What is the largest separation between quantum and classical query complexity?
نویسندگان
چکیده
منابع مشابه
Interpolating Between Quantum and Classical Complexity Classes
We reveal a natural algebraic problem whose complexity appears to interpolate between the well-known complexity classes BQP and NP: ⋆ Decide whether a univariate polynomial with exactly m monomial terms has a p-adic rational root. In particular, we show that while (⋆) is doable in quantum randomized polynomial time when m=2 (and no classical randomized polynomial time algorithm is known), (⋆) i...
متن کامل1 Sharp quantum vs . classical query complexity separations ∗
We obtain the strongest separation between quantum and classical query complexity known to date—specifically, we define a black-box problem that requires exponentially many queries in the classical bounded-error case, but can be solved exactly in the quantum case with a single query (and a polynomial number of auxiliary operations). The problem is simple to define and the quantum algorithm solv...
متن کاملQuery Complexity: Worst-Case Quantum Versus Average-Case Classical
In this note we investigate the relationship between worst-case quantum query complexity and average-case classical query complexity. Specifically, we show that if a quantum computer can evaluate a total Boolean function f with bounded error using T queries in the worst case, then a deterministic classical computer can evaluate f using O(T ) queries in the average case, under a uniform distribu...
متن کاملTowards Better Separation between Deterministic and Randomized Query Complexity
We show that there exists a Boolean function F which gives the following separations among deterministic query complexity (D(F )), randomized zero error query complexity (R0(F )) and randomized one-sided error query complexity (R1(F )): R1(F ) = Õ( √ D(F )) and R0(F ) = Õ(D(F ))3/4. This refutes the conjecture made by Saks and Wigderson that for any Boolean function f , R0(f) = Ω(D(f))0.753... ...
متن کاملA new exponential separation between quantum and classical one-way communication complexity
We present a new example of a partial boolean function whose one-way quantum communication complexity is exponentially lower than its one-way classical communication complexity. The problem is a natural generalisation of the previously studied Subgroup Membership problem: Alice receives a bit string x, Bob receives a permutation matrix M , and their task is to determine whether Mx = x or Mx is ...
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: Science Bulletin
سال: 2017
ISSN: 2095-9273
DOI: 10.1016/j.scib.2017.06.002