This series consists of talks in the area of Quantum Information Theory.
I will present an efficient quantum algorithm for an additive
approximation of the famous Tutte polynomial of any planar graph at
any point. The Tutte polynomial captures an extremely wide range of
interesting combinatorial properties of graphs, including the
partition function of the q-state Potts model. This provides a new
class of quantum complete problems.
Thermodynamics places surprisingly few fundamental constraints on
information processing. In fact, most people would argue that it imposes
only one, known as Landauer's Principle: a process erasing one bit of
information must release an amount kT ln 2 of heat. It is this simple
observation that finally led to the exorcism of Maxwell's Demon from
statistical mechanics, more than a century after he first appeared.
Ignoring the lesson implicit in this early advance, however, quantum
In this talk I will expose different results concerning the properties of quantum many-body systems: on the one hand, I will introduce the concept of fine-grained entanglement loss together with its relation with majorization relations along parameter flows and Renormalization Group flows. The machinery of Conformal Field Theory will allow us to derive very general analytical properties, and some examples -like the XY quantum spin chain- will also be considered.
I will discuss the design of degenerate quantum error correcting codes for an arbitrary Pauli channel. At noise levels slightly beyond those for which a random stabilizer code does not allow high fidelity transmission with a nonzero rate, our codes usually have a rate which is strictly positive. In fact, there exist Pauli channels for which our codes outperform a random stabilizer code whenever the random coding rate is less than 0.04, which is a couple of orders of magnitude larger than the previous examples of this effect.
The concept of entanglement plays a central role in the field of strongly correlated quantum systems: it gives rise to fascinating phenomena such as quantum phase transitions and topological quantum order, but also represents a main obstacle to our ability to simulate such systems. We will discuss some new developments in which ideas, originating from the field of quantum information theory, led to valuable insights into the structure of entanglement in quantum spin systems and to novel powerful simulation methods