12 citations · 40 across the 46 of their papers we have counts for
7 papers · 1 filter
The bulk spectral gap is semi-decidable: a convergent family of certified upper bounds
Xiangling Xu, Matthias Schötz, Jie Wang +4
Determining spectral gaps in the thermodynamic limit is a central challenge in quantum many-body physics. Existing rigorous methods are largely limited to special settings, while v…
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…
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…
Certified bounds on optimization problems in quantum theory
Younes Naceur, Jie Wang, Victor Magron +1
Semidefinite relaxations of polynomial optimization have become a central tool for addressing the non-convex optimization problems over non-commutative operators that are ubiquitou…
Inclusion constants for free spectrahedra with applications to quantum incompatibility
Andreas Bluhm, Eric Evert, Igor Klep +2
Building on the matrix cube problem, inclusions of free spectrahedra have been used successfully to obtain relaxations of hard spectrahedral inclusion problems. The quality of such…
Positivity of state, trace, and moment polynomials, and applications in quantum information
Felix Huber, Victor Magron, Jurij Volčič
State, trace, and moment polynomials are polynomial expressions in several operator or random variables and positive functionals on their products (states, traces or expectations).…