Research interests: High-Dimensional Optimization & Sampling, Classical & Quantum Spin Glasses, Matrix Models, Phase Transitions in Gibbs measures, Analysis & Geometry of Gaussian Processes, Gaussian Free Field, Liouville Quantum Gravity.
My papers can be found on Google Scholar or DBLP. I (primarily) work with:
- David Jekel and Jonathan Shi to optimize spin glasses, operator-valued functions & CSPs, analyze Gaussian processes on symmetric domains (ex: Lie groups), and design sum-of-squares hierarchies to certify algorithmic thresholds in random optimization.
- Saeed Mehraban to develop & extend probabilistic techniques from mathematical spin-glass theory with complex-analytic ideas to study mathematical and algorithmic questions surrounding the random-permanent problem.
- Ewan Davies to extend the theory of local occupancy to higher moments of Gibbs measures, and study the implications of this on the hard-core model on explicit families of graphs (including phase transitions).
Publications
Potential Hessian Ascent II: Duality, Robustness & Approximate Message Passing
David Jekel, Juspreet Singh Sandhu, Jonathan Shi
Submitted
On Expectations and Variances in the Hard-Core Model on Bounded Degree Graphs
Ewan Davies, Juspreet Singh Sandhu, Brian Tan
Submitted
PDF
Monogamy of Entanglement Bounds and Improved Approximation Algorithms for Qudit Hamiltonians
Zachary Jorquera, Alexandra Kolla, Steven Kordonowy, Juspreet Singh Sandhu, Stuart Wayland
Submitted
PDF
Potential Hessian Ascent: The Sherrington-Kirkpatrick Model
David Jekel, Juspreet Singh Sandhu, Jonathan Shi
SODA 2025
PDF
Sum-of-Squares & Gaussian Processes I: Certification
Juspreet Singh Sandhu, Jonathan Shi
Submitted
PDF
Random Max-CSPs Inherit Algorithmic Hardness from Spin Glasses
Chris Jones, Kunal Marwaha, Juspreet Singh Sandhu, Jonathan Shi
ITCS 2023
PDF
Video
Limitations of Local Quantum Algorithms on Random MAX-k-XOR and Beyond
Chi-Ning Chou, Peter J. Love, Juspreet Singh Sandhu, Jonathan Shi
ICALP 2022
PDF
Video
Efficient Quantum Voting with Information-Theoretic Security
Emil T. Khabiboulline, Juspreet Singh Sandhu, Marco Ugo Gambetta, Mikhail D. Lukin, Johannes Borregaard
Under Revision, PRX Quantum
PDF
A General Framework for Analyzing Stochastic Dynamics in Learning Algorithms
Chi-Ning Chou, Juspreet Singh Sandhu, Mien Brabeeba Wang, Tiancheng Yu
Submitted
PDF
Working Papers
Potential Hessian Ascent III: Mixed p-Spin Models & HES Distributions
David Jekel, Juspreet Singh Sandhu, Jonathan Shi
In Preparation
Potential Hessian Ascent IV: Sampling in Total Variation Distance
Ewan Davies, Holden Lee, Juspreet Singh Sandhu, Jonathan Shi
In Preparation
Gaussian Processes Over The Symmetric Group: High-Temperature Regime
Saeed Mehraban, Juspreet Singh Sandhu, Jonathan Shi
In Preparation
Sum-of-Squares & Gaussian Processes II: Rounding
Juspreet Singh Sandhu, Jonathan Shi
In Preparation