Quantum Algorithms for Modular Factorials
Quantum
Summary
arXiv:2607.29453v1 Announce Type: new Abstract: We give a bounded-error quantum algorithm that, given a prime $p$, a divisor $q\mid(p-1)$, and an integer $0 <1/2$. To our knowledge, this is the first algorithm to break the exponent $1/2$ barrier for modular factorials under such a divisor promise. The main technical ingredient is a quantum algorithm that reconstructs the relevant Jacobi sum exactly in compact algebraic form, with polynomial dependence on $q$ and $\log p$.
Why It Matters
This Quantum development moves quantum capability closer to commercial and national-security relevance. For Asia, it is a signal worth tracking: it shapes who supplies, who scales, and who sets the standard over the next five years.
Key Facts
- SectorQuantum
- Market—
- ImpactMedium (58/100)
- SignalResearch