Related papers: Towards Optimal Separations between Quantum and Ra…
We present a number of results related to quantum algorithms with small error probability and quantum algorithms that are zero-error. First, we give a tight analysis of the trade-offs between the number of queries of quantum search…
We prove that any exact quantum algorithm searching an ordered list of N elements requires more than \frac{1}{\pi}(\ln(N)-1) queries to the list. This improves upon the previously best known lower bound of {1/12}\log_2(N) - O(1). Our proof…
Let a Boolean function be available as a black-box (oracle) and one likes to devise an algorithm to test whether it has certain property or it is $\epsilon$-far from having that property. The efficiency of the algorithm is judged by the…
While exponential separations are known between quantum and randomized communication complexity for partial functions (Raz, STOC 1999), the best known separation between these measures for a total function is quadratic, witnessed by the…
In Exact Quantum Query model, almost all of the Boolean functions for which non-trivial query algorithms exist are symmetric in nature. The most well known techniques in this domain exploit parity decision trees, in which the parity of two…
We study a new type of separation between quantum and classical communication complexity which is obtained using quantum protocols where all parties are efficient, in the sense that they can be implemented by small quantum circuits with…
We use quantum walks to construct a new quantum algorithm for element distinctness and its generalization. For element distinctness (the problem of finding two equal items among N given items), we get an O(N^{2/3}) query quantum algorithm.…
The pointer function of G{\"{o}}{\"{o}}s, Pitassi and Watson \cite{DBLP:journals/eccc/GoosP015a} and its variants have recently been used to prove separation results among various measures of complexity such as deterministic, randomized and…
Simon's problem is an essential example demonstrating the faster speed of quantum computers than classical computers for solving some problems. The optimal separation between exact quantum and classical query complexities for Simon's…
Many quantum algorithms can be analyzed in a query model to compute Boolean functions where input is given by a black box. As in the classical version of decision trees, different kinds of quantum query algorithms are possible: exact,…
We show a nearly quadratic separation between deterministic communication complexity and the logarithm of the partition number, which is essentially optimal. This improves upon a recent power 1.5 separation of G\"o\"os, Pitassi, and Watson…
Given a classical query algorithm as a decision tree, when does there exist a quantum query algorithm with a speed-up over the classical one? We provide a general construction based on the structure of the underlying decision tree, and…
This work studies the quantum query complexity of Boolean functions in a scenario where it is only required that the query algorithm succeeds with a probability strictly greater than 1/2. We show that, just as in the communication…
A quantum algorithm is exact if, on any input data, it outputs the correct answer with certainty (probability 1). A key question is: how big is the advantage of exact quantum algorithms over their classical counterparts: deterministic…
Quantum algorithms can be analyzed in a query model to compute Boolean functions where input is given in a black box and the aim is to compute function value for arbitrary input using as few queries as possible. We concentrate on quantum…
This paper considers the quantum query complexity of {\it $\eps$-biased oracles} that return the correct value with probability only $1/2 + \eps$. In particular, we show a quantum algorithm to compute $N$-bit OR functions with…
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…
Quantum query complexity is typically characterized in terms of XOR queries |x,y> to |x,y+f(x)> or phase queries, which ensure that even queries to non-invertible functions are unitary. When querying a permutation, another natural model is…
Non-linearity of a Boolean function indicates how far it is from any linear function. Despite there being several strong results about identifying a linear function and distinguishing one from a sufficiently non-linear function, we found a…
We give new quantum algorithms for evaluating composed functions whose inputs may be shared between bottom-level gates. Let $f$ be an $m$-bit Boolean function and consider an $n$-bit function $F$ obtained by applying $f$ to conjunctions of…