Date: Friday 10 March

Who: Roman Orus

Seminar type: Research Seminar

Time: 12 Noon

Where: Interaction Room

Abstract:
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. On the other hand, I will describe results concerning the classical simulability of quantum many-body systems by means of Matrix Product States. In particular, I will present an approximated classical simulation of a quantum algorithm by adiabatic evolution solving hard instances of an NP-Complete problem up to 100 qubits.

Date: Thursday 9 March

Who: Rolando Somma

Seminar type: Research Seminar

Time: 4pm-5pm

Where: Conference Room

Abstract:
During the last decade it has been shown that the generalized coherent states (GCSs), which are a generalization of the known bosonic gaussian states to other physical systems like spins, fermions, etc., play a decisive role in different areas of quantum mechanics and quantum information. In this talk, I’ll review the notion of GCSs and I will show how they can be used to characterize the entanglement of different physical systems that satisfy a particle statistics other than the one given by the Pauli algebra. This will lead to the definition of “generalized entanglement”, a relative measure of entanglement that depends on the features of the observer (i.e., the relevant observables of the physical system). In particular, I’ll show how such a measure can be used to characterize quantum phase transitions in some many-body models.

Second, I will show that if a quantum computation involves only GCSs relative to a “small” set of observables (i.e., a computation evolving generalized unentangled states only), then such a computation can be simulated efficiently with a conventional computer at exponential accuracy. Other results include the properties of GCSs to faithfully represent the ground state of a family of many-body Hamiltonians, the efficient preparation of GCSs on a quantum computer, their role in open quantum systems, etc.

Date: Tuesday 7 March

Who: Roman Orus

Seminar type: Tutorial Seminar

Time: 4-5pm

Where: Conference Room

Abstract:
Part 2: Here I will present the basic notions on conformal field theory, trying not to enter in too many technicalities. The notions of conformal symmetry, conformal field theory, and concepts like the central charge, the Virasoro operators and the Verma module will be introduced.

Date: Friday 3 March

Who: Robert Spalek

Seminar type: Research Seminar

Time: 12 Midday

Where: Interaction Room

Abstract:
Quantum computers can solve certain problems substantially faster than classical computers, for example they can factor numbers in polynomial time whereas the best known classical algorithm runs in (almost) exponential time. However, for most practical problems like Grover’s search, the speedup of the quantum algorithm is only polynomial.
Surprisingly, a (tight) lower bound for quantum search was shown 2 years before the discovery of the algorithm in a very influential paper by Bennett, Bernstein, Brassard, and Vazirani.

The method of BBBV which only worked for the OR function, was extended by Ambainis to all functions, and later generalized in many directions by many people. Szegedy and myself then showed that all versions of this so-called adversary method are actually equivalent (hence one can forget about the complicated looking ones The adversary method is very simple to apply and yet it gives tight lower bounds for most functions, for example for OR, majority, parity, binary search, sorting, and graph problems.

I would like to present a variant of the adversary bound called spectral bound, which is based on the spectral norm of a non-negative symmetric matrix. This lower bound has an amazingly simple one-page proof and all other lower bounds easily follow from it.

Date: Thursday 2 March

Who: Roman Orus

Seminar type: Tutorial Seminar - Part I

Time: 4-5pm

Where: Conference Room

Abstract:
Part 1: here I will present the basic ideas of the renormalization group and sketch its importance in quantum many-body systems. After a motivation in real space, I will explain the basics of renormalization in momentum space through the example of a gaussian theory. The renormalization of non-gaussian theories will also be introduced.