Ground-state energy estimation compiled on cat qubits: 7 164 qubits for FeMoco-54 in 23.5 hours

arXiv:2610.37840v1 Announce Type: new Abstract: We provide a detailed resource estimate of the state-of-the-art sum-of-squares block encoding algorithm for electronic structure Hamiltonians of Low et al. on superconducting cat qubits. To achieve this, we present compilations with closed-form costs of the dominant subroutines such as skew-tree Qrom, a Swap network and a Phaseup for both a repetition-cat and an LDPC-cat architecture. Our compilation represents algorithmic qubits in the $X$ basis, taking advantage of the asymmetric cost of $X$ and $Z$ access that the concatenation of cat qubits with phase-flip classical code brings.