Semidefinitni pristopi h kvantnim kodam: konvergenca, meje in konstrukcije

Fault-tolerant quantum computation relies on quantum error correction to rein in decoherence and on the distillation of special “magic” states, yet the fundamental limits and practical design principles of such schemes are still poorly understood. SDPCode brings together five European partners to develop a semidefinite-programming–based foundation for analysing and constructing quantum codes and related resources over 36 months. The project has three main goals: (i) to establish rigorous convergence rates for widely used non-commutative semidefinite hierarchies, turning them from heuristic tools into algorithms with quantitative guarantees; (ii) to obtain scalable and exact bounds on the parameters of quantum error-correcting codes and magic-state distillation protocols, including new higher-order MacWilliams-type identities; and (iii) to devise constructive algorithms that turn convex relaxations into concrete quantum objects – stabilizer codes, many-body ground states, and continuous-variable codes. Methodologically, SDPCode adapts kernel techniques to quantify how fast SDP hierarchies approach the true optimum, develops symmetry- and sparsity-exploiting solvers for quantum coding problems, and designs randomized rounding schemes for tensor-network and circuit ansätze, as well as sphere-packing–based CV codes with improved robustness to Gaussian noise. The project will deliver general theorems, benchmark tables and open-source software implementing these methods, providing a mathematically solid and practically useful toolbox for quantum error correction, resource estimation and quantum simulation.