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The sum-of-squares (SoS) hierarchy is a powerful technique based on semi-definite programming that can be used for both classical and quantum optimization problems.
Structure of fermion density matrices
A. John Coleman · 1963
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Representability
R. M. Erdahl · 1978
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The role of model systems in the few-body reduction of the N N -fermion problem
Jerome Percus · 1978
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Gapless spin-fluid ground state in a random quantum Heisenberg magnet
Subir Sachdev and Jinwu Ye · 1993
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Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming
Michel Goemans and David Williamson · 1995
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Uncertainty relations and reduced density matrices: Mapping many-body quantum mechanics onto four particles
David Mazziotti and Robert Erdahl · 2001
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Variational calculations of fermion second-order reduced density matrices by semidefinite programming algorithm
Maho Nakata, Hiroshi Nakatsuji, Masahiro Ehara, Mitsuhiro Fukuda, Kazuhide Nakata, and Katsuki Fujisawa · 2001
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Maximizing quadratic programs: extending Grothendieck’s inequality
Moses Charikar and Anthony Wirth · 2004
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A Positivstellensatz for non-commutative polynomials
J. William Helton and Scott McCullough · 2004
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Quantum marginal problem and N N -representability
Alexander Klyachko · 2006
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The algebraic degree of semidefinite programming
Jiawang Nie, Kristian Ranestad, and Bernd Sturmfels · 2008
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Convergent relaxations of polynomial optimization problems with noncommuting variables
Stefano Pironio, Miguel Navascués, and Antonio Acín · 2010
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Structure of fermionic density matrices: Complete N N -representability conditions
David Mazziotti · 2012
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A simple model of quantum holography
Alexei Kitaev · 2015
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Optimizing strongly interacting fermionic hamiltonians
Matthew B Hastings and Ryan O’Donnell · 2021
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Andrew Doherty, Yeong-Cherng Liang, Ben Toner, and Stephanie Wehner · 2008
Cited alongside, same era.