aiqbench analysis
This research establishes a rigorous equational theory for Detector Error Models, enabling efficient quasilinear-time verification of quantum error correction circuits. By providing the first static decision procedure that scales to adaptive protocols like lattice surgery without exponential overhead, it significantly advances compiler optimization and fault-tolerance validation in quantum computing pipelines.
Quasilinear Equivalence Checking for Detector Error Models
arXiv:2606.14677v1 Announce Type: new Abstract: A Detector Error Model (DEM) is a structured representation of error mechanisms in quantum circuits, which has gained popularity in quantum compilation pipelines for its ability to capture fault-tolerance at a circuit level. It lists error mechanisms as instructions targeting detectors and observables, specifying for each physical fault channel the probability that the fault fires, the detectors it triggers, and the observables it flips. In this paper, we develop an equational theory for DEMs, with its associated categorical semantics. We present a sound, terminating, confluent rewriting system for DEM terms, formulating it as a symmetric monoidal theory (a PROP) over the Giry monad. We prove that every DEM term has a unique normal form, which can be computed efficiently in quasilinear time $O(k|E|\log|E|)$, where $|E|$ is the number of instructions and $k$ bounds the size of a target set. This provides a complete set of invariants (via Tanner graphs) for structural DEM equivalence. We provide the first static decision procedure for DEM equivalence, with rigorous correctness guarantees. It is complete (decides full decoder-equivalence exactly) for non-adaptive quantum error correction (QEC) pipelines, and scales to a sound and applicable decision procedure for partially-adaptive circuits (lattice surgery, distributed QEC, ...) without suffering exponential overhead. We discuss its application to the verification and optimisation of quantum compilers.
Abstract:A Detector Error Model (DEM) is a structured representation of error mechanisms in quantum circuits, which has gained popularity in quantum compilation pipelines for its ability to capture fault-tolerance at a circuit level. It lists error mechanisms as instructions targeting detectors and observables, specifying for each physical fault channel the probability that the fault fires, the detectors it triggers, and the observables it flips. In this paper, we develop an equational theory for DEMs, with its associated categorical semantics. We present a sound, terminating, confluent rewriting system for DEM terms, formulating it as a symmetric monoidal theory (a PROP) over the Giry monad. We prove that every DEM term has a unique normal form, which can be computed efficiently in quasilinear time $O(k|E|\log|E|)$, where $|E|$ is the number of instructions and $k$ bounds the size of a target set. This provides a complete set of invariants (via Tanner graphs) for structural DEM equivalence. We provide the first static decision procedure for DEM equivalence, with rigorous correctness guarantees. It is complete (decides full decoder-equivalence exactly) for non-adaptive quantum error correction (QEC) pipelines, and scales to a sound and applicable decision procedure for partially-adaptive circuits (lattice surgery, distributed QEC, ...) without suffering exponential overhead. We discuss its application to the verification and optimisation of quantum compilers.
Quantum Physics (quant-ph); Logic in Computer Science (cs.LO); Programming Languages (cs.PL); Software Engineering (cs.SE); Category Theory (math.CT)
arXiv:2606.14677 [quant-ph]
(or arXiv:2606.14677v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2606.14677 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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