Other Physics

With the groundbreaking gravitational wave detections from LIGO/VIRGO, we have entered the era where we can actually observe the action of strongly curved spacetime originally predicted by Einstein.  Going hand in hand with this, there has been a renaissance in the theoretical and computational tools we use to understand and interpret the dynamics of gravity and matter in this regime.  I will describe some of the rich behavior exhibited by sources of gravitational waves such as the mergers of black holes and neutron stars. I will also discuss some of the open questions, and what these events could teach us, not only about the extremes of gravity, but about the behavior of matter at nuclear densities, the solution of astrophysical mysteries, and even the existence of new particles.

The surface code is currently the leading proposal to achieve fault-tolerant quantum computation. Among its strengths are the plethora of known ways in which fault-tolerant Clifford operations can be performed, namely, by deforming the topology of the surface, by the fusion and splitting of codes, and even by braiding engineered Majorana modes using twist defects. Here, we present a unified framework to describe these methods, which can be used to better compare different schemes and to facilitate the design of hybrid schemes. Our unification includes the identification of twist defects with the corners of the planar code. This identification enables us to perform single-qubit Clifford gates by exchanging the corners of the planar code via code deformation. We analyze ways in which different schemes can be combined and propose a new logical encoding. We also show how all of the Clifford gates can be implemented with the planar code, without loss of distance, using code deformations, thus offering an attractive alternative to ancilla-mediated schemes to complete the Clifford group with lattice surgery.

I will give an overview of the causal set approach to quantum gravity, and what makes this "fork in the road" distinct from other approaches.  Motivated by deep theorems in Lorentzian geometry, causal set theory (CST) posits that the underlying fabric of spacetime is  atomistic and encoded in a locally finite partially ordered set. In  the continuum  approximation,  the partial order corresponds to the causal structure, and the cardinality to the conformal factor.  Together, these give the approximate continuum geometry.  Lorentz invariance emerges as a consequence, but brings with it a certain  "non-locality”, which distinguishes CST  from other approaches in an essential way. It also makes the  reconstruction of spacetime geometry from the causal set particularly challenging.  I will describe some of the progress we have made in this geometric reconstruction program. I will then describe a particular formulation of CST dynamics inspired by the continuum path integral and discuss what we have learnt so far and where it is taking us. 

There is a long tradition of formulating Quantum Theory in an operational manner.  In one version of this a circuit is formed by wiring together operations. Each operation has knob settings and outcomes (lights flashing, detectors clicking, ..).  The question raised and answered in this colloquium is whether we can do the same for General Relativity.  There are hurdles that have to be overcome to do this - in particular, we need to define a diffeomorphism invariant notion of operations, identify what the knob settings and outcomes are, and what the wiring corresponds to.   In this colloquium I will provide an outline of how to formulate General Relativity like this providing a possibilistic calculus (we can calculate whether operationally described situations are possible or not).  This provides the beginnings of an operational approach to the problem of Quantum Gravity.  This talk is based on arxiv:1608.06940.  

 I will present several studies showing a surprising pattern. Not only can preschoolers learn abstract higher-order principles from data, but younger learners are actually better at inferring unusual or unlikely principles than older learners and adults. This pattern also holds for children in Peru and in Headstart programs in Oakland, California. I relate this pattern to computational ideas about search and sampling, to evolutionary ideas about human life history, and to neuroscience findings about the negative effects of frontal control on wide exploration. My hypothesis is that our distinctively long, protected human childhood allows an early period of broad hypothesis search, exploration and creativity, before the demands of goal-directed action set in.

The theory of alphabits is a natural generalisation of approximate quantum error correction that proves fundamental to the study of asymptotic quantum resources. In particular, it leads to an asymptotically reversible variation on quantum teleportation, called zerobit teleportation, which decomposes qubits of communication into correlation and transmission components. They also naturally arise in the study of black holes with significant consequences for the nature of quantum error correction in AdS/CFT.

Quantum complexity is conjectured to probe inside of black hole horizons (or wormhole) via gauge gravity correspondence. In order to have a better understanding of this correspondence, we study time evolutions of complexities for generic Abelian pure gauge theories. For this purpose, we discretize U(1) gauge group as Z_N and also continuum spacetime as lattice spacetime, and this enables us to define a universal gate set for these gauge theories, and evaluate time evolutions of the complexities explicitly. We find that to achieve a large complexity ∼exp(entropy), which is one of the conjectured criteria necessary to have a dual  black hole, the Abelian gauge theory needs to be maximally nonlocal. (Based on collaboration with Norihiro Iizuka and Sotaro Sugishita, https://arxiv.org/abs/1707.03840)

Transversality is one of the most desirable features of fault-tolerant circuits because it automatically limits the propagation of errors. However, it was shown by Eastin & Knill that no universal set of quantum gates on any quantum code is transversal. In this talk, we strengthen this result for stabilizer codes to say that transversal gates must in fact be contained in the Clifford hierarchy. Moreover, we present new circuits on Bacon-Shor codes that saturate our bounds. In particular, we show how a k-qubit controlled-Z gate can be implemented by a transversal circuit on m-by-m^k Bacon-Shor codes and provide some estimates of its performance in terms of pseudo-thresholds and resource overhead.

Gravitational wave astronomy provides an unprecedented opportunity to test the nature of black holes and search for exotic, compact alternatives. Recent studies have shown that exotic compact objects (ECOs) can ring down in a manner similar to black holes, but can also produce a sequence of distinct pulses resembling the initial ringdown. These “echoes” would provide definite evidence for the existence of ECOs. In this work we study the generation of these echoes in a generic, parameterized model for the ECO, using Green’s functions. We show how to reprocess radiation in the near-horizon region of a Schwarzschild black hole into the radiation from the corresponding source in an ECO spacetime. Our methods allow us to understand the connection between distinct echoes and ringing at the resonant frequencies of the compact object. We find that the quasinormal mode ringing in the black hole spacetime plays a central role in determining the shape of the first few echoes. We use this observation to develop a simple template for echo waveforms. This template performs well over a variety of ECO parameters, and with improvements may prove useful in the analysis of gravitational waves.
Related Arxiv #: https://arxiv.org/abs/1706.06155

One of the basic puzzles of black hole thermodynamics is the simplicity and universality of the  Bekenstein-Hawking entropy. The idea that this entropy might be governed by a symmetry at the horizon is an old one, but until now efforts have focused on conformal symmetries, either at infinity or on a "stretched horizon."  I argue that a better approach uses a BMS-like symmetry of the horizon itself.  This avoids the limitations of previous attempts (including my own), and explains the entropy in terms of a generalization of the Cardy formula for the density of states.