Scientific Series

I will explain how a quantum circuit together with measurement apparatuses and EPR sources can be fully verified without any reference to some other trusted set of quantum devices. Our main assumption is that the physical system we are working with consists of several identifiable sub-systems, on which we can apply some given gates locally. To achieve our goal we define the notions of simulation and equivalence. The concept of simulation refers to producing the correct probabilities when measuring physical systems. The notion of equivalence is used to enable the efficient testing of the composition of quantum operations. Unlike simulation, which refers to measured quantities (i.e., probabilities of outcomes), equivalence relates mathematical objects like states, subspaces or gates. Using these two concepts, we prove that if a system satisfies some simulation conditions, then it is equivalent to the one it is supposed to implement. In addition, with our formalism, we can show that these statements are robust, and the degree of robustness can be made explicit. Finally, we design a test for any quantum circuit whose complexity is linear in the number of gates and qubits, and polynomial in the required precision. Joint work with Frederic Magniez, Dominic Mayers and Harold Ollivier.

Complexity class MA is a class of yes/no problems for which the answer `yes\' has a short certificate that can be efficiently checked by a classical randomized algorithm. We prove that MA has a natural complete problem: stoquastic k-SAT. This is a quantum-mechanical analogue of the satisfiability problem such that k-bit clauses are replaced by k-qubit projectors with non-negative matrix elements. Complexity class AM is a generalization of MA in which the certificate may include a short conversation between Prover and Verifier. We prove that AM also has a natural complete problem: stoquastic Local Hamiltonian with a quenched disorder. The problem is to evaluate expectation value of the ground state energy of disordered local Hamiltonian with non-positive matrix elements.

The nature of an unusual class of cosmic X-ray source, dubbed "Anomalous X-ray Pulsars," was a mystery since 1982 when the first example was discovered. In this talk, I will show the recent observational evidence that unambiguously links them with another equally exotic class of object, the explosive "Soft Gamma Repeaters." The evidence todate strongly supports the picture that both are "magnetars:" isolated young neutron stars having surface magnetic fields ~1000 times greater than those in conventional neutron stars.

The initial conditions for structure formation, and hence the dark matter distribution on sub-galactic scales, depend on the microphysics of the dark matter in the early Universe. I will focus on WIMPs and explain how collisional damping and free-streaming erase perturbations on comoving scales k> ~1/pc. Consequently the first structures to form in the Universe are mini-halos with mass of order the Earth. I will then describe the status of calculations of the subsequent dynamical evolution of these mini-halos. Finally, if time permits, I'll briefly overview the microphysics of axions.

Boundary conformal field theory finds applications not only to high energy physics but also to condensed matter systems containing quantum impurities, whose world lines can sometimes be modelled as boundaries of 2-dimensional space-time. This technique leads to exact predictions for the low temperature behaviour of gated semi-conductor quantum dot devices which have been recently confirmed experimentally. I will give a non-technical overview of both the theory and the experiments.

If low-scale supersymmetry exists in nature, then it it will be very likely that a number of superpartners will be discovered at the LHC. It is also very likely, however, that much of the supersymmetric spectrum will go unobserved, leaving many important holes in our understanding of the TeV scale. Direct and indirect astrophysical probes of neutralino dark matter can enable for some of these holes to be filled. By studying the interactions of the lightest neutralino, in many models, a much more complete understanding of supersymmetry can be achieved than is possible by using hadron colliders alone.

We discuss motivations, observational constraints and consequences of modifying the fundamental laws of gravity at large distances. Such modifications of gravity can be the reason for the observed late-time acceleration of the Universe, and can be differentiated from conventional dark energy via precision cosmology. The inevitable additional polarizations of graviton lead to observably large perihelion precession of the Lunar and Martian orbits. These theories also have potentially observable consequences at LHC .