aiqbench analysis
This research establishes fundamental lower bounds on the circuit depth required for syndrome extraction in quantum error correction, linking information-theoretic requirements directly to hardware connectivity constraints. By introducing an intrinsic measure derived from the stabilizer group, the authors provide a practical method to assess unavoidable computational costs before finalizing hardware layouts and present counterexamples to previous theoretical limits. These findings clarify the space-depth tradeoffs essential for designing efficient fault-tolerant quantum architectures.
The Intrinsic Cost of Quantum Syndrome Extraction
arXiv:2609.39705v1 Announce Type: new Abstract: How much time is fundamentally required to extract the syndrome of a stabilizer code on hardware with a given connectivity graph? Previous work by Delfosse--Beverland--Tremblay (2021) and Baspin--Fawzi--Shayeghi (2023) established bounds connecting syndrome extraction to locality constraints on quantum hardware. Here, we address this question by first formulating an intrinsic measure of the interaction required for syndrome extraction directly from the stabilizer group, independent of the generating set used to describe the code. We then show that this measure yields hardware-dependent lower bounds on exact syndrome-extraction depth for arbitrary stabilizer codes. Guided by this measure, we also construct annular surface-code examples with constant-depth local syndrome extraction that provide a counterexample to Corollary 1 of DBT21. Furthermore, for a fixed quantum Tanner family, this measure strengthens the depth bound explicitly stated in BFS23 and, together with our matching construction, establishes an asymptotically tight space--depth tradeoff. In theory, our results connect the information required by syndrome extraction to the communication capacity of a device; while in practice, they provide a way to assess unavoidable circuit costs before committing to a hardware layout.
Abstract:How much time is fundamentally required to extract the syndrome of a stabilizer code on hardware with a given connectivity graph? Previous work by Delfosse--Beverland--Tremblay (2021) and Baspin--Fawzi--Shayeghi (2023) established bounds connecting syndrome extraction to locality constraints on quantum hardware. Here, we address this question by first formulating an intrinsic measure of the interaction required for syndrome extraction directly from the stabilizer group, independent of the generating set used to describe the code. We then show that this measure yields hardware-dependent lower bounds on exact syndrome-extraction depth for arbitrary stabilizer codes. Guided by this measure, we also construct annular surface-code examples with constant-depth local syndrome extraction that provide a counterexample to Corollary 1 of DBT21. Furthermore, for a fixed quantum Tanner family, this measure strengthens the depth bound explicitly stated in BFS23 and, together with our matching construction, establishes an asymptotically tight space--depth tradeoff. In theory, our results connect the information required by syndrome extraction to the communication capacity of a device; while in practice, they provide a way to assess unavoidable circuit costs before committing to a hardware layout.
Quantum Physics (quant-ph); Information Theory (cs.IT)
arXiv:2609.39705 [quant-ph]
(or arXiv:2609.39705v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2609.39705 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 277 words
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