Logical CCZ state cultivation
Abstract
Logical CCZ states enable Toffoli gates, a central building block of fault-tolerant quantum arithmetic. We introduce an end-to-end protocol for direct CCZ-state preparation on bivariate tricycle and bicycle (BT/BB) codes. Our factory combines the cup-product CCZ gates native to BT codes with two novel ingredients, both enabled by engineering the logical coupling between BT and BB codes through projection-preserving lifts. Index-2 lifted BB ancillas enable selective Z-basis initialization, allowing the native cup-product gates to directly prepare two disjoint logical CCZ states. The prepared CCZ states are faithfully transferred to index-3 lifted BB memories with high code distance. We use decoder-based postselection to obtain high-fidelity output states with low overhead. We perform exact simulations of our factory under a circuit-level noise model motivated by neutral-atom hardware, obtaining joint infidelities of 1.84×10−5 at 21.94% acceptance and 4.10×10−7 at 8.89% acceptance for single-qubit, CZ, and CCZ error rates of 0.01%, 0.1%, and 0.5%, respectively. At the output-infidelity target of our smallest factory, its estimated spacetime cost per CCZ state is lower than that of T-state cultivation followed by CCZ conversion, providing an efficient route to logical CCZ states for fault-tolerant quantum computation.
Related
- Exact logical error rates for magic state cultivation
- The practical cost of magic state cultivation
- MagiCFirm: A Runtime for Magic-State Cultivation with Algorithm-Hardware Co-Design
- Diagnosing and Restoring the Degraded Fault Distance of Magic State Cultivation
- Demonstration of a logical Bell-state measurement beyond the linear-optical limit
BibTeX
@misc{hirasaki2026logical,
title = {{Logical CCZ state cultivation}},
author = {Yuta Hirasaki and Jong Yeon Lee},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.20591},
eprint = {2610.20591},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.20591},
}
RIS
TY - UNPB
TI - Logical CCZ state cultivation
AU - Yuta Hirasaki
AU - Jong Yeon Lee
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.20591
UR - https://arxiv.org/abs/2610.20591
AB - Logical CCZ states enable Toffoli gates, a central building block of fault-tolerant quantum arithmetic. We introduce an end-to-end protocol for direct CCZ-state preparation on bivariate tricycle and bicycle (BT/BB) codes. Our factory combines the cup-product CCZ gates native to BT codes with two novel ingredients, both enabled by engineering the logical coupling between BT and BB codes through projection-preserving lifts. Index-2 lifted BB ancillas enable selective Z-basis initialization, allowing the native cup-product gates to directly prepare two disjoint logical CCZ states. The prepared CCZ states are faithfully transferred to index-3 lifted BB memories with high code distance. We use decoder-based postselection to obtain high-fidelity output states with low overhead. We perform exact simulations of our factory under a circuit-level noise model motivated by neutral-atom hardware, obtaining joint infidelities of 1.84×10^−5 at 21.94% acceptance and 4.10×10^−7 at 8.89% acceptance for single-qubit, CZ, and CCZ error rates of 0.01%, 0.1%, and 0.5%, respectively. At the output-infidelity target of our smallest factory, its estimated spacetime cost per CCZ state is lower than that of T-state cultivation followed by CCZ conversion, providing an efficient route to logical CCZ states for fault-tolerant quantum computation.
ER -