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Simulating magic state cultivation with few Clifford terms

Quantum Journal

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Researchers developed methods to simulate non-Clifford magic state cultivation circuits using only ~8 Clifford ZX-diagrams at 0.1% noise. This achieves a 700,000-fold reduction in terms compared to traditional stabilizer decompositions requiring 6.3 million terms. The approach represents non-Clifford states as sums of Clifford diagrams, aiding integration into larger Clifford circuits. Performance tests show nearly 4 million shots per second on a laptop for d=3 circuits at low noise. The work demonstrates efficient simulation of high T-count circuits with internal structure.

Simulating magic state cultivation with few Clifford terms

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AbstractBuilding upon $\textit{Wan, Zhong (2025)}$ [5] we present a few methods on how to simulate the non-Clifford $d=5$ magic state cultivation circuits[4] with a sum of $\approx 8$ Clifford ZX-diagrams on average, at $0.1\%$ noise. Compared to a magic cat state stabiliser decomposition of all $53$ non-Clifford spiders ($6{,}377{,}292$ terms required), this is more than $7 \times 10^{5}$ times reduction in the number of terms. Our stabiliser decomposition has the advantage of representing the final non-Clifford state (in light of circuit errors) as a sum of Clifford ZX-diagrams. This will be useful in simulating the escape stage of magic state cultivation, where one needs to port the resultant state of cultivation into a larger Clifford circuit with many more qubits. Still, it's necessary to only track $\approx 8$ Clifford terms. Our result sheds light on the simulability of operationally relevant, high $T$-count quantum circuits with some internal structure. Finally, we provide numerical results for full non-Clifford stabiliser rank simulation based on $\mathtt{tsim}$ along with optimisations using our cutting decompositions. Nearly $4\times 10^{6}$ shots per second can be obtained on a laptop for the smaller $d = 3$ circuits at uniform circuit level noise $p=0.0005$, making it only $\sim$$1.1$ times slower than its (circuit-unspecific and un-optimised) fully Clifford proxy simulation via $\mathtt{stim}$ using $S$ gates.Featured image: Distance 3 magic state cultivation circuit as a ZX-diagram.► BibTeX data@article{Wan2026simulatingmagic, doi = {10.22331/q-2026-06-12-2134}, url = {https://doi.org/10.22331/q-2026-06-12-2134}, title = {Simulating magic state cultivation with few {C}lifford terms}, author = {Wan, Kwok Ho and Zhong, Zhenghao and Zapirain, Ainhoa}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {10}, pages = {2134}, month = jun, year = {2026} }► References [1] Sergey Bravyi and Alexei Kitaev. Universal quantum computation with ideal Clifford gates and noisy ancillas. Physical Review A, 71 (2), February 2005. ISSN 1094-1622. 10.1103/physreva.71.022316. URL http://dx.doi.org/10.1103/PhysRevA.71.022316. https://doi.org/10.1103/physreva.71.022316 [2] Daniel Litinski.

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Accelerated Exact Sampling for Magic State Cultivation, 2026. URL https://github.com/kh428/accel-cutting-magic-state. Apache-2.0 License. https://github.com/kh428/accel-cutting-magic-stateCited by[1] William J. Huggins, Tanuj Khattar, Amanda Xu, Matthew Harrigan, Christopher Kang, Guang Hao Low, Austin Fowler, Nicholas C. Rubin, and Ryan Babbush, "The FLuid Allocation of Surface code Qubits (FLASQ) cost model for early fault-tolerant quantum algorithms", arXiv:2511.08508, (2025). [2] Samyak Surti, Lucas Daguerre, and Isaac H. Kim, "Efficient Simulation of Logical Magic State Preparation Protocols", PRX Quantum 7 2, 020329 (2026). [3] Jordan Hines, Corey Ostrove, Kenneth Rudinger, Stefan Seritan, Kevin Young, Robin Blume-Kohout, and Timothy Proctor, "Simulating Quantum Error Correction beyond Pauli Stochastic Errors", arXiv:2603.18457, (2026). [4] Beatriz Dias, Jan Lukas Bosse, and James R. Seddon, "Optimal and improved gate decompositions for accelerated classical simulation of near-Gaussian fermionic circuits", arXiv:2603.18869, (2026). [5] Dongmin Kim, Jeonggeun Seo, Aniket Patra, and Youngsun Han, "Reducing Postselection Overhead in Magic-State Cultivation by In-Patch Multiplexing", arXiv:2605.03616, (2026). The above citations are from SAO/NASA ADS (last updated successfully 2026-06-12 12:07:26). The list may be incomplete as not all publishers provide suitable and complete citation data.Could not fetch Crossref cited-by data during last attempt 2026-06-12 12:07:24: Could not fetch cited-by data for 10.22331/q-2026-06-12-2134 from Crossref. This is normal if the DOI was registered recently.This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions. AbstractBuilding upon $\textit{Wan, Zhong (2025)}$ [5] we present a few methods on how to simulate the non-Clifford $d=5$ magic state cultivation circuits[4] with a sum of $\approx 8$ Clifford ZX-diagrams on average, at $0.1\%$ noise. Compared to a magic cat state stabiliser decomposition of all $53$ non-Clifford spiders ($6{,}377{,}292$ terms required), this is more than $7 \times 10^{5}$ times reduction in the number of terms. Our stabiliser decomposition has the advantage of representing the final non-Clifford state (in light of circuit errors) as a sum of Clifford ZX-diagrams. This will be useful in simulating the escape stage of magic state cultivation, where one needs to port the resultant state of cultivation into a larger Clifford circuit with many more qubits. Still, it's necessary to only track $\approx 8$ Clifford terms. Our result sheds light on the simulability of operationally relevant, high $T$-count quantum circuits with some internal structure. Finally, we provide numerical results for full non-Clifford stabiliser rank simulation based on $\mathtt{tsim}$ along with optimisations using our cutting decompositions. Nearly $4\times 10^{6}$ shots per second can be obtained on a laptop for the smaller $d = 3$ circuits at uniform circuit level noise $p=0.0005$, making it only $\sim$$1.1$ times slower than its (circuit-unspecific and un-optimised) fully Clifford proxy simulation via $\mathtt{stim}$ using $S$ gates.Featured image: Distance 3 magic state cultivation circuit as a ZX-diagram.► BibTeX data@article{Wan2026simulatingmagic, doi = {10.22331/q-2026-06-12-2134}, url = {https://doi.org/10.22331/q-2026-06-12-2134}, title = {Simulating magic state cultivation with few {C}lifford terms}, author = {Wan, Kwok Ho and Zhong, Zhenghao and Zapirain, Ainhoa}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {10}, pages = {2134}, month = jun, year = {2026} }► References [1] Sergey Bravyi and Alexei Kitaev. Universal quantum computation with ideal Clifford gates and noisy ancillas. Physical Review A, 71 (2), February 2005. ISSN 1094-1622. 10.1103/physreva.71.022316. URL http://dx.doi.org/10.1103/PhysRevA.71.022316. https://doi.org/10.1103/physreva.71.022316 [2] Daniel Litinski.

Picturing Quantum Processes: A First Course in Quantum Theory and Diagrammatic Reasoning.

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Simulating magic state cultivation with few Clifford terms

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