Talks

Colloquium: tba

Phases Transitions of Quantum Control

The ability to study quantum matter with the help of quantum simulators depends on our ability to prepare and manipulate the state of physical systems. Key to understanding the difficulty of preparing states of interacting degrees of freedom is the control landscape -- the mapping assigning to every control protocol its figure-of-merit (or cost-function) value. Numerically, optimal control algorithms strive to find a better local minimum of the control landscape; the global minimum corresponds to the optimal protocol. In few- and multi-qubit systems, I will show that rapid changes can appear in the search for optimal two-mode (or bang-bang) state preparation protocols, reminiscent of phase transitions. These "control phase transitions" can be interpreted within the framework of Statistical Mechanics by viewing the cost function as "energy" and control protocols – as "spin configurations". I will show that optimal qubit control exhibits continuous and discontinuous phase transitions familiar from macroscopic systems: correlated/glassy phases, and spontaneous symmetry breaking. Time permitting, I will then present numerical evidence for a universal spin-glass-like transition controlled by the protocol time duration. In the transverse field Ising model, the glassy critical point is distinguished by a control landscape that features a proliferation of clusters of local minima separated by extensive barriers, which bears a strong resemblance with random satisfiability problems.

Korrelationstage 2021

WS Colloquium: Unconventional superconductivity

Superconductivity comes in a wide variety of incarnations including conventional s-wave, high-Tc d-wave, and topological p-wave. While these states are well defined theoretically, they are extremely difficult to distinguish experimentally: all superconductors have Cooper pairs, a Meissner effect, and a zero-resistance state, while any differences between states are subtle. I will give an overview of the experimental situation with a particular focus on how to find a bulk, three-dimensional topological superconductor, drawing on my own group's research on Sr2RuO4 and UTe2.

tba

Colloquium: What to do with a near-term quantum computer?

In 2019, Google researchers carried out an experiment where they achieved "quantum supremacy". This is defined as when a quantum computer performs *any* task in a way that a classical computer takes impractical amounts of time to simulate its outcome. This is a huge milestone for the field, but several milestones lie ahead. In this talk, I will describe a potential algorithmic road to "quantum advantage", ie. the moment when a quantum computer carries out a *practical* task on a system that is unreachable by current classical computers. To reach quantum advantage presumably many years of hardware development and algorithmic development lie ahead of us. The current era of quantum computing, coined near-term intermediate-scale quantum computing (NISQ) by John Preskill presents many challenges and opportunities. I will discuss this algorithmic road in the context of algorithms for the simulation of molecules and materials, as well as will briefly mention quantum machine learning applications.

Field theory of higher-order topological crystalline responses, generalized global symmetries and elasticity tetrads

I discuss the higher-order topological field theory and response of topological crystalline insulators with no other symmetries. The geometry and topology of the system is organised in terms of the elasticity tetrads which are ground state degrees of freedom labelling the lattice geometry, topological responses and higher-form conservation laws on sub-dimensional manifolds of the bulk system. In a crystalline insulator in arbitrary dimensions, they classify the topological responses in a transparent fashion in terms of a lattice embedding and higher-order global symmetries. In the continuum limit of the lattice, the elasticity tetrads can be used to derive the higher-order or embedded topological responses to global U(1) symmetries, such as electromagnetic gauge fields with explicit formulas for the quasi-topological invariants in terms Green's functions. I will discuss the examples of topological polarisation, quantum Hall and axionic charge density wave and multipole insulators in detail. The proposed framework further bridges the recently appreciated connections between topological field theory, higher form symmetries and gauge fields, fractonic excitations, elasticity and topological defects with restricted mobility in crystalline insulators.

Colloquium: tba

IMPRS Seminar: tba

IMPRS Seminar: tba

Confining Vorticity Surfaces and Irreversibility

Colloquium: tba

IMPRS Online Seminar: tba

IMPRS Online Seminar: tba

Colloquium: May's Instability in Firm Networks

Colloquium: tba

Colloquium: tba

IMPRS Online Seminar: tba

IMPRS Online Seminar: tba

Colloquium: tba

Colloquium: tba