Talks

We construct a simple translationally invariant, nearest-neighbor Hamiltonian on a chain of 10-dimensional qudits that makes it possible to realize universal quantum computing without any external control during the computational process, requiring only initial product state preparation. Both the quantum circuit and its input are encoded in an initial canonical basis state of the qudit chain. The computational process is then carried out by the autonomous Hamiltonian time evolution. After a time greater than a polynomial in the size of the quantum circuit has passed, the result of the computation can be obtained with high probability by measuring a few qudits in the computational basis. This result also implies that there cannot exist efficient classical simulation methods for generic translationally invariant nearest-neighbor Hamiltonians on qudit chains, unless quantum computers can be efficiently simulated by classical computers (or, put in complexity theoretic terms, unless BPP=BQP). This is joint work with Daniel Nagaj.

The history of human knowledge is often highlighted by our efforts to explore beyond our apparent horizon. In this talk, I will describe how this challenge has now evolved into our quest to understand the physics at/beyond the cosmological horizon, some twenty orders of magnitude above Columbus’s original goal. I also argue why inflationary paradigm predicts the existence of non-trivial physics beyond the cosmological horizon, and how we can use the Integrated Sachs-Wolfe effect in the Cosmic Microwave Background to probe this physics, including the nature of gravity and primordial non-gaussianity on the horizon scale.

We show that the matrix-model for noncommutative U(n) gauge theory actually describes SU(n) gauge theory coupled to gravity. The nonabelian gauge fields as well as additional scalar fields couple to a dynamical metric G_ab, which is given in terms of a Poisson structure. This leads to a gravity theory which is naturally related to noncommutativity, encoding those degrees of freedom which are usually interpreted as U(1) gauge fields. Essential features such as gravitational waves and the Newtonian limit are reproduced correctly. UV/IR mixing is understood in terms of an induced gravity action. The framework appears suitable for quantizing gravity.