相关论文: Discrete-query quantum algorithm for NAND trees

Quantum mechanics can speed up a range of search applications over unsorted data. For example imagine a phone directory containing N names arranged in completely random order. To find someone's phone number with a probability of 50%, any…

The quantum search algorithm is a technique for searching N possibilities in only sqrt(N) steps. Although the algorithm itself is widely known, not so well known is the series of steps that first led to it, these are quite different from…

We present the results of a detailed analysis of a general, unstructured adiabatic quantum search of a data base of $N$ items. In particular we examine the effects on the computation time of adding energy to the system. We find that by…

We study the power of nonadaptive quantum query algorithms, which are algorithms whose queries to the input do not depend on the result of previous queries. First, we show that any bounded-error nonadaptive quantum query algorithm that…

Studies on Quantum Computing have been developed since the 1980s, motivating researches on quantum algorithms better than any classical algorithm possible. An example of such algorithms is Grover's algorithm, capable of finding $k$ (marked)…

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…

Quantum walk has been successfully used to search for targets on graphs with vertices identified as the elements of a database. This spacial search on a two-dimensional periodic grid takes $\mathcal{O}\left(\sqrt{N\log N}\right)$ oracle…

Motion planning problems can be simplified by admissible projections of the configuration space to sequences of lower-dimensional quotient-spaces, called sequential simplifications. To exploit sequential simplifications, we present the…

We introduce a structured quantum search algorithm that leverages entanglement maps and a fixed-point method to minimize oracle query complexity in unsorted datasets. By partitioning qubits into rows based on their entanglement order, the…

We describe a general method to obtain quantum speedups of classical algorithms which are based on the technique of backtracking, a standard approach for solving constraint satisfaction problems (CSPs). Backtracking algorithms explore a…

We propose a quantum algorithm for closest pattern matching which allows us to search for as many distinct patterns as we wish in a given string (database), requiring a query function per symbol of the pattern alphabet. This represents a…

While quantum computing provides an exponential advantage in solving system of linear equations, there is little work to solve system of nonlinear equations with quantum computing. We propose quantum Newton's method (QNM) for solving…

Low-energy estimation and state preparation for general $k$-local Hamiltonians are fundamental challenges in quantum complexity theory. For constant relative accuracy, Buhrman et al. (PRL 2025) recently broke the natural Grover bound…

We study quantum algorithms for testing bipartiteness and expansion of bounded-degree graphs. We give quantum algorithms that solve these problems in time O(N^(1/3)), beating the Omega(sqrt(N)) classical lower bound. For testing expansion,…

Traditional tree search algorithms supply a blueprint for modeling problem solving behaviour. A diverse spectrum of problems can be formulated in terms of tree search. Quantum computation, in particular Grover's algorithm, has aroused a…

This paper gives a simple proof of why a quantum computer, despite being in all possible states simultaneously, needs at least 0.707 sqrt(N) queries to retrieve a desired item from an unsorted list of items. The proof is refined to show…

We present a quantum algorithm for sampling random spanning trees from a weighted graph in $\widetilde{O}(\sqrt{mn})$ time, where $n$ and $m$ denote the number of vertices and edges, respectively. Our algorithm has sublinear runtime for…

We present a number of quantum computing patterns that build on top of fundamental algorithms, that can be applied to solving concrete, NP-hard problems. In particular, we introduce the concept of a quantum dictionary as a summation of…

It's the key research topic of signal processing that recognizing genuine targets real time from the disturbed signal which has giant amount of data. A quantum algorithm for pattern recognition of classical signal which has time complexity…

We present a quantum circuit implementation of the quantum hashing algorithm (quantum fingerprinting) for a quantum device with restrictions on the application of two-qubit gates by a qubit connectivity graph. We present an optimization…