Direct Cultivation of Entangled |CS⟩ Magic States
Abstract
Magic-state cultivation has largely targeted single-qubit non-Clifford resources. We show that the entangled state |CS⟩=CS|++⟩ can be cultivated directly rather than synthesized from three T-type resources. Two commuting Hermitian Clifford involutions project onto four Pauli-frame branches, so no ideal branch is discarded, while a minimal six-bit [6,2,4] record protects their history. The small-code state cannot itself be certified: late two-fault patterns evade its record, placing the certified boundary after surface-code growth. Under a fixed decoder that sees 136 operational detector bits per patch and withholds 168, exact audits find no accepted closed-boundary logical failure through fault order two, while order-three mechanisms exist. Escaping from the small code directly into a distance-3 patch and growing it to distance 13 in a single round keeps this certificate. Compared with a re-decoded three-T comparator matched to the same binary logical-error target, the direct route uses 2% fewer active locations at p=5×10−4 and $16−−28\%$ more at 8×10−4--10−3, without charging the comparator for T-state storage. Counted in qubit-ticks under one rule for both routes, it uses $21−−39\%$ less spacetime. Adding idle-memory noise to both routes under one rule and one optimized schedule raises the direct route's cost more, to 8% and 46% above the comparator at 5×10−4 and 10−3, because that cost is limited by acceptance. The result is architectural: an entangled non-Clifford state can itself be cultivated with a certified output interface.
Related
- Comparing magic state cultivation methods using matrix product states
- 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
BibTeX
@misc{min2026direct,
title = {{Direct Cultivation of Entangled $|CS\rangle$ Magic States}},
author = {Gunsik Min and Jun Heo},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.09993},
eprint = {2609.09993},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.09993},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Direct Cultivation of Entangled |CS⟩ Magic States
AU - Gunsik Min
AU - Jun Heo
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2609.09993
UR - https://arxiv.org/abs/2609.09993
AB - Magic-state cultivation has largely targeted single-qubit non-Clifford resources. We show that the entangled state |CS⟩=CS|++⟩ can be cultivated directly rather than synthesized from three T-type resources. Two commuting Hermitian Clifford involutions project onto four Pauli-frame branches, so no ideal branch is discarded, while a minimal six-bit [6,2,4] record protects their history. The small-code state cannot itself be certified: late two-fault patterns evade its record, placing the certified boundary after surface-code growth. Under a fixed decoder that sees 136 operational detector bits per patch and withholds 168, exact audits find no accepted closed-boundary logical failure through fault order two, while order-three mechanisms exist. Escaping from the small code directly into a distance-3 patch and growing it to distance 13 in a single round keeps this certificate. Compared with a re-decoded three-T comparator matched to the same binary logical-error target, the direct route uses 2% fewer active locations at p=5×10^−4 and $16−−28\%$ more at 8×10^−4--10^−3, without charging the comparator for T-state storage. Counted in qubit-ticks under one rule for both routes, it uses $21−−39\%$ less spacetime. Adding idle-memory noise to both routes under one rule and one optimized schedule raises the direct route's cost more, to 8% and 46% above the comparator at 5×10^−4 and 10^−3, because that cost is limited by acceptance. The result is architectural: an entangled non-Clifford state can itself be cultivated with a certified output interface.
ER -