This will be a reading group across Tufts, Harvard and MIT. The focus will be on analytic and probabilistic tools used to study the mathematical properties and algorithmic tractability of approximating (and sampling from statistics of) low-energy states of certain families of classical hamiltonians (spin glasses) and quantum hamiltonians (bosonic/fermionic systems).

Meeting Time: Thursdays, 11 AM - 1 PM EST

Location: Zoom room

Organizers: Saeed Mehraban, Juspreet Singh Sandhu

Recordings: Google Drive

Talk Schedule

No meeting on 02/09/2023, on account of the QIP conference scheduled 02/04/2023 through 02/10/2023

Relevant Papers

For a survey of Barvinok’s method, a good reference is the monograph by Barvinok [Bar] with Chapter-2 giving an overview of the technical toolkit, which uses complex analysis to study the roots of real-valued polynomials. Another source are the talks on “Computing Partition Functions” from the Simon’s workshop on the geometry of polynomials. A good historical reference for the overlap-gap property and its use in obstructing algorithms on random optimization problems is the survey by Gamarnik [G21]. A more technical survey is the one by Auffinger, Montanari and Subag [AMS22]. The three most accessible and comprehensive texts on the proof of the Parisi formula along with the applications of these techniques to solve other problems in mathematical and statistical physics are the ones by Talagrand ([Vol. 1],[Vol. 2]) and Panchenko [Pan13].

Deterministic Counting and Approximation of Quantum Hamiltonians

Analysis and Probability in Mean-Field Spin-Glasses

Interpolations, Ultrametricity and the TAP Approach

Analytic Properties of the Parisi Formula

Overlap Concentration, Low-Degree Stability and Overlap-Gap Properties: Algorithmic Hardness