Walsh Codes for Multi-Qubit Decoupling with Fluctuating Ising Crosstalk

Digital dynamical decoupling (DD) of an n-qubit register assigns each qubit a Walsh switching function. Static pairwise ZZ crosstalk is removed to first order by any set of distinct indices (orthogonal arrays). When Ising couplings fluctuate, the products of pair switching functions must also be filtered. Nested sequences achieve this but scale exponentially. We treat the index selection under a fixed slot budget (~4n) as a code-design problem. The infidelity is additive: a spectral cost per single-qubit function plus one per pair product. This cost ranks fidelities with Spearman ρ = 0.97–0.98. With static couplings, the maximal-sequency assignment reaches the computed optimum. With fluctuating couplings, the maximal-sequency sequence collapses (F = 0.302 vs 0.700 at n = 10, 64 slots). The optimum moves to a fast subspace closed under XOR. At fixed total time the code outperforms nested Uhrig decoupling (n = 5: F = 0.929 with 221 pulses versus 0.576 with 1023). In a 6-qubit density-matrix check with T1 and finite pulses it is the best design in all four conditions tested, with paired differences over the natural Hadamard order all above zero. Scripts and data: doi:10.5281/zenodo.23661132.