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Tuesday, October 18, 2011 12:00 pm - 1:00 pm EDT (GMT -04:00)

David Gosset: Small gaps, localization, and the quantum adiabatic algorithm

Abstract

Stoquastic Hamiltonians are the class of Hamiltonians that can be studied numerically using standard Quantum Monte Carlo methods--these are the Hamiltonians which do not suffer from the sign problem. These Hamiltonians can also be easier to study analytically because of their connection to nonnegative matrices. In the first part of this talk I will review the arsenal of analytic and numerical tools pertaining to stoquastic Hamiltonians. I will then discuss a variational lower bound for the ground state energy of these Hamiltonians.

Monday, October 31, 2011 12:30 pm - 1:30 pm EDT (GMT -04:00)

Fernando Brandao: Random quantum circuits are approximate polynomial-designs

Abstract

An approximate unitary t-design is a distribution of unitaries that mimic properties of the Haar measure for polynomials (in the entries of the unitaries) of degree up to t. It has been a conjecture in the theory of quantum pseudo-randomness that polynomial sized random quantum circuits form an approximate unitary poly(n)-design. Unfortunately, up to now, the best result known is that polynomial random quantum circuits are unitary 3-designs.