Hamza Fawzi

Publications

• Certified algorithms for equilibrium states of local quantum Hamiltonians (with Omar Fawzi and Samuel Scalet), QIP 2024
• Efficient Computation of the Quantum Rate-Distortion Function (with Kerry He and James Saunderson), preprint
• A Bregman Proximal Perspective on Classical and Quantum Blahut-Arimoto Algorithms (with Kerry He and James Saunderson), preprint
• Rational approximations of operator monotone and operator convex functions (with Oisín Faust), preprint
• Entropy constraints for ground state optimization (with Omar Fawzi and Samuel Scalet), to appear in Journal of Mathematical Physics
• A subpolynomial-time algorithm for the free energy of one-dimensional quantum systems in the thermodynamic limit (with Omar Fawzi and Samuel Scalet), Quantum, also appeared in ITCS 2023, QIP 2023
• Optimal self-concordant barriers for quantum relative entropies (with James Saunderson), SIAM Journal on Optimization.
• Local Linear Convergence of Douglas-Rachford for Linear Programming: a Probabilistic Analysis (with Oisín Faust), ICML 2022.
• Strong data processing inequalities via sums of squares (with Oisín Faust), ISIT 2022.
• Semidefinite programming lower bounds on the squashed entanglement (with Omar Fawzi), QIP 2022 (merged with below)
• Device-independent lower bounds on the conditional von Neumann entropy (with Peter Brown and Omar Fawzi), QIP 2022.
• Sum-of-squares proofs of logarithmic Sobolev inequalities on finite Markov chains (with Oisín Faust), to appear in IEEE Transactions in Information Theory.
• Faster proximal algorithms for matrix optimization using Jacobi-based eigenvalue methods (with Harry Goulbourne), NeurIPS'21.
• Lifting for Simplicity: Concise Descriptions of Convex Sets (with João Gouveia, Pablo Parrilo, James Saunderson, and Rekha Thomas), SIAM Review.
• The set of separable states has no finite semidefinite representation except in dimension 3x2, Communications in Mathematical Physics.
• Defining quantum divergences using convex optimization (with Omar Fawzi), Quantum, QIP 2021 (merged with below).
• Computing conditional entropies for quantum correlations (with Peter Brown and Omar Fawzi), Nature Communications, QIP 2021.
• The geometric Rényi divergence and its applications in quantum channel capacities (with Kun Fang), Communications in Mathematical Physics.
• The sum-of-squares hierarchy on the sphere, and applications in quantum information theory (with Kun Fang), Mathematical Programming.
• Learning dynamic polynomial proofs (with Alhussein Fawzi, Mateusz Malinowski, Omar Fawzi), NeurIPS 2019 (spotlight).
• On polyhedral approximations of the positive semidefinite cone, Mathematics of Operations Research.
• Efficient optimization of the quantum relative entropy (with Omar Fawzi), Journal of Physics A (erratum)
  (arXiv version with the title "Relative entropy optimization in quantum information theory via semidefinite programming approximations")
• Adversarial vulnerability for any classifier (with Alhussein Fawzi and Omar Fawzi), NeurIPS 2018.
• A lower bound on the positive semidefinite rank of convex bodies (arXiv link), SIAM Journal on Applied Algebra and Geometry
  Hamza Fawzi, Mohab Safey El Din.
• Semidefinite approximations of the matrix logarithm (arXiv link), Foundations of Computational Mathematics
  Hamza Fawzi, James Saunderson, Pablo A. Parrilo. Matlab code
  Recipient of SIAM Activity Group on Optimization Best Paper Prize 2020
• On representing the positive semidefinite cone using the second-order cone, Mathematical Programming.
• (PhD thesis) Power and limitations of convex formulations via linear and semidefinite programming lifts
  Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology
• Lieb's concavity theorem, matrix geometric means, and semidefinite optimization (corrigendum)
  Hamza Fawzi, James Saunderson, Linear Algebra and its Applications, vol.513, pp.240--263, 2017. Matlab code
  
• Sparse sums of squares on finite abelian groups and improved semidefinite lifts
  Hamza Fawzi, James Saunderson, Pablo A. Parrilo, Mathematical Programming Series A, vol.160, no.1, pp.149--191, 2016
• Equivariant semidefinite lifts of regular polygons
  Hamza Fawzi, James Saunderson, Pablo A. Parrilo, Mathematics of Operations Research, vol.42, no.2, pp.472--494, 2017
  
• Equivariant semidefinite lifts and sum-of-squares hierarchies
  Hamza Fawzi, James Saunderson, Pablo A. Parrilo
  SIAM Journal on Optimization, vol.25, no.4, pp.2212--2243, 2015. (Erratum)
• Rational and real positive semidefinite rank can be different
  João Gouveia, Hamza Fawzi, Richard Z. Robinson, Operations Research Letters
  
• Positive semidefinite rank
  Hamza Fawzi, João Gouveia, Pablo A. Parrilo, Richard Z. Robinson, Rekha R. Thomas
  Mathematical Programming Series B, special issue on "Lifts of Convex Sets", vol.153, no.1, pp.133--177, 2015
  
• Self-scaled bounds for atomic cone ranks: applications to nonnegative rank and cp-rank
  Hamza Fawzi, Pablo A. Parrilo
  Mathematical Programming Series A, vol.158, no.1, pp.417--465, 2016
  Accompanying Matlab code: tauplus_sos.m, tauplus_sos_tensor.m, taucp_sos.m
• Lower bounds on nonnegative rank via nonnegative nuclear norms
  Hamza Fawzi, Pablo A. Parrilo
  Mathematical Programming Series B, special issue on "Lifts of Convex Sets", vol.153, no.1, pp.41--66, 2015
  (The same paper previously had the title "New lower bounds on nonnegative rank using conic programming")
  Accompanying Matlab code
  
• Exponential lower bounds on fixed-size psd rank and semidefinite extension complexity, arXiv preprint 2013
  Hamza Fawzi, Pablo A. Parrilo
  
• Secure estimation and control for cyber-physical systems under adversarial attacks
  Hamza Fawzi, Paulo Tabuada, Suhas Diggavi
  IEEE Transactions on Automatic Control, vol.59, no.6, pp.1454--1467, June 2014
  Preliminary conference versions of this paper:

  • Security for control systems under sensor and actuator attacks, IEEE CDC 2012 (doi)
  • Secure state-estimation for dynamical systems under active adversaries, IEEE Allerton Conference 2011 (doi)
• An improved self-triggered implementation for linear controllers (doi)
  Jose Araujo, Hamza Fawzi, Manuel Mazo Jr., Paulo Tabuada and Karl Henrik Johansson
  Proceedings of the 3rd IFAC Workshop on Distributed Estimation and Control in Networked Systems (NecSys 2012)