Related papers: Unbounded Error Quantum Query Complexity
We show that any quantum algorithm searching an ordered list of n elements needs to examine at least 1/12 log n-O(1) of them. Classically, log n queries are both necessary and sufficient. This shows that quantum algorithms can achieve only…
Quantum algorithms for graph problems are considered, both in the adjacency matrix model and in an adjacency list-like array model. We give almost tight lower and upper bounds for the bounded error quantum query complexity of Connectivity,…
We study randomized and quantum query (a.k.a. decision tree) complexity for all total Boolean functions, with emphasis to derandomization and dequantization (removing quantumness from algorithms). Firstly, we show that $D(f) = O(Q_1(f)^3)$…
Large-scale quantum computation will only be achieved if experimentally implementable quantum error correction procedures are devised that can tolerate experimentally achievable error rates. We describe a quantum error correction procedure…
Quantum computations promise the ability to solve problems intractable in the classical setting. Restricting the types of computations considered often allows to establish a provable theoretical advantage by quantum computations, and later…
Blind quantum computation allows a client with limited quantum capabilities to interact with a remote quantum computer to perform an arbitrary quantum computation, while keeping the description of that computation hidden from the remote…
We consider quantum search algorithms that have access to a noisy oracle that, for every oracle call, with probability $p>0$ completely depolarizes the query registers, while otherwise working properly. Previous results had not ruled out…
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…
We obtain a query lower bound for quantum algorithms solving the phase estimation problem. Our analysis generalizes existing lower bound approaches to the case where the oracle Q is given by controlled powers Q^p of Q, as it is for example…
The hidden shift problem is a natural place to look for new separations between classical and quantum models of computation. One advantage of this problem is its flexibility, since it can be defined for a whole range of functions and a…
Let $\R(\cdot)$ stand for the bounded-error randomized query complexity. We show that for any relation $f \subseteq \{0,1\}^n \times \mathcal{S}$ and partial Boolean function $g \subseteq \{0,1\}^n \times \{0,1\}$, $\R_{1/3}(f \circ g^n) =…
Quantum query complexity studies the number of queries needed to learn some property of a black box. A closely related question is how well an algorithm can succeed with this learning task using only a fixed number of queries. In this work,…
Although quantum algorithms realizing an exponential time speed-up over the best known classical algorithms exist, no quantum algorithm is known performing computation using less space resources than classical algorithms. In this paper, we…
This paper considers the query complexity of the functions in the family F_{N,M} of N-variable Boolean functions with onset size M, i.e., the number of inputs for which the function value is 1, where 1<= M <= 2^{N}/2 is assumed without loss…
We study randomized and quantum efficiency lower bounds in communication complexity. These arise from the study of zero-communication protocols in which players are allowed to abort. Our scenario is inspired by the physics setup of Bell…
We study the problem of simulating protocols in a quantum communication setting over noisy channels. This problem falls at the intersection of quantum information theory and quantum communication complexity, and it will be of importance for…
Quantum query complexity plays an important role in studying quantum algorithms, which captures the most known quantum algorithms, such as search and period finding. A query algorithm applies $U_tO_x\cdots U_1O_xU_0$ to some input state,…
Although a quantum state requires exponentially many classical bits to describe, the laws of quantum mechanics impose severe restrictions on how that state can be accessed. This paper shows in three settings that quantum messages have only…
We consider the number of quantum queries required to determine the coefficients of a degree-d polynomial over GF(q). A lower bound shown independently by Kane and Kutin and by Meyer and Pommersheim shows that d/2+1/2 quantum queries are…
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…