Quantum codes as robust phases of matter
Abstract: There is a deep connection between quantum error correction and phases of matter for spatially local codes in finite dimensions. I will show how this analogy extends to more general settings: quantum codes with check soundness are absolutely stable phases of matter. These codes include constant-rate quantum low-density parity-check codes, which shows that the third law of thermodynamics is false: there exist absolutely stable phases of matter with constant entropy density at zero temperature.
Rapid quantum ground state preparation via dissipative dynamics
Abstract: Inspired by natural cooling processes, dissipation has become a promising approach for preparing low-energy states of quantum systems. However, the potential of dissipative protocols remains unclear beyond certain commuting Hamiltonians.
A Constructive Approach to Zauner’s Conjecture via the Stark Conjectures
Abstract: 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.
Glasses: From Physical Hamiltonians to Neural Networks and Back
Abstract: 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.
A Constructive Approach to Zauner’s Conjecture via the Stark Conjectures
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.
Glasses: From Physical Hamiltonians to Neural Networks and Back
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.
CANCELLED - Glasses: From Physical Hamiltonians to Neural Networks and Back
Abstract: 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.
Rapid quantum ground state preparation via dissipative dynamics
The title and abstract for this talk are forthcoming.
*We strongly encourage attendees to use their full name (and if possible, their UMD credentials) to join the zoom session.*
Quantum codes as robust phases of matter
The title and abstract for this talk are forthcoming.
*We strongly encourage attendees to use their full name (and if possible, their UMD credentials) to join the zoom session.*
Optimization by Decoded Quantum Interferometry
In this talk I will describe Decoded Quantum Interferometry (DQI), a quantum algorithm for reducing classical optimization problems to classical decoding problems by exploiting structure in the Fourier spectrum of the objective function. (See: https://arxiv.org/abs/2408.08292.) For a regression problem called optimal polynomial intersection, which has been previously studied in the contexts of coding theory and cryptanalysis, we believe DQI achieves an exponential quantum speedup.