Quantum

Hypergraph cycle enumeration for efficient inference of planted k-XOR with smooth trade-off

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Briefings

A new spectral framework called hypergraph cycle enumeration (HCE) was introduced for detecting planted signals in noisy hypergraph inference problems, specifically planted noisy k-XOR. The study compares HCE against the Kikuchi method, finding comparable recovery behavior and identifying specific parameter regimes where HCE outperforms Kikuchi. A subquadratic quantum speedup was achieved by replacing a step with a quantum walk, though classical and quantum algorithms do not refute the existing quartic quantum speedup of quantum Kikuchi method for large-scale, high-noise scenarios.

Key points

• Hypergraph cycle enumeration (HCE) is a spectral framework for detecting planted signals in noisy hypergraph inference problems.
• HCE achieves comparable recovery behavior to the Kikuchi method, matching the Kikuchi hierarchy.

Context

The research addresses efficient inference of planted k-XOR signals, a sparse Learning Parity with Noise problem. The findings clarify algorithmic trade-offs between classical and quantum approaches for noisy hypergraph settings.

Limitations

The study covers one representative problem from the class of planted noisy k-XOR problems. The quantum speedup is limited to specific parameter regimes; classical and quantum algorithms do not refute the quartic quantum speedup of quantum Kikuchi method for large size and high noise strength.

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