  In the quest for fault-tolerant quantum computation using superconducting
processors, accurate performance assessment and continuous design optimization
stands at the forefront. To facilitate both meticulous simulation and
streamlined design optimization, we introduce a multi-level simulation
framework that spans both Hamiltonian and quantum error correction levels, and
is equipped with the capability to compute gradients efficiently. This toolset
aids in design optimization, tailored to specific objectives like quantum
memory performance. Within our framework, we investigate the often-neglected
spatially correlated unitary errors, highlighting their significant impact on
logical error rates. We exemplify our approach through the multi-path coupling
scheme of fluxonium qubits.
