Shor's 1994 polynomial-time factoring algorithm reset what people thought a computer could do. Three decades later, we are still asking what comes next. This dashboard is an opinionated, citation-backed attempt to answer that question across the five frontiers we judge most likely to deliver the next decisive event.
What "Shor-level" means here
A breakthrough qualifies as Shor-level when it (a) provides a provable, ideally exponential, speedup over the best known classical algorithm; (b) solves a problem people actually care about; and (c) is realisable on a plausible roadmap of fault-tolerant hardware. Shor's hit all three; most candidates discussed here hit two.
The five families
- QSVT — a single algorithmic primitive that recovers Shor, Grover, HHL, and Hamiltonian simulation as corollaries. The current best bet for an algorithmic unification.
- Fault-tolerant software stack — codes, decoders, magic states, and compilers. Doesn't change asymptotic complexity, but compresses the practical threshold by orders of magnitude.
- Post-Shor cryptanalysis — Regev's reduced-qubit factoring, Kuperberg's dihedral HSP attack on isogenies, and the still-open question of polynomial-time quantum LWE.
- QTDA — exponential speedup for Betti numbers; the most concrete candidate for a quantum advantage on natural data, modulo the dequantization frontier.
- QML / HHL-class — the broadest in scope, the hardest to deliver end-to-end, blocked by QRAM and dequantization.
Why a dashboard
"What will the next Shor be?" is a question best answered in the plural. The interactive scoring weights let you re-rank the field by the criteria you find most important — and the embedded Guppy + Selene demos make the underlying primitives concrete instead of abstract.