Simulating magic state cultivation with few Clifford terms
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912997137448960 |
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| author | Wan, Kwok Ho Zhong, Zhenghao Zapirain, Ainhoa |
| author_facet | Wan, Kwok Ho Zhong, Zhenghao Zapirain, Ainhoa |
| contents | Building upon [arXiv:2509.01224], we present a few methods on how to simulate the non-Clifford $d=5$ magic state cultivation circuits [arXiv:2409.17595] 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 SD6 circuit level noise $p=0.0005$, making it only $\sim$$1.1$ times slower than its (circuit-unspecific and un-optimised) fully Clifford proxy simulation via $\mathtt{stim}$ using $S$ gates. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_08658 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Simulating magic state cultivation with few Clifford terms Wan, Kwok Ho Zhong, Zhenghao Zapirain, Ainhoa Quantum Physics Building upon [arXiv:2509.01224], we present a few methods on how to simulate the non-Clifford $d=5$ magic state cultivation circuits [arXiv:2409.17595] with a sum of $\approx 8$ Clifford ZX-diagrams on average, at $0.1\%$ noise. Compared to a magic cat state stabiliser decomposition of all $53$ non-Clifford spiders ($6{,}377{,}292$ terms required), this is more than $7 \times 10^{5}$ times reduction in the number of terms. Our stabiliser decomposition has the advantage of representing the final non-Clifford state (in light of circuit errors) as a sum of Clifford ZX-diagrams. This will be useful in simulating the escape stage of magic state cultivation, where one needs to port the resultant state of cultivation into a larger Clifford circuit with many more qubits. Still, it's necessary to only track $\approx 8$ Clifford terms. Our result sheds light on the simulability of operationally relevant, high $T$-count quantum circuits with some internal structure. Finally, we provide numerical results for full non-Clifford stabiliser rank simulation based on $\mathtt{tsim}$ along with optimisations using our cutting decompositions. Nearly $4\times 10^{6}$ shots per second can be obtained on a laptop for the smaller $d = 3$ circuits at SD6 circuit level noise $p=0.0005$, making it only $\sim$$1.1$ times slower than its (circuit-unspecific and un-optimised) fully Clifford proxy simulation via $\mathtt{stim}$ using $S$ gates. |
| title | Simulating magic state cultivation with few Clifford terms |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2509.08658 |