## Q-Math Seminar

### A. Balmaseda (UC3M)

#### Quantum Control at the Boundary: Quantum Circuits

##### Thursday 13th of December 2018, 13:00, UC3M, Seminar Room 2.2D08

The development of Quantum Information Theory and the aim for building quantum computers has increased the relevance of controlling quantum systems. For that reason, some quantum control paradigms have been studied. The controllability of finite dimensional quantum systems is a well understood problem where one can apply the classical theory of control. However, applying such ideas to the infinite dimensional setting is not straightforward, but despite technical difficulties some results on controllability of bilinear systems are known (see for instance Chambrion et. al. [1]).

The quantum control at the boundary (QCB) method is a radically different approach to the problem of controlling the state of a qubit. Instead of seeking the control of the quantum state by directly interacting with it using external magnetic or electric fields, the control of the state will be achieved by manipulating the boundary conditions of the system. The spectrum of a quantum system, for instance an electron moving in a box, depends on the boundary conditions imposed on it, either Dirichlet or Neumann in most cases. A modification of such boundary conditions modifies the state of the system allowing for its manipulation and, eventually, its control.

The QCB paradigm has been used to show how to generate entangled states in composite systems by suitable modifications of the boundary conditions [2], but in spite of its intrinsic interest some basic issues such as the QCB controllability of simple systems has never been addressed. This talk's aim is to explore the (approximate) controllability of such a simple system, a quantum circuit (that is, a free quantum system on a graph), by using QCB.

References:

[1] T. Chambrion, P. Mason, M. Sigalotti, U. Boscain. *Controllability of the discrete-spectrum Schrödinger equation driven by an external field*. Ann. I. H. Poincaré, **26**, 329-349 (2009).

[2] A. Ibort, G. Marmo, J.M. Pérez-Pardo. *Boundary dynamics driven entanglement.* J. Phys. A: Math. Gen. **47**(38), 385301.

### Diego Martínez (UC3M)

#### Amenability in inverse semigroups and C*-algebras

##### Thursday 29th of November 2018, 13:00, UC3M, Seminar Room 2.2D08

Amenability, since von Neumann defined it back in 1929, has been an active field of study. By results of various hands, it is well known the amenability (or non-paradoxicality) of a discrete group is equivalent to the existence of a trace in the associated Roe algebra. In this talk we will continue this line of research and prove a similar result for inverse semigroups. We shall prove, for instance, that every amenable inverse semigroup has a tracial Roe algebra, while every properly infinite Roe algebra must come from a paradoxical semigroup. Furthermore, should time allow, we will discuss how these results translate into the groupoid framework. This is joint work with Pere Ara and Fernando Lledó.

### Erik Torrontegui (Instituto de Física Fundamental - CSIC)

#### Implementation and applications of a quantum neuron

##### Thursday 15th of November 2018, 13:00, UC3M, Seminar Room 2.2D08

We demonstrate that it is possible to implement a neural network with a sigmoid activation function as an efficient, many-body unitary operation. This unitary operation can be optimally implemented using an Ising model with a transverse field and fast quasi-adiabatic passage. The resulting operation is fully reversible and may have applications also in the realms of quantum sensing or entangled states generation.

### Alberto Ibort (UC3M & ICMAT)

#### On Atiyah’s ‘proof’ of Riemann’s hypothesis

##### Thursday 18th of October 2018, 13:00, UC3M, Seminar Room 2.2D08

Quite recently M. Atiyah claimed to have proved the Riemann hypothesis.

In this talk, using Atiyah’s scientific bio as a guide, we will try to understand some of the reasons that could have led him to make such an extraordinary claim.