Stabilizer expansions expose phase-dependent quantum complexity shifts in fermionic systems

The study examines a fermionic Hamiltonian with pairing and deformation terms using entanglement entropy, stabilizer Rényi entropy, and fermionic non-Gaussianity measures. Researchers decomposed the Hamiltonian into graph-state components and tested variational basis rotations that preserve particle-number symmetry. In the deformed phase a single stabilizer state sufficed for high fidelity, whereas the pairing phase required a number of states that scaled exponentially with system size unless a symmetry-adapted rotation reduced the count dramatically. These resource estimates were obtained on lattices up to 20 sites with exact diagonalization benchmarks. The perspective shift from raw entanglement to non-stabilizerness directly affects how quantum simulators allocate magic resources when modeling materials for superconducting interconnects. Low non-stabilizerness in deformed phases implies that certain many-body states can be approximated with Clifford circuits plus few T-gates, lowering the overhead for variational quantum eigensolvers that design low-loss transmission lines. Pairing phases, by contrast, concentrate non-stabilizerness, raising the gate cost for accurate simulation of quasiparticle dynamics that limit data rates in quantum networks. A symmetry-preserving basis rotation identified in the work offers a practical starting ansatz for hybrid quantum-classical refinement, cutting the number of required stabilizer states by more than an order of magnitude on tested sizes. This approach could accelerate classical pre-optimization steps in protocols that certify entanglement distribution across metropolitan fiber links. Next steps include embedding the rotated states into fault-tolerant surface-code simulations to quantify logical error thresholds under realistic decoherence.