Related papers: Exact Quantum Search by Parallel Unitary Discrimin…
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…
We propose a scalable implementation of Grover's quantum search algorithm in a trapped-ion quantum information processor. The system is initialized in an entangled Dicke state by using simple adiabatic techniques. The…
Grover discovered a quantum algorithm for identifying a target element in an unstructured search universe of N items in approximately square-root of N queries to a quantum oracle, thus achieving a square-root speed-up over classical…
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…
We study the problem of learning an unknown graph provided via an oracle using a quantum algorithm. We consider three query models. In the first model ("OR queries"), the oracle returns whether a given subset of the vertices contains any…
Variational quantum algorithms have become the de facto model for current quantum computations. A prominent example of such algorithms -- the quantum approximate optimization algorithm (QAOA) -- was originally designed for combinatorial…
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.…
A binary constant weight code is a type of error-correcting code with a wide range of applications. The problem of finding a binary constant weight code has long been studied as a combinatorial optimization problem in coding theory. In this…
This paper presents a parallel solution based on the coarse-grained multicomputer (CGM) model using the four-splitting technique to solve the optimal binary search tree problem. The well-known sequential algorithm of Knuth solves this…
A quantum algorithm is a set of instructions for a quantum computer, however, unlike algorithms in classical computer science their results cannot be guaranteed. Quantum search algorithm can be described as the rotation of state vectors in…
We investigate the quantum state discrimination task for sets of linear independent pure states with an intrinsic ordering. This structured discrimination problems allow for a novel scheme that provides a certified level of error, that is,…
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.…
In this paper, we consider the partial database search problem where given a database on N items, we are required to determine the first k bits of an address x such that f(x)=1. We derive an algorithm and a lower bound for this problem in…
Quantum algorithms for unstructured search problems rely on the preparation of a uniform superposition, traditionally achieved through Hadamard gates. However, this incidentally creates an auxiliary search space consisting of nonsensical…
Overlapping clusters are common in models of many practical data-segmentation applications. Suppose we are given $n$ elements to be clustered into $k$ possibly overlapping clusters, and an oracle that can interactively answer queries of the…
We describe a general framework for regarding oracle-assisted quantum algorithms as tools for discriminating between unitary transformations. We apply this to the Deutsch-Jozsa problem and derive all possible quantum algorithms which solve…
This paper provides a block coordinate descent algorithm to solve unconstrained optimization problems. In our algorithm, computation of function values or gradients is not required. Instead, pairwise comparison of function values is used.…
A quantum algorithm for combinatorial search is presented that provides a simple framework for utilizing search heuristics. The algorithm is evaluated in a new case that is an unstructured version of the graph coloring problem. It performs…
Sorting is a fundamental computational process, which facilitates subsequent searching of a database. It can be thought of as factorisation of the search process. The location of a desired item in a sorted database can be found by classical…
The hardness to solve an unstructured quantum search problem by a standard quantum search algorithm mainly originates from the low efficiency to amplify the amplitude of the marked state by the oracle unitary operation associated with other…