Quantum-accelerated algorithms for generating random primitive polynomials over finite fields

Primitive polynomials over finite fields are crucial for various domains of computer science, including classical pseudo-random number generation, coding theory and post-quantum cryptography. Nevertheless, the pursuit of an efficient classical algorithm for generating random primitive polynomials over finite fields remains an ongoing challenge. In this paper, we show how to solve this problem efficiently through hybrid quantum-classical algorithms, and designs of the specific quantum circuits to implement them are also presented. Our research paves the way for the rapid and real-time generation of random primitive polynomials in diverse quantum communication and computation applications

Quasi-Periodic Variations in X-ray Emission and Long-Term Radio Observations: Evidence for a Two-Component Jet in Sw J1644+57

The continued observations of Sw J1644+57 in X-ray and radio bands accumulated a rich data set to study the relativistic jet launched in this tidal disruption event. The X-ray light curve of Sw J1644+57 from 5-30 days presents two kinds of quasi-periodic variations: a 200 second quasi-periodic oscillation (QPO) and a 2.7-day quasi-periodic variation. The latter has been interpreted by a precessing jet launched near the Bardeen-Petterson radius of a warped disk. Here we suggest that the $\sim$ 200s QPO could be associated with a second, narrower jet sweeping the observer line-of-sight periodically, which is launched from a spinning black hole in the misaligned direction with respect to the black hole's angular momentum. In addition, we show that this two-component jet model can interpret the radio light curve of the event, especially the re-brightening feature starting $\sim 100$ days after the trigger. From the data we infer that inner jet may have a Lorentz factor of $\Gamma_{\rm j} \sim 5.5$ and a kinetic energy of $E_{\rm k,iso} \sim 3.0 \times 10^{52} {\rm erg}$, while the outer jet may have a Lorentz factor of $\Gamma_{\rm j} \sim 2.5$ and a kinetic energy of $E_{\rm k,iso} \sim 3.0 \times 10^{53} {\rm erg}$.Comment: 11 pages, 7 figures, accepted for publication in Ap