Quantum & Statistical Physics

Statistical Physics of Learning

Connections between statistical mechanics and learning theory: partition functions, free energy, and phase transitions in inference.

Statistical Physics of Optimization & Random CSP Phase Transitions

Phase transitions in random constraint satisfaction problems and their implications for optimization algorithms.

Replica Symmetry Breaking in High-Dimensional Learning

Advanced replica method for analyzing high-dimensional inference, including GAMP and state evolution.

Thermodynamics of Computation & Information

Landauer's principle, Maxwell's demon, and thermodynamic costs of computation and information processing.

Quantum Information for ML

Quantum entropy, channels, and entanglement as foundations for quantum-enhanced machine learning.

Models of Quantum Computation & Complexity

Quantum circuit model, complexity classes BQP and QMA, and their implications for quantum advantage in ML.

Quantum Error Correction & Threshold Theorems

Stabilizer codes, fault-tolerant computation, and threshold theorems for scalable quantum computing.

Hamiltonian Complexity & Adiabatic Computation

Computational complexity of local Hamiltonian problems and adiabatic quantum computation as optimization.

HHL & Quantum Linear Algebra Foundations

Harrow-Hassidim-Lloyd algorithm for linear systems and quantum speedups for linear algebra tasks.

Quantum ML: Generalization Limits & No-Free-Lunch Results

Generalization theory for quantum ML models, including expressivity bounds and no-free-lunch theorems.

Variational Quantum Algorithms & Barren Plateaus

Theory of variational quantum eigensolvers, QAOA ansatze, and the barren plateau phenomenon.

Quantum Approximate Optimization Algorithms (QAOA)

Theory and analysis of QAOA for combinatorial optimization, including performance guarantees and limitations.