Accelerating Regression Tasks with Quantum Algorithms

A claim-by-claim audit of six universal quantum runtime guarantees
ICML 2026 #7771
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Core sparsification

CLAIM 1 · FALSIFIED
Algorithm 2 requests M proportional to n/ε² samples although its cited MultiSample contract requires M≤m. Its explicit loop is Ω(ε⁻²), contradicting the displayed ε⁻¹ runtime at fixed dimensions.
CLAIM 2 · FALSIFIED
Its exact pipeline explicitly processes Θ̃(n/ε²) samples, leaving the cited sampler domain and contradicting the displayed ε⁻¹ runtime at fixed dimensions.
Exact audit: 11/11 source-valid ε cells violate M≤m; the threshold control passes.

Regularized regression

CLAIM 3 · FALSIFIED
Quantum Lasso algorithms from 2021 and 2023 predate the target. Separately, a λ omission gives an exact 7/40 impossibility gap.
CLAIM 4 · FALSIFIED
The valid Ridge augmentation [A;√λI],[b;0] inherits Claim 2's sampler-domain and ε-power contradictions.
Primary dates: 2021-10-25 and 2023-12-21 precede 2025-09-29.

Robust and ℓp losses

CLAIM 5 · FALSIFIED
γ₁ matches Huber, but the all-ε framework eventually invokes MultiSample outside its stated M≤m domain.
CLAIM 6 · FALSIFIED
A valid p=3/2 family contradicts the all-ε framework domain. The restricted constant-ε, large-m regime is not denied.
Claims 5–6 are MEDIUM confidence because their hidden polynomial term absorbs the loop power.
Compute
CPU only; no GPU or quantum hardware
Controls
Independent checkers and fail-closed tests
Live judge
12/12; all six FALSIFIED