Talks

Finding a quantum phase transition between two even well-studied phases of matter can be a hard problem. Free probability theory suggests a new method which can give an answer if the Hamiltonians of two phases satisfy certain conditions. In the latter case, the spectral gap behavior can be calculated without solving the full Hamiltonian but using probabilistic estimation instead. As an example, I will consider generic artificial topological systems created by a periodic drive, including Floquet Majorana modes, and show how FPT can be used to predict and characterize disorder-driven phase transitions.

See also: Phys. Rev. Lett. 121, 126803

I show that Unruh effect can be associated with the partitioning of the real line, and derived from the basic representation theory of the group of affine transformations in one dimension. This result shows that thermal distributions naturally emerge in connecting quantum
states belonging to representations related to distinct notions of translational symmetry.

Neutron stars host the densest stable matter in the universe. Accurately modeling their multi-messenger astrophysics relies on a detailed description of the equation of state above nuclear density, and astronomical observations of neutron stars can in turn be used to constrain the properties of such dense matter. On August 17, 2017 the Advanced LIGO and Advanced Virgo detectors discovered the first gravitational-wave signal consistent with a binary neutron star inspiral. The three-dimensional localization of GW170817’s source using LIGO and Virgo data enabled a successful electromagnetic follow-up campaign. We are also able to constrain the equation of state of dense matter in neutron stars using the signature of tidal interaction in the gravitational-wave signal. I will outline these constraints, the methods by which they are made, how the gravitational-wave information connects with other observations of neutron stars, and outline future prospects for gravitational-wave astronomy with neutron stars.

We show that there are two distinct obstacles to an efficient
classical simulation of a general quantum circuit. The first obstacle, which
has been well-studied, is the difficulty of efficiently estimating the
probability associated with a particular measurement outcome. We show that
this alone does not determine whether a quantum circuit can be efficiently
simulated. The second obstacle is that, in general, there can be an
exponential number of `relevant' outcomes that are needed for an accurate
simulation, and so efficient simulation may not be possible even in
situations where the probabilities of individual outcomes can be efficiently
estimated. We show that these two obstacles are distinct, overcoming the
former obstacle being necessary but not sufficient for simulability whilst
overcoming the pair is jointly sufficient for simulability. Specifically, we
prove that a family of quantum circuits is efficiently simulable if it
satisfies two properties: one related to the efficiency of Born rule
probability estimation, and the other related to the sparsity of the outcome
distribution. We then prove a pair of hardness results (using standard
complexity assumptions and a variant of a commonly-used average case
hardness conjecture), where we identify families of quantum circuits that
satisfy one property but not the other, and for which efficient simulation
is not possible. To prove our results, we consider a notion of simulation of
quantum circuits that we call epsilon-simulation. This notion is less
stringent than exact sampling and is now in common use in quantum hardness
proofs.

Most machine learning algorithms involve optimizing a single set of parameters to decrease a single cost function. In adversarial machine learning, two or more "players" each adapt their own parameters to decrease their own cost, in competition with the other players. In some adversarial machine learning algorithms, the algorithm designer contrives this competition between two machine learning models in order to produce a beneficial side effect. For example, the generative adversarial networks framework involves a contrived conflict between a generator network and a discriminator network that results in the generator learning to produce realistic data samples. In other contexts, adversarial machine learning models a real conflict, for example, between spam detectors and spammers. In general, moving machine learning from optimization and a single cost to game theory and multiple costs has led to new insights in many application areas.