QuICS

Instabilities, where initially small fluctuations seed the formation of large-scale structures, govern the dynamics in various fluid flows. The Rayleigh-Taylor instability (RTI) is an iconic example that leads to the development of mushroom-shaped incursions when immiscible fluids are accelerated into each other. RTI drives structure formation throughout science and engineering including table-top oil and water mixtures; supernova explosions; and inertial confinement fusion.  Despite its ubiquity, controlled laboratory RTI experiments are technically challenging.

A cryptographic proof of quantumness is a hypothetical test that could be used to prove a quantum computational advantage based on hardness assumptions from cryptography.  An experimental realization of such a test would be a major milestone in the development of quantum computation.  However, error tolerance is a persistent challenge for implementing such tests: we need a test that not only can be passed by an efficient quantum prover, but one that can be passed by a prover that exhibits a certain amount of computational error.

We extend entropy production to a deeply quantum regime involving noncommuting conserved quantities. Consider a unitary transporting conserved quantities (“charges”) between two systems initialized in thermal states. Three common formulae model the entropy produced. They respectively cast entropy as an extensive thermodynamic variable, as an information-theoretic uncertainty measure, and as a quantifier of irreversibility. Often, the charges are assumed to commute with each other (e.g., energy and particle number). Yet quantum charges can fail to commute.

In quantum information, symmetric informationally complete measurements (SIC-POVMs) serve as elegant and efficient tools for numerous tasks like state tomography, QKD, and more. These objects have appeared in other contexts such as frame theory and design theory; for example, they are minimal spherical 2-designs. There are even intriguing connections to open problems in number theory. It has been an open problem for 25 years to prove that SIC-POVMs exist in infinitely many dimensions.

The abstract for this dissertation defense is forthcoming.

This talk will review our recent work on classical and quantum glasses. I will start with a discussion of spin glasses from the perspective of chaos theory.

Unlike the traditional study of algorithms which attempts to solve a certain task using minimal space and time resources, I will discuss data structures to solve certain algorithmic tasks after an initial pre-processing phase. The interest here is to study the tradeoffs between the resources such as the space and time required to perform the algorithmic task when asked a query; and the resources in the pre-processing phase such as the time required to prepare the data structure or its size.