A note on quantum black-box complexity of almost all Boolean functions
نویسندگان
چکیده
منابع مشابه
A note on quantum black-box complexity of almost all Boolean functions
We show that, for almost all N -variable Boolean functions f , N/4 − O( √ N log N) queries are required to compute f in quantum black-box model with bounded error.
متن کاملOptimal quantum query bounds for almost all Boolean functions
We show that almost all n-bit Boolean functions have bounded-error quantum query complexity at least n/2, up to lower-order terms. This improves over an earlier n/4 lower bound of Ambainis [1], and shows that van Dam’s oracle interrogation [9] is essentially optimal for almost all functions. Our proof uses the fact that the acceptance probability of a T -query algorithm can be written as the su...
متن کاملExact quantum algorithms have advantage for almost all Boolean functions
It has been proved that almost all n-bit Boolean functions have exact classical query complexity n. However, the situation seemed to be very different when we deal with exact quantum query complexity. In this paper, we prove that almost all n-bit Boolean functions can be computed by an exact quantum algorithm with less than n queries. More exactly, we prove that ANDn is the only n-bit Boolean f...
متن کاملA Note on Black-Box Complexity of Indistinguishability Obfuscation
Mahmoody et al. (TCC 2016-A) showed that basing indistinguishability obfuscation (IO) on a wide range of primitives in a semi-black-box way is as hard as basing public-key cryptography on one-way functions. The list included any primitive P that can be realized relative to random trapdoor permutations or degree-O(1) graded encoding model for any finite ring secure against computationally unboun...
متن کاملOn the Quantum Black-Box Complexity of Majority
We describe a quantum black-box network computing the majority of N bits with zerosided error ǫ using only 2 3 N +O( √ N log(ǫ logN)) queries: the algorithm returns the correct answer with probability at least 1 − ǫ, and “I don’t know” otherwise. Our algorithm is given as a randomized “XOR decision tree” for which the number of queries on any input is strongly concentrated around a value of at ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Information Processing Letters
سال: 1999
ISSN: 0020-0190
DOI: 10.1016/s0020-0190(99)00079-4