Ground-state energy estimation compiled on cat qubits: 7 164 qubits for FeMoco-54 in 23.5 hours
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. Additionally, we provide a protocol for | i ⟩-state distillation and a two-level Toffoli-like | CXCX X ⟩ magic state distillation protocol, including three factory layouts. To minimize the cost of Clifford corrections induced by magic state injections we tailor injection gadgets to each subroutine. Combining our compilation work with the adder compilation from the companion work Pappalardo et al., we provide global layouts for the block encoding in both architectures which we use to obtain resource estimates for ground-state energy estimation for the benchmarks of FeMoco-54 and FeMoco-76. Assuming a cycle time of 1μs, a reaction time of 10μs, a phase estimation precision of 1 mHa and circuit-level phase-flip noise with probability pZ = 5 × 10−4 with negligible bit-flip error, FeMoco-54 requires fewer than 7 500 cat qubits with an expected runtime of under one day for a single phase estimation run using an LDPC-cat architecture. Relaxing the bit-flip requirement to pX = 10−11 with an additional layer of elevator codes raises this to an estimated 13 000 cat qubits.
Related
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BibTeX
@misc{kroell2026groundstate,
title = {{Ground-state energy estimation compiled on cat qubits: 7 164 qubits for FeMoco-54 in 23.5 hours}},
author = {Larissa Kroell and Hugo Jacinto and Victor Hertz and Axel Pappalardo and Adel Ben Moussa and Manuel Rispler and Peter Shanahan and Élie Gouzien and Christophe Vuillot and Vivien Londe},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.37840},
eprint = {2610.37840},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.37840},
}
RIS
TY - UNPB
TI - Ground-state energy estimation compiled on cat qubits: 7 164 qubits for FeMoco-54 in 23.5 hours
AU - Larissa Kroell
AU - Hugo Jacinto
AU - Victor Hertz
AU - Axel Pappalardo
AU - Adel Ben Moussa
AU - Manuel Rispler
AU - Peter Shanahan
AU - Élie Gouzien
AU - Christophe Vuillot
AU - Vivien Londe
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.37840
UR - https://arxiv.org/abs/2610.37840
AB - 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. Additionally, we provide a protocol for | i ⟩-state distillation and a two-level Toffoli-like | C_XC_X X ⟩ magic state distillation protocol, including three factory layouts. To minimize the cost of Clifford corrections induced by magic state injections we tailor injection gadgets to each subroutine. Combining our compilation work with the adder compilation from the companion work Pappalardo et al., we provide global layouts for the block encoding in both architectures which we use to obtain resource estimates for ground-state energy estimation for the benchmarks of FeMoco-54 and FeMoco-76. Assuming a cycle time of 1μs, a reaction time of 10μs, a phase estimation precision of 1 mHa and circuit-level phase-flip noise with probability p_Z = 5 × 10^−4 with negligible bit-flip error, FeMoco-54 requires fewer than 7 500 cat qubits with an expected runtime of under one day for a single phase estimation run using an LDPC-cat architecture. Relaxing the bit-flip requirement to p_X = 10^−11 with an additional layer of elevator codes raises this to an estimated 13 000 cat qubits.
ER -