Scientific Series

By storing quantum information in the degenerate ground state of a Hamiltonian, it is hoped that it can be made quite robust against noise processes. We will examine this situation, with particular emphasis on the Toric code in 2D, and show how adversarial effects, either perturbations to the Hamiltonian or interactions with an environment, destroy the stored information extremely quickly.

We show that if a condensed matter system (a quantum qbit system) is in a string-net condensed state, then the low energy excitation in such a system can be gauge bosons (such as photons) and fermions (such as electrons). Such a system is actually the ether that we have been looking for 150 years. We will also discuss a quantum qbit system that may even give rise to emergent gravitons.

I show that physical devices that perform observation, prediction, or recollection share an underlying mathematical structure. I call devices with that structure ``inference devices\'\'. I present a set of existence and impossibility results concerning inference devices. These results hold independent of the precise physical laws governing our universe. In a limited sense, the impossibility results establish that Laplace was wrong to claim that even in a classical, non-chaotic universe the future can be unerringly predicted, given sufficient knowledge of the present. Alternatively, these impossibility results can be viewed as a non-quantum mechanical ``uncertainty principle\'\'. Next I explore the close connections between the mathematics of inference devices and of Turing Machines. I end by informally discussing the philosophical implications of these results, e.g., for whether the universe ``is\'\' a computer.

The Lee-Wick model has recently been put forwards as an alternative to supersymmetry for solving the hierarchy problem of particle physics. I will show that, modulo important consistency questions, coupling the Lee-Wick model to cosmology leads to a bouncing universe cosmology with a scale-invariant spectrum of cosmological fluctuations emerging from quantum vacuum fluctuations in the contracting phase.

We discuss the possibility that spacetime geometry may be an emergent phenomenon. This idea has been motivated by the Analogue Gravity programme. An \'effective gravitational field\' dominates the kinematics of small perturbations in an Analogue Model. In these models there is no obvious connection between the \'gravitational\' field tensor and the Einstein equations, as the emergent spacetime geometry arises as a consequence of linearising around some classical field. After a brief introduction on this topic, we present our recent contributions to the field.

We analyze how quantum complexity poses bounds to the simulation of quantum systems. While methods as Density Functional Theory (DFT) and the Density Matrix Renormalization Group (DMRG) work very well in practice, essentially nothing on the formal requirements is known. In this talk, we consider these methods from a quantum complexity perspective: First, we discuss DFT which encapsulates the difficulty of solving the Schroedinger equation in a universal functional and show that this functional cannot be efficiently computed unless several complexity classes collapse. Second, we consider DMRG, a method to deal with quantum spin chains, and show that even under reasonable assumptions -- a polynomial gap and matrix product ground states -- finding the ground state is still a computationally hard problem. Beyond pinpointing the limitations of the methods, this helps us to understand under which assumptions we might be able to prove their convergence.

We review how renormalization, born in quantum field theory has evolved into a rather universal tool to analyze the change of physical laws under scaling. Recent developments in non commutative geometry with hopefully potential applications to the quantization of gravity will be discussed.

The unparalleled empirical success of quantum theory strongly suggests that it accurately captures fundamental aspects of the workings of the physical world. The clear articulation of these aspects is of inestimable value --- not only for the deeper understanding of quantum theory in itself, but for its further development, particularly for the development of a theory of quantum gravity. Recently, there has been growing interest in elucidating these aspects by expressing, in a less abstract mathematical language, what we think quantum theory might be telling us about how nature works, and trying to derive, or reconstruct, quantum theory from these postulates. In this talk, I describe a simple reconstruction of the finite- dimensional quantum formalism. The derivation takes places with a classical probabilistic framework equipped with the information (or Fisher-Rao) metric, and rests upon a small number of elementary ideas (such as complementarity and global gauge invariance). The complex structure of quantum formalism arises very naturally. The derivation provides a number of non-trivial insights into the quantum formalism, such as the extensive nature of the role of information geometry in determining the quantum formalism, the importance of global gauge invariance, and the importance (or lack thereof) of assumptions concerning separated systems.