research
Coherent Oracle Access Cut Hidden-Subgroup Error Scaling
The query model achieved a quadratic improvement that arbitrary collective sample measurements could not match.
Summary
The query model achieved a quadratic improvement that arbitrary collective sample measurements could not match.
For finite abelian groups, the authors prove matching upper and lower bounds for the state hidden-subgroup problem. Coherent access to state preparation and its inverse improves dependence on error from inverse-linear to inverse-square-root, while the sample-only model remains inverse-linear even with collective measurements. The separation depends on the stronger access model.
Why it matters
The query model achieved a quadratic improvement that arbitrary collective sample measurements could not match.
Limits and context
- Coherent access to state preparation and its inverse improves dependence on error from inverse-linear to inverse-square-root, while the sample-only model remains inverse-linear even with collective measurements.
Key claims
The query model achieved a quadratic improvement that arbitrary collective sample measurements could not match.
Qualification: Coherent access to state preparation and its inverse improves dependence on error from inverse-linear to inverse-square-root, while the sample-only model remains inverse-linear even with collective measurements.
Evidence: source-2026-09-29-017
Sources
- arXiv preprint 2609.35656arXiv · primary research
Corrections
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