9 papers
Quantitative semidefinite certificates for ground-state energies of Pauli Hamiltonians
Igor Klep, Nando Leijenhorst, Victor Magron
The -local Hamiltonian problem is a central model for quantum many-body systems and Hamiltonian complexity. Semidefinite programming and noncommutative sum-of-squares hierarchie…
Operator-Valued Positivstellensätze on Matrix Convex Sets and Free Products of Finite Abelian Groups
Abhay Jindal, Igor Klep, Scott McCullough
We prove a Positivstellensatz for operator-valued noncommutative polynomials that are positive on matrix convex sets. Specifically, let be an operator-valued polynomial in $B(H…
Positive operator-valued noncommutative polynomials are squares
Abhay Jindal, Igor Klep, Scott McCullough
We establish operator-valued versions of the earlier foundational factorization results for noncommutative polynomials due to Helton (Ann.~Math., 2002) and one of the authors (Line…
Classifying minimal vanishing sums of roots of unity
Louis Christie, Kenneth J. Dykema, Igor Klep
A vanishing sum of roots of unity is called minimal if no proper, nonempty sub-sum of it vanishes. This paper classifies all minimal vanishing sums of roots of unity of weight at m…
Fejér--Riesz factorization for positive noncommutative trigonometric polynomials
Igor Klep, Jacob Levenson, Scott McCullough
We prove a Fejér-Riesz type factorization for positive matrix-valued noncommutative trigonometric polynomials on , where is either the…
Upper bound hierarchies for noncommutative polynomial optimization
Igor Klep, Victor Magron, Gaël Massé +1
This work focuses on minimizing the eigenvalue of a noncommutative polynomial subject to a finite number of noncommutative polynomial inequality constraints. Based on the Helton-Mc…