Talks

There has been a dream that matter and gravity can be unified in a fundamental theory of quantum gravity. One of the main philosophies to realize this dream is that matter may be emergent degrees of freedom of a quantum theory of gravity. We study the propagation and interactions of braid-like chiral states in models of quantum gravity in which the states are (framed) four-valent spin networks embedded in a topological three manifold and the evolution moves are given by the dual Pachner moves. There are results for both the framed and unframed case. We study simple braids made up of two nodes which share three edges, which are possibly braided and twisted. We find three classes of such braids, those which both interact and propagate, those that only propagate, and the majority that do neither. These braids may serve as fundamental matter content.

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.