Dynamic T-decomposition for classical simulation of quantum circuits
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arXiv
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| Format: | Preprint |
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2024
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| author | Ahmad, Wira Azmoon Sutcliffe, Matthew |
| author_facet | Ahmad, Wira Azmoon Sutcliffe, Matthew |
| contents | It is known that a quantum circuit may be simulated with classical hardware via stabilizer state (T-)decomposition in $O(2^{αt})$ time, given $t$ non-Clifford gates and a decomposition efficiency $α$. The past years have seen a number of papers presenting new decompositions of lower $α$ to reduce this runtime and enable simulation of ever larger circuits. More recently, it has been demonstrated that well placed applications of apparently weaker (higher $α$) decompositions can in fact result in better overall efficiency when paired with the circuit simplification strategies of ZX-calculus.
In this work, we take the most generalized T-decomposition (namely vertex cutting), which achieves a poor efficiency of $α=1$, and identify common structures to which applying this can, after simplification via ZX-calculus rewriting, yield very strong effective efficiencies $α_{\text{eff}}\ll1$. By taking into account this broader scope of the ZX-diagram and incorporating the simplification facilitated by the well-motivated cuts, we derive a handful of efficient T-decompositions whose applicabilities are relatively frequent. In benchmarking these new 'dynamic' decompositions against the existing alternatives, we observe a significant reduction in overall $α$ and hence overall runtime for classical simulation, particularly for certain common circuit classes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_17182 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dynamic T-decomposition for classical simulation of quantum circuits Ahmad, Wira Azmoon Sutcliffe, Matthew Quantum Physics Computational Complexity 81P40, 68Q17, 68W10 It is known that a quantum circuit may be simulated with classical hardware via stabilizer state (T-)decomposition in $O(2^{αt})$ time, given $t$ non-Clifford gates and a decomposition efficiency $α$. The past years have seen a number of papers presenting new decompositions of lower $α$ to reduce this runtime and enable simulation of ever larger circuits. More recently, it has been demonstrated that well placed applications of apparently weaker (higher $α$) decompositions can in fact result in better overall efficiency when paired with the circuit simplification strategies of ZX-calculus. In this work, we take the most generalized T-decomposition (namely vertex cutting), which achieves a poor efficiency of $α=1$, and identify common structures to which applying this can, after simplification via ZX-calculus rewriting, yield very strong effective efficiencies $α_{\text{eff}}\ll1$. By taking into account this broader scope of the ZX-diagram and incorporating the simplification facilitated by the well-motivated cuts, we derive a handful of efficient T-decompositions whose applicabilities are relatively frequent. In benchmarking these new 'dynamic' decompositions against the existing alternatives, we observe a significant reduction in overall $α$ and hence overall runtime for classical simulation, particularly for certain common circuit classes. |
| title | Dynamic T-decomposition for classical simulation of quantum circuits |
| topic | Quantum Physics Computational Complexity 81P40, 68Q17, 68W10 |
| url | https://arxiv.org/abs/2412.17182 |