Related papers: Nonadaptive quantum query complexity
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 give a quantum algorithm for evaluating a class of boolean formulas (such as NAND trees and 3-majority trees) on a restricted set of inputs. Due to the structure of the allowed inputs, our algorithm can evaluate a depth $n$ tree using…
Quantum algorithms can be analyzed in a query model to compute Boolean functions where input is given in a black box, but the aim is to compute function value for arbitrary input using as few queries as possible. In this paper we…
We describe a method to upper bound the quantum query complexity of Boolean formula evaluation problems, using fundamental theorems about the general adversary bound. This nonconstructive method can give an upper bound on query complexity…
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…
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…
This paper employs a powerful argument, called an algorithmic argument, to prove lower bounds of the quantum query complexity of a multiple-block ordered search problem in which, given a block number i, we are to find a location of a target…
Quantum amplitude estimation is a key sub-routine of a number of quantum algorithms with various applications. We propose an adaptive algorithm for interval estimation of amplitudes. The quantum part of the algorithm is based only on…
We present several families of total boolean functions which have exact quantum query complexity which is a constant multiple (between 1/2 and 2/3) of their classical query complexity, and show that optimal quantum algorithms for these…
We define and study a new type of quantum oracle, the quantum conditional oracle, which provides oracle access to the conditional probabilities associated with an underlying distribution. Amongst other properties, we (a) obtain speed-ups…
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, and shows that van Dam's oracle interrogation is…
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…
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…
It has long been known that any Boolean function that depends on n input variables has both degree and exact quantum query complexity of Omega(log n), and that this bound is achieved for some functions. In this paper we study the case of…
In this paper, we consider a quantum algorithm for solving the following problem: ``Suppose $f$ is a function given as a black box (that is also called an oracle) and $f$ is invariant under some AND-mask. Examine a property of $f$ by…
We prove lower bounds on the error probability of a quantum algorithm for searching through an unordered list of N items, as a function of the number T of queries it makes. In particular, if T=O(sqrt{N}) then the error is lower bounded by a…
We will show that if there exists a quantum query algorithm that exactly computes some total Boolean function f by making T queries, then there is a classical deterministic algorithm A that exactly computes f making O(T^3) queries. The best…
Given a prior probability distribution over a set of possible oracle functions, we define a number of queries to be useless for determining some property of the function if the probability that the function has the property is unchanged…
Fault-tolerant quantum computations require alternating quantum and classical computations, where the classical computations prove vital in detecting and correcting errors in the quantum computation. Recently, interest in using these…
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…