QuICS

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 this talk, I will present a construction of symmetric informationally complete POVMs (SIC-POVMs), a special class of quantum measurements whose existence in all dimensions was conjectured by Zauner in 1999. Equivalently, these are maximal sets of d^2 equiangular lines in ℂ^d. Our approach introduces an explicit mathematical object, the ghost SIC, built from number-theoretic properties of a special modular function, and we show that it is Galois conjugateto an actual SIC.

This thesis explores the quantum extension of a fundamental theme in theoretical computer science: the interplay between graph theory, computational complexity, and multiprover interactive proof systems. Specifically, we examine the connections between quantum graph properties, computability theory, and entangled nonlocal games.

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.

I'll give theorems characterizing finite-dimensional quantum theory's framework of 

In this talk, I present an experimental realization of a quantum absorption refrigerator formed from superconducting circuits. The refrigerator is used to reset a transmon qubit to a temperature lower than that achievable with any one available bath. The process is driven by a thermal gradient and is autonomous -- requires no external control. The refrigerator exploits an engineered three-body interaction between the target qubit and two auxiliary qudits coupled to thermal environments, formed from microwave waveguides populated with thermal photons.

In this seminar, we are interested in all aspects of research at the intersection between quantum information science and mathematics. Goals for the seminar include: