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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2604.25532 |
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| _version_ | 1866915963146862592 |
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| author | Guerrero, Rubén Darío |
| author_facet | Guerrero, Rubén Darío |
| contents | We identify a missing local-refinement stage in the cotengra tensor-network contraction pipeline and show that its impact grows monotonically with bond dimension on the \emph{connectivity graph} of Sycamore-like topologies. Appending a nearest-neighbor interchange (NNI) search to the \cotengra{} output at matched 8-s wallclock yields a median \emph{predicted} cost-model gap $Δ\fT$ at $n{=}500$ that grows monotonically and approximately linearly in $χ$, from $\sim\!15$~bits at $χ{=}2$ to $\sim\!116$~bits at $χ{=}16$ (Fig.~\ref{fig:chi_sweep}), with the refiner winning on $25/25$ seeds at every tested $χ$. Two control families -- random $3$-regular and QAOA $p{=}2$ interaction graphs -- show median $|Δ\fT| \leq 0.71$~bits across both controls at every $χ$, with refiner win rate falling toward chance as $χ$ grows; the signal is topology-specific, not a generic refinement-budget effect. An ablation establishes that refinement itself, not the four-axis Pareto acceptance rule, drives the gain ($|Δ\fT| \lesssim 0.1$ bits between scalar and Pareto arms at $χ{=}2$). The Sycamore-circuit envelope (App.~\ref{em:sec:results:syccirc}) reports the corresponding refinement on actual random circuits at depths $m \in \{4, 6, 8, 10, 12\}$, where the refiner wins on $5/5$ instances at every depth. The advantage is therefore largest precisely in the bond-dimension regime relevant to physical contraction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_25532 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Bond-dimension scaling of a local-refinement advantage over hyperoptimized tensor-network contraction on Sycamore like topologies Guerrero, Rubén Darío Quantum Physics 81P68, 91A10, 90C29 I.2.8; G.1.6; G.1.6 We identify a missing local-refinement stage in the cotengra tensor-network contraction pipeline and show that its impact grows monotonically with bond dimension on the \emph{connectivity graph} of Sycamore-like topologies. Appending a nearest-neighbor interchange (NNI) search to the \cotengra{} output at matched 8-s wallclock yields a median \emph{predicted} cost-model gap $Δ\fT$ at $n{=}500$ that grows monotonically and approximately linearly in $χ$, from $\sim\!15$~bits at $χ{=}2$ to $\sim\!116$~bits at $χ{=}16$ (Fig.~\ref{fig:chi_sweep}), with the refiner winning on $25/25$ seeds at every tested $χ$. Two control families -- random $3$-regular and QAOA $p{=}2$ interaction graphs -- show median $|Δ\fT| \leq 0.71$~bits across both controls at every $χ$, with refiner win rate falling toward chance as $χ$ grows; the signal is topology-specific, not a generic refinement-budget effect. An ablation establishes that refinement itself, not the four-axis Pareto acceptance rule, drives the gain ($|Δ\fT| \lesssim 0.1$ bits between scalar and Pareto arms at $χ{=}2$). The Sycamore-circuit envelope (App.~\ref{em:sec:results:syccirc}) reports the corresponding refinement on actual random circuits at depths $m \in \{4, 6, 8, 10, 12\}$, where the refiner wins on $5/5$ instances at every depth. The advantage is therefore largest precisely in the bond-dimension regime relevant to physical contraction. |
| title | Bond-dimension scaling of a local-refinement advantage over hyperoptimized tensor-network contraction on Sycamore like topologies |
| topic | Quantum Physics 81P68, 91A10, 90C29 I.2.8; G.1.6; G.1.6 |
| url | https://arxiv.org/abs/2604.25532 |