Comparing magic state cultivation methods using matrix product states
Abstract
Magic state cultivation prepares high-fidelity magic states at low expected space-time costs; however, the exact performance of some schemes is unsettled due to the difficulty in simulating non-Clifford circuits. Here, we use matrix-product states (MPS) based methods to compute the exact performance of two types of fold-transversal cultivation schemes: (i) the Sahay et al method based on the regular surface code S gate, and (ii) a method we propose based on a partially fault-tolerant fold-transversal S gate. We show that for the former protocol at d=5, the |T⟩ output reaches similar logical error rates to the |S⟩ output, traditionally used as a cheap full Clifford proxy. This contrasts with the ∼10× discrepancy reported for the d=5 colour-code scheme of Gidney et al. We also find that our new d=5 scheme has ∼1.3× lower expected space-time cost while still reaching 10−9 logical error rate. We show that MPS and Clifford-augmented MPS (CAMPS) perform on par with or even better than the recently introduced near-Clifford simulator Clifft on the hardest d=5 regular surface code scheme. Additionally, to speed up simulation, we propose a new pre-screening method based on simple Pauli propagation, lowering by up to three orders of magnitude the required number of exact simulations, and use several simulator-agnostic sampling methods such as subset sampling.
Related
- Efficient time-dependent dynamics of matrix product states using average Hamiltonians
- Probing the Error-Mitigation Threshold with Matrix Product States
- Random Gaussian Augmented Matrix Product States
- The Quasiparticle Ansatz for Relativistic Continuous Matrix Product States
- Symmetry defects and gauging for quantum states with matrix product unitary symmetries
BibTeX
@misc{hartweg2026comparing,
title = {{Comparing magic state cultivation methods using matrix product states}},
author = {Tom Hartweg and Asier Piñeiro Orioli},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.19116},
eprint = {2609.19116},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.19116},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Comparing magic state cultivation methods using matrix product states
AU - Tom Hartweg
AU - Asier Piñeiro Orioli
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.19116
UR - https://arxiv.org/abs/2609.19116
AB - Magic state cultivation prepares high-fidelity magic states at low expected space-time costs; however, the exact performance of some schemes is unsettled due to the difficulty in simulating non-Clifford circuits. Here, we use matrix-product states (MPS) based methods to compute the exact performance of two types of fold-transversal cultivation schemes: (i) the Sahay et al method based on the regular surface code S gate, and (ii) a method we propose based on a partially fault-tolerant fold-transversal S gate. We show that for the former protocol at d=5, the |T⟩ output reaches similar logical error rates to the |S⟩ output, traditionally used as a cheap full Clifford proxy. This contrasts with the ∼10× discrepancy reported for the d=5 colour-code scheme of Gidney et al. We also find that our new d=5 scheme has ∼1.3× lower expected space-time cost while still reaching 10^−9 logical error rate. We show that MPS and Clifford-augmented MPS (CAMPS) perform on par with or even better than the recently introduced near-Clifford simulator Clifft on the hardest d=5 regular surface code scheme. Additionally, to speed up simulation, we propose a new pre-screening method based on simple Pauli propagation, lowering by up to three orders of magnitude the required number of exact simulations, and use several simulator-agnostic sampling methods such as subset sampling.
ER -