Library

Research digests

A digest compares claims across papers. It is dated, cited, and short on purpose. RSS.

Quantum algorithms is the guide. The complexity table is the row-by-row comparison.

• 26 Oct 2026Sublinear-depth Trotter steps for electrons in atomic orbitalsGünther and Harrow implement one Trotter stage for a localized atomic-orbital Hamiltonian in polylogarithmic depth, and prove a three-dimensional gate count of N to the 5/3 times t, up to a sub-power factor.
• 19 Oct 2026Learning halfspaces with logarithmically many quantum queriesKrivcenko, Nguyen, and de Wolf learn a linear threshold function to Gaussian error ε with O(log(n/ε)) quantum membership queries. The other gates are still linear in the dimension.
• 12 Oct 2026A noise threshold for Shor's Fourier transformCai and Young prove a sharp threshold for relative Gaussian noise on the small controlled rotations in Shor's quantum Fourier transform. Below it, expected polynomial time; above it, failure on a positive-density set of primes.
• 7 Oct 2026What the source papers claimThe opening note of this library: four algorithms, four different kinds of claim, and the sentence in each source paper that should travel with the result.