Related papers: Exact quantum lower bound for Grover's problem
We propose a scheme for translating metrological precision bounds into lower bounds on query complexity of quantum search algorithms. Within the scheme the link between quadratic performance enhancement in idealized quantum metrological and…
Ordered search is the task of finding an item in an ordered list using comparison queries. The best exact classical algorithm for this fundamental problem uses $\lceil \log_{2}{n}\rceil$ queries for a list of length $n$. Quantum computers…
Grover's search algorithm has attracted great attention due to its quadratic speedup over classical algorithms in unsorted database search problems. However, Grover's algorithm is inefficient in multi-target search problems, except in the…
We systematically investigate quantum algorithms and lower bounds for mean estimation given query access to non-identically distributed samples. On the one hand, we give quantum mean estimators with quadratic quantum speed-up given samples…
We are presented with a graph, $G$, on $n$ vertices with $m$ edges whose edge set is unknown. Our goal is to learn the edges of $G$ with as few queries to an oracle as possible. When we submit a set $S$ of vertices to the oracle, it tells…
Grover search is one of the most important quantum algorithms. In this paper, we consider a kind of search that the conditions of satisfaction $T$ can be rewritten as $T=T_1\bigcap T_2$. Then we present a new Grover search with smaller…
In order to provide a guaranteed precision and a more accurate judgement about the true value of the Cram\'{e}r-Rao bound and its scaling behavior, an upper bound (equivalently a lower bound on the quantum Fisher information) for precision…
This paper discusses an improvement to Grover's algorithm for searches where target states are Hamming weight eigenstates and search space is not ordered. It is shown that under these conditions search efficiency depends on the smaller…
We solve the unstructured search problem in constant time by computing with a physically motivated nonlinearity of the Gross-Pitaevskii type. This speedup comes, however, at the novel expense of increasing the time-measurement precision.…
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 study the average case approximation of the Boolean mean by quantum algorithms. We prove general query lower bounds for classes of probability measures on the set of inputs. We pay special attention to two probabilities, where we show…
We consider the quantum complexities of the following three problems: searching an ordered list, sorting an un-ordered list, and deciding whether the numbers in a list are all distinct. Letting N be the number of elements in the input list,…
In this paper, we introduce a new quantum query lower bound framework. It is inspired by Zhandry's compressed oracle technique, but it also subsumes the polynomial method as a special case. Compared to Zhandry's technique, our approach has…
The approximate degree of a Boolean function is the minimum degree of real polynomial that approximates it pointwise. For any Boolean function, its approximate degree serves as a lower bound on its quantum query complexity, and generically…
Here we extend the concept of blind client-server quantum computation, in which a client with limited quantum power controls the execution of a quantum computation on a powerful server, without revealing any details of the computation. Our…
Search is one of the most commonly used primitives in quantum algorithm design. It is known that quadratic speedups provided by Grover's algorithm are optimal, and no faster quantum algorithms for Search exist. While it is known that at…
Topology optimization is a key methodology in engineering design for finding efficient and robust structures. Due to the enormous size of the design space, evaluating all possible configurations is typically infeasible. In this work, we…
Hamiltonian oracles are the continuum limit of the standard unitary quantum oracles. In this limit, the problem of finding the optimal query algorithm can be mapped into the problem of finding shortest paths on a manifold. The study of…
Grover's database search algorithm, although discovered in the context of quantum computation, can be implemented using any physical system that allows superposition of states. A physical realization of this algorithm is described using…
We invoke an efficient search algorithms as a key challenge in multi-qubit quantum systems. An original algorithm called dynamical quantum search algorithm from which Grover algorithm is obtained at a specified time is presented. This…