Dr. Jim Freericks from Georgetown University gave a talk titled "Operator Mechanics: A new form of quantum mechanics without waves or matrices" in the Pittsburgh Quantum Institute Fall Seminar series on Sept. 3rd, 2020.
His presentation slides can be found here: https://drive.google.com/drive/folders/1zLohpkcooZx7fPrht0gZOfWvBg9Ja34B
Abstract: Quantum mechanics was created with the matrix mechanics of Heisenberg, Born, and Jordan. Schroedinger's wave mechanics shortly followed and allowed for simpler and more powerful calculations. Both Pauli and Dirac introduced a formulation of quantum mechanics based on operators and commutation relations, but it was never fully developed in the 1920's. Instead, Schroedinger formulated the operator approach with his factorization method, which later was adopted by the high-energy community as supersymmetric quantum mechanics. In this talk, I will explain how one can formulate nearly all of quantum mechanics algebraically by a proper use of the translation operator on top of Schroedinger's factorization method. I will give examples of how one can compute spherical harmonics algebraically, how one can find harmonic oscillator wavefunctions, and will even describe an operator-based derivation of the wavefunctions of Hydrogen. I will end with a proposal for a novel way to teach quantum mechanics, focusing first on conceptual ideas related to superposition, projective measurements, and entanglement. Then developing more conventional topics like spin, harmonic oscillator, angular momentum, interacting spin models, central potentials, particles in a box and so on. This is the subject of a book in progress entitled Quantum Mechanics without Calculus.
Dr. Scott J. Aaronson, David J. Bruton Centennial Professor of Computer Science at the University of Texas at Austin, gave the PQI2020 Public Lecture.
Last fall, a team at Google announced the first-ever demonstration of "quantum computational supremacy"---that is, a clear quantum speedup over a classical computer for some task---using a 53-qubit programmable superconducting chip called Sycamore. In addition to engineering, Google's accomplishment built on a decade of research in quantum complexity theory. This talk will discuss questions like: what exactly was the contrived problem that Google solved? How does one verify the outputs using a classical computer? And how confident are we that the problem is classically hard---especially in light of subsequent counterclaims by IBM? He'll end with a proposed application for Google's experiment---namely, the generation of certified random bits, for use (for example) in proof-of-stake cryptocurrencies---that he has been developing and that Google is now working to demonstrate.
This week's focus is on quantum computing and we are pleased to be joined by our featured speaker, So Hirata from UI Urbana-Champaign. Rongchao Jin was unable to join due to unforeseen circumstances.
So Hirata, UIUC, “Numerical Evidence Invalidating Textbook Finite-Temperature Perturbation Theory”
This week's focus is on quantum materials and we are pleased to be joined by our featured speaker, Chris Van de Walle from UC Santa Barbara, and PQI member contributing speaker, Linda Peteanu from CMU.
Linda Peteanu (CMU) "Probing Single- and Bi-excitonic States in Silicon Nanoparticles"
Chris Van de Walle, UCSB, “Modeling Point Defects for Quantum Information Science”
This weeks focus is on quantum optics and we are pleased to be joined by our featured speaker, Dan Stamper-Kurn from UC Berkeley, and PQI member contributing speakers, Andrew Daley from the University of Strathclyde and Tom Purdy from Pitt.
Andrew Daley (UStrathclyde), “Reaching practical quantum advantage in quantum simulation”
Dan Stamper-Kurn (UC Berkeley) “Using Light to Measure and Control Quantum Systems"
Tom Purdy (Pitt), "The Quantum Optical Level”