2014/09/04 by Hongwei Li, Li Yang, Li, Hong-Wei +1
Computer Science · #Data Structures and Algorithms (cs.DS) #Error Correcting Code Techniques #FOS: Computer and information sciences #FOS: Physical sciences #Machine Learning and Algorithms #Quantum Computing Algorithms and Architecture #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.1409.1416
openalex publication_date 2014/09/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate the influences of variables on a Boolean function f based on the quantum Bernstein-Vazirani algorithm. A previous paper (Floess et al. in Math. Struct. in Comp. Science 23: 386, 2013) has proved that if a n-variable Boolean function f(x1,…,xn) does not depend on an input variable xi, using the Bernstein-Vazirani circuit to f will always obtain an output y that has a 0 in the ith position. We generalize this result and show that after one time running the algorithm, the probability of getting a 1 in each position i is equal to the dependence degree of f on the variable xi, i.e. the influence of xi on f. On this foundation, we give an approximation algorithm to evaluate the influence of any variable on a Boolean function. Next, as an application, we use it to study the Boolean functions with juntas, and construct probabilistic quantum algorithms to learn certain Boolean functions. Compared with the deterministic algorithms given by Floess et al., our probabilistic algorithms are faster.