C

“The Ising framework maps the decoding problem in quantum error correction onto ground-state optimization of a classical Hamiltonian, in which X-Z error correlations enter as cross terms. Under phenomenological depolarizing noise, the exact joint formulation contains up to 8-body interactions for the toric code and 10-body for the 6.6.6 color code. These high-order terms degrade solver convergence, inflate runtime, and raise the auxiliary spin overhead when embedding into native 2-body Ising hard”