Gerard Anglès Munné, Felix Huber (Mar 23 2026).
Abstract: A fundamental problem in quantum coding theory is to determine the maximum size of quantum codes of given block length and distance. A recent work introduced bounds based on semidefinite programming, strengthening the well-known quantum linear programming bounds. However, floating-point inaccuracies prevent the extraction of rigorous non-existence proofs from the numerical methods. Here, we address this by providing rational infeasibility certificates for a range of quantum codes. Using a clustered low-rank solver with heuristic rounding to algebraic expressions, we can improve upon
18 upper bounds on the maximum size of
n-qubit codes with
6≤n≤19. Our work highlights the practicality and scalability of semidefinite programming for quantum coding bounds.
