عوام کا خوف اس وجہ سے ہے کہ سہیل آفریدی کے ساتھ پورا کا پورا کے پی ایسے جڑا ہوا ہے جیسے شہد کی مکھیاں چھتے سے۔۔ سہیل آفریدی اس وقت پاکستان کا سب سے مقبول لیڈر بن گیا ہے کیونکہ وہ اپنے لیڈر کے نظریے کے...

Gowers, Green, Manners, and Tao (Annals '25) recently resolved Marton's polynomial Freiman-Ruzsa conjecture. We give an algorithmic counterpart to their result: given uniform sampling and membership-o...

**Authors:** Srinivasan Arunachalam, Arkopal Dutt, Sabee Grewal, Aparna Gupte Gowers, Green, Manners, and Tao (Annals '25) recently resolved Marton's polynomial Freiman-Ruzsa conjecture. We give an algorithmic counterpart to their result: given uniform sampling and membership-oracle access to a set $A \subseteq \mathbb{F}_2^n$ with doubling constant at most $K$, our algorithm outputs a subspace of size at most $|A|$ whose $K^{O(1)}$ translates cover $A$. The algorithm runs in $\textsf{poly}(n,K)$ time. As applications, we obtain polynomial-time algorithms for a variety of learning problems, including quadratic Goldreich-Levin, improper agnostic tomography of stabilizer states, and tomography of quantum states with bounded stabilizer extent.

arXiv abstract link

**Authors:** Sabee Grewal, Dorian Rudolph We prove $\mathsf{QMA} = \mathsf{QMA_1}$, i.e., every quantum Merlin-Arthur proof system can be made perfectly complete. Our construction uses only Hadamard, Toffoli, and $X$ gates, yielding a universal gate set for $\mathsf{QMA_1}$. As a consequence, quantum $3$-SAT is $\mathsf{QMA}$-complete. The construction relativizes to classical oracles, so known classical-oracle separations of $\mathsf{QMA}$ from $\mathsf{QCMA}$ extend to $\mathsf{QMA_1}$.