Quantum Lower Bound for Graph Collision Implies Lower Bound for Triangle Detection

نویسندگان
چکیده

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Quantum Lower Bound for Graph Collision Implies Lower Bound for Triangle Detection

We show that an improvement to the best known quantum lower bound for Graph-Collision problem implies an improvement to the best known lower bound for Triangle problem in the quantum query complexity model. In Graph-Collision we are given free access to a graph (V,E) and access to a function f : V → {0, 1} as a black box. We are asked to determine if there exist (u, v) ∈ E, such that f(u) = f(v...

متن کامل

Quantum Lower Bound for the Collision Problem with Small Range

We extend Aaronson and Shi’s quantum lower bound for the r-to-one collision problem. An r-to-one function is one where every element of the image has exactly r preimages. The r-to-one collision problem is to distinguish between one-to-one functions and r-to-one functions over an n-element domain. Recently, Aaronson and Shi proved a lower bound of Ω((n/r)1/3) quantum queries for the r-to-one col...

متن کامل

Quantum lower bound for sorting ∗

Needless to say, sorting, especially sorting by comparisons, has been a classical problem in computer science. Despite its enormous importance, the complexity, in terms of the number of comparisons needed, is simple to analyze. Straightforward information theoretical argument gives the tight lower bound of log2(n!), which is achieved by several simple sorting algorithms, for example, Insertion ...

متن کامل

Quantum lower bound for recursive fourier sampling

We revisit the oft-neglected ‘recursive Fourier sampling’ (RFS) problem, introduced by Bernstein and Vazirani to prove an oracle separation between BPP and BQP. We show that the known quantum algorithm for RFS is essentially optimal, despite its seemingly wasteful need to uncompute information. This implies that, to place BQP outside of PH [log] relative to an oracle, one needs to go outside th...

متن کامل

0 Quantum lower bound for sorting 1

We prove that Ω(n log n) comparisons are necessary for any quantum algorithm that sorts n numbers with high success probability and uses only comparisons. If no error is allowed, at least 0.110n log2 n − 0.067n + O(1) comparisons must be made. The previous known lower bound is Ω(n).

متن کامل

ذخیره 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: Baltic Journal of Modern Computing

سال: 2016

ISSN: 2255-8950

DOI: 10.22364/bjmc.2016.4.4.10