspond to the corresponding desired solutions. The solution is then found by, for example, adiabatically connecting some easy-to-prepare ground state of a different Hamiltonian to the desired ground state. The simplest example of a quantum algorithm to do so is the Quantum Approximate Optimisation Algorithm (QAOA), which is effectively a trotterization of quantum annealing. In this talk I will explore the theory, challenges and recent advances in the study of QAOA, as well as a practical look into what kind of real-world applications one might address with quantum optimisation.