Efficient learning of Clifford disentanglers and typical t-doped unitaries with exponentially more T gates
Abstract
Highly entangled and highly non-stabilizer quantum states need not be hard to learn. We give efficient algorithms for testing and recovering hidden tensor-product structure in unknown pure state vectors of the form lvertψ⟩ = UC ⨂i lvertψi⟩, where UC is an arbitrary unknown Clifford unitary. Although the Clifford can thoroughly scramble the visible product structure, we prove that the Bell distribution retains a characteristic family of quadratic symmetries. By simultaneously block-diagonalising these symmetries, our algorithms linearize the problem and manage to recover both a disentangling Clifford and the hidden partitions with polynomial sample and computational complexity. This may be viewed as an extension of the abelian StateHSP paradigm in which classical post-processing exposes genuinely quadratic structure. Applied to Choi states, the method yields efficient proper learning algorithms for typical t-doped Clifford unitaries in regimes containing exponentially more T gates than previously accessible: the required condition fails only for an exponentially small fraction of circuits when t∼ n, and continues to hold for a constant fraction even when t=2n. Our framework also provides tools for compressing structured many-body Hamiltonians and suggests benchmarking protocols for encoded logical product states in the early fault-tolerant regime.
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BibTeX
@misc{aguilar2026efficient,
title = {{Efficient learning of Clifford disentanglers and typical $t$-doped unitaries with exponentially more $T$ gates}},
author = {Gerard Aguilar and Sofiene Jerbi and Jens Eisert and Lennart Bittel},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.27565},
eprint = {2609.27565},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.27565},
}
RIS
TY - UNPB
TI - Efficient learning of Clifford disentanglers and typical t-doped unitaries with exponentially more T gates
AU - Gerard Aguilar
AU - Sofiene Jerbi
AU - Jens Eisert
AU - Lennart Bittel
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.27565
UR - https://arxiv.org/abs/2609.27565
AB - Highly entangled and highly non-stabilizer quantum states need not be hard to learn. We give efficient algorithms for testing and recovering hidden tensor-product structure in unknown pure state vectors of the form lvertψ⟩ = U_C ⨂_i lvertψ_i⟩, where U_C is an arbitrary unknown Clifford unitary. Although the Clifford can thoroughly scramble the visible product structure, we prove that the Bell distribution retains a characteristic family of quadratic symmetries. By simultaneously block-diagonalising these symmetries, our algorithms linearize the problem and manage to recover both a disentangling Clifford and the hidden partitions with polynomial sample and computational complexity. This may be viewed as an extension of the abelian StateHSP paradigm in which classical post-processing exposes genuinely quadratic structure. Applied to Choi states, the method yields efficient proper learning algorithms for typical t-doped Clifford unitaries in regimes containing exponentially more T gates than previously accessible: the required condition fails only for an exponentially small fraction of circuits when t∼ n, and continues to hold for a constant fraction even when t=2n. Our framework also provides tools for compressing structured many-body Hamiltonians and suggests benchmarking protocols for encoded logical product states in the early fault-tolerant regime.
ER -