# SDP relaxations for the certification of properties of many-body quantum states (Flavio Baccari)

### SDP relaxations for the certification of properties of many-body quantum states

- Date: Dec 6, 2018
- Time: 11:30
- Speaker: Flavio Baccari
- ICFO – The Institute of Photonic Sciences
- Location: Max-Planck-Institut für Quantenoptik
- Room: B 2.46
- Host: MPQ, Theory Division

In both these cases, the certification problem is challenging due to the well-known fact that the number of parameters needed to describe a many-body system increases exponentially with the number of particles. In the talk, I will first review methods for polynomial optimisation based on hierarchies of semidefinite programming (SDP). Then, I will show two applications of these methods in a many-body context. First, I will present a technique for device-independent entanglement detection that involves a polynomial number of correlation functions. I will apply this technique to several physically relevant situations allowing us to detect entangled states for systems up to few tens of qubits. Second, I will move to the computation of ground states of classical spin systems. I will show that by combining SDP methods with two other techniques, known as branch and bound and chordal extension, it is possible to design a method for the computation of ground-state spin configurations with a favorable scaling. An advantage of the resulting method is that, with polynomial effort, it provides upper and lower bounds to the ground-state energy, so that the error in the approximation is under control. I will also present a benchmark on a D-Wave 2000Q device, showing that the method can be used to verify the solutions of the quantum annealer, as well as detect situations in which the quantum solution differs from the actual ground-state configuration.