Spring 2020

The first part of this talk will introduce generalized Jordan–Wigner transformation on arbitrary triangulation of any manifold in 2d, 3d, and general dimensions. This gives a duality between all fermionic systems and a new class of Z2 lattice gauge theories. This map preserves the locality and has an explicit dependence on the second Stiefel–Whitney class and a choice of spin structure on the manifold. In the Euclidean picture, this mapping is equivalent to introducing topological terms (Chern-Simon term in 2d or the Steenrod square term in general) to the Euclidean action.

 Intro.  Physics and statistics  (a) where theory and experiment meet, (b) divergent world views, (c) underlying probabilistic nature of the world:  Bell's theorem and random number generation.
The calibration of a few photon detector.  (a) What is a Transition Edge Sensor?  What needs to be calibrated?  (b) The K-means algorithm as maximum likelihood.  (c) Adaptation of the K-means algorithm to Poisson statistics:  a new maximum likelihood objective function: PIKA.  (d) Application of PIKA to calibration of an attenuator at near-ideal quantum efficiency.

Dissertation Committee Chair: Luis Orozco
Committee:
Alicia Kollar
Mohammad Hafezi (Dean’s rep)
William D. Phillips
Ian Spielman (Advisor)
Abstract:

Resource theories have mushroomed in quantum information theory over the past decade. Resource theories are simple models for situations in which constraints limit the operations performable and the systems accessible. In a fixed-temperature environment, for instance, the first law of thermodynamics constrains operations to preserve energy, and thermal states can be prepared easily.  Scores of resource-theory theorems have been proved. Can they inform science beyond quantum information theory? Can resource theories answer pre-existing questions about the real physical world?

Can a quantum computer help us analyze a large classical data set? Data stored classically cannot be queried in superposition, which rules out direct Grover searches, and it can often be classically accessed with some level of parallelism, which would negate the advantage of Grover even if it were possible.

The interaction of a single photon with an individual two-level system is the textbook example of quantum electrodynamics. Achieving strong coupling in this system has so far required confinement of the light field inside resonators or waveguides. Experiments with Rydberg superatoms [1,2] have demonstrated the ability to realize strong coupling to a propagating light pulse containing only a few photons in free space.

The past decade has seen a dramatic increase in the degree, quality, and sophistication of control over quantum-mechanical interactions available between artificial degrees of freedom in a variety of experimental platforms. The geometrical structure of these interactions, however, remains largely constrained by the underlying rectilinear geometry of three-dimensional Euclidean space.

We are in the midst of a second quantum revolution fueled by the remarkable quantum mechanical properties of physical systems. Therefore, characterization and engineering of these quantum systems is vitally important in emerging quantum optical science and technology. The Wigner quasi-probability distribution function provides such a characterization.

Density matrices represent our knowledge about quantum systems. We can use them to calculate any physical property of quantum systems via the Born rule. Since the density matrix grows exponentially with the number of qubits, already at about 50 qubits, simply writing and storing the density matrix in a classical computer, becomes impossible, let alone calculating anything with it.

Quantum photonics provides a powerful toolbox with vast applications ranging from quantum simulation, photonic information processing, all optical universal quantum computation, secure quantum internet as well as quantum enhanced sensing.