Related papers: Generalised Quantum Tree Search
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,…
Quantum computers are designed to outperform standard computers by running quantum algorithms. Areas in which quantum algorithms can be applied include cryptography, search and optimisation, simulation of quantum systems, and solving large…
One of the most basic computational problems is the task of finding a desired item in an ordered list of N items. While the best classical algorithm for this problem uses log_2 N queries to the list, a quantum computer can solve the problem…
In general, a quantum algorithm wants to avoid decoherence or perturbation, since such factors may cause errors in the algorithm. In this letter, we will supply the answer to the interesting question: can the factors seemingly harmful to a…
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…
Quantum walks have been very successful in the development of search algorithms in quantum information, in particular in the development of spatial search algorithms. However, the construction of continuous-time quantum search algorithms in…
Quantum computers use the quantum interference of different computational paths to enhance correct outcomes and suppress erroneous outcomes of computations. In effect, they follow the same logical paradigm as (multi-particle)…
In this work, we generalize the recently-introduced graph composition framework to the non-boolean setting. A quantum algorithm in this framework is represented by a hypergraph, where each hyperedge is adjacent to multiple vertices. The…
Quantum computation, in particular Grover's algorithm, has aroused a great deal of interest since it allows for a quadratic speedup to be obtained in search procedures. Classical search procedures for an $N$ element database require at most…
Grover's quantum algorithm for an unstructured search problem and the Count algorithm by Brassard et al. are generalized to the case when the initial state is arbitrarily and maximally entangled. This ansatz might be relevant with quantum…
Continuous search problems (CSPs), which involve finding solutions within a continuous domain, frequently arise in fields such as optimization, physics, and engineering. Unlike discrete search problems, CSPs require navigating an…
An algorithm for structured database searching is presented and used to solve the set partition problem. O(n) oracle calls are required in order to obtain a solution, but the probability that this solution is optimal decreases exponentially…
Augmentation makes search trees tremendously more versatile, allowing them to support efficient aggregation queries, order-statistic queries, and range queries in addition to insertion, deletion, and lookup. In this paper, we present the…
The structure of satisfiability problems is used to improve search algorithms for quantum computers and reduce their required coherence times by using only a single coherent evaluation of problem properties. The structure of random k-SAT…
Algorithms for learning decision trees often include heuristic local-search operations such as (1) adjusting the threshold of a cut or (2) also exchanging the feature of that cut. We study minimizing the number of classification errors by…
The standard quantum search algorithm lacks a feature, enjoyed by many classical algorithms, of having a fixed-point, i.e. a monotonic convergence towards the solution. Here we present two variations of the quantum search algorithm, which…
Numerous analysis methods for quantitative attack tree analysis have been proposed. These algorithms compute relevant security metrics, i.e. performance indicators that quantify how good the security of a system is, such as the most likely…
Quantum algorithms and circuits can, in principle, outperform the best non-quantum (classical) techniques for some hard computational problems. However, this does not necessarily lead to useful applications. To gauge the practical…
Algorithms for searching and sorting data sets on quantum annealing systems are presented. Search algorithms for unordered data sets are developed. A sorting algorithm for data sets is provided, with a consideration of sort stability.…
Despite the promise that fault-tolerant quantum computers can efficiently solve classically intractable problems, it remains a major challenge to find quantum algorithms that may reach computational advantage in the present era of noisy,…