相关论文: Solving mathematical problems with quantum search …

Consider the unstructured search of an unknown number l of items in a large unsorted database of size N. The multi-object quantum search algorithm consists of two parts. The first part of the algorithm is to generalize Grover's…

Although entanglement is widely considered to be necessary for quantum algorithms to improve on classical ones, Lloyd has observed recently that Grover's quantum search algorithm can be implemented without entanglement, by replacing…

Given a parameterized quantum circuit such that a certain setting of these real-valued parameters corresponds to Grover's celebrated search algorithm, can a variational algorithm recover these settings and hence learn Grover's algorithm? We…

An important and usual problem is to search all states we want from a database with a large number of states. In such, recall is vital. Grover's original quantum search algorithm has been generalized to the case of multiple solutions, but…

In this paper, we extend a previously presented Grover-based heuristic to tackle general combinatorial optimization problems with linear constraints. We further describe the introduced method as a framework that enables performance…

In a previous paper [quant-ph/0408045] we described a quantum algorithm to prepare an arbitrary state of a quantum register with arbitrary fidelity. Here we present an alternative algorithm which uses a small number of quantum oracles…

Grover's search algorithm was a groundbreaking advancement in quantum algorithms, displaying a quadratic speed-up of querying for items. Since the creation of this algorithm it has been utilized in various ways, including in preparing…

Quantum computers require quantum logic, something fundamentally different to classical Boolean logic. This difference leads to a greater efficiency of quantum computation over its classical counter-part. In this review we explain the basic…

Quantum Search Algorithm made a big impact by being able to solve the search problem for a set with $N$ elements using only $O(\sqrt{N})$ steps. Unfortunately, it is impossible to reduce the order of the complexity of this problem, however,…

The simplest technique for simulating a quantum algorithm - QA described based on the direct matrix representation of the quantum operators. Using this approach, it is relatively simple to simulate the operation of a QA and to perform…

Solving linear systems of equations is ubiquitous in all areas of science and engineering. With rapidly growing data sets, such a task can be intractable for classical computers, as the best known classical algorithms require a time…

In a fundamental paper [Phys. Rev. Lett. 78, 325 (1997)] Grover showed how a quantum computer can find a single marked object in a database of size N by using only O(N^{1/2}) queries of the oracle that identifies the object. His result was…

Grover's algorithm accelerates unstructured database search quadratically compared to classical algorithms. In the NISQ era, distributed quantum computing can decrease circuit depth and reduce noise. In this paper, an algorithm for…

Many quantum algorithms for attacking symmetric cryptography involve the rank problem of quantum linear equations. In this paper, we first propose two quantum algorithms for solving quantum linear systems of equations with coherent…

The phenomenon of quantum entanglement is fundamental to the implementation of quantum computation, and requires at least two qubits for its demonstration. However, both Deutsch algorithm and Grover's search algorithm for two bits do not…

There exist quantum algorithms that are more efficient than their classical counterparts; such algorithms were invented by Shor in 1994 and then Grover in 1996. A lack of invention since Grover's algorithm has been commonly attributed to…

This paper presented two general quantum search algorithms. We derived the iterated formulas and the simpler approximate formulas and the precise formula for the amplitude in the desired state. A mathematical proof of Grover's algorithm…

This paper presents a quantum search approach to combinatorial constraint satisfaction problems, demonstrated through the generation of magic squares. We reformulate magic square construction as a quantum search problem in which a…

Quantum algorithms are conventionally formulated for implementation on a single system of qubits amenable to projective measurements. However, in expectation value quantum computation, such as nuclear magnetic resonance realizations, the…

Quite often in database search, we only need to extract portion of the information about the satisfying item. Recently Radhakrishnan & Grover [RG] considered this problem in the following form: the database of $N$ items was divided into $K$…