The "gold standard" math rule for quantum computing algorithms has just been proven wrong.
April 14, 2026
Original Paper
On Worst-Case Optimal Polynomial Intersection
arXiv · 2604.09533
The Takeaway
It overturns the 'semicircle law,' a math assumption previously thought to be the unbeatable limit for solving complex intersections. This discovery proves that more efficient solutions exist, opening the door for quantum algorithms that are faster and more powerful than current designs.
From the abstract
The Optimal Polynomial Intersection (OPI) problem is the following: Given sets $S_1, \ldots, S_m \subseteq \mathbb{F}$ and evaluation points $a_1, \ldots, a_m \in \mathbb{F}$, find a polynomial $Q \in \mathbb{F}[x]$ of degree less than $n$ so that $Q(a_i) \in S_i$ for as many $i \in \{1, 2, \ldots, m\}$ as possible. Decoded Quantum Interferometry (DQI) is a quantum algorithm that efficiently returns good solutions to the problem, even on worst-case instances (Jordan et. al., 2025). The quality o