84 citations · 342 across the 90 of their papers we have counts for
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The bulk spectral gap is certifiable from above but uncomputable from below
Xiangling Xu, Matthias Schötz, Jie Wang +4
Determining spectral gaps in the thermodynamic limit is a central challenge in quantum many-body physics. When a fixed boundary condition is imposed, this problem is undecidable: n…
Sums of squares in polynomial time
Nikolas Gärtner, Victor Magron, Frank Vallentin
In this paper, we analyze the bit complexity of deciding whether a given polynomial can be represented as a sum of squares of polynomials. We show that the weak membership problem…
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…
Duality attainment and strict feasibility of the generalized moment problem and its relaxations
Sami Halaseh, Victor Magron, Mateusz Skomra
The generalized moment problem (GMP) is an infinite dimensional linear problem over the cone of finite nonnegative Borel measures. When a GMP instance involves finitely many polyno…
Robust self-testing with CHSH mod 3
Igor Klep, Nando Leijenhorst, Victor Magron
The CHSH mod 3 Bell inequality is a natural testbed for higher-dimensional quantum nonlocality, yet its maximal quantum violation and self-testing properties have remained unresolv…
Scalable Ground-State Certification of Quantum Spin Systems via Structured Noncommutative Polynomial Optimization
Jie Wang, David Jansen, Irénée Frerot +3
A fundamental challenge in quantum physics is determining the ground-state properties of many-body systems. Whereas standard variational approaches posit a wave-function ansatz and…
The Effective Lasserre's Perturbative Positivstellensatz
Igor Klep, Victor Magron, Matthias Schötz
We study sum-of-squares (SOS) certificates for nonnegative polynomials on and their implications for polynomial optimization over unbounded domains. Building on…