Related papers: A novel SO(3) picture for quantum searching

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…

We describe a simulation method for a quantum spin model of a generic, general purpose quantum computer. The use of this quantum computer simulator is illustrated through several implementations of Grover's database search algorithm. Some…

This paper extends the quantum search class of algorithms to the multiple solution case. It is shown that, like the basic search algorithm, these too can be represented as a rotation in an appropriately defined two dimensional vector space.…

We establish a lower bound concerning the computational complexity of Grover's algorithms on fractal networks. This bound provides general predictions for the quantum advantage gained for searching unstructured lists. It yields a…

Grover's quantum search algorithm provides a quadratic speedup over the classical one. The computational complexity is based on the number of queries to the oracle. However, depth is a more modern metric for noisy intermediate-scale quantum…

Here we suggest a modification of Grover's algorithm, based on a multiphase oracle which marks each solution with a different phase when there is more than one solution. Such a modification can be used to maintain a high probability of…

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…

Grover's algorithm is usually described in terms of the iteration of a compound operator of the form $Q = - H I_{0} H I_{x_0}$. Although it is quite straightforward to verify the algebra of the iteration, this gives little insight into why…

In this paper, we will define a quantum operator that performs the inversion about the mean only on a subspace of the system (Partial Diffusion Operator). This operator is used in a quantum search algorithm that runs in O(sqrt{N/M}) for…

In this paper we investigate the entanglement nature of quantum states generated by Grover's search algorithm by means of algebraic geometry. More precisely we establish a link between entanglement of states generated by the algorithm and…

We investigate a set of discrete-time quantum search algorithms on the n-dimensional hypercube following a proposal by Shenvi, Kempe and Whaley. We show that there exists a whole class of quantum search algorithms in the symmetry reduced…

Spatial search on graphs is one of the most important algorithmic applications of quantum walks. To show that a quantum-walk-based search is more efficient than a random-walk-based search is a difficult problem, which has been addressed in…

A quantum circuit to construct all maximal cliques using Grover search algorithm is presented. This oracle circuit takes as input an n-qubit state |x> and the adjacency matrix data A of an n-node network, and outputs the state (-1)^f(x) |x>…

In the emerging domain of quantum algorithms, the Grover's quantum search is certainly one of the most significant. It is relatively simple, performs a useful task and more importantly, does it in an optimal way. However, due to the success…

The optimal runtime of a quantum computer searching a database is typically cited as the square root of the number of items in the database, which is famously achieved by Grover's algorithm. With parallel oracles, however, it is possible to…

This paper researches how the systematic errors in phase inversions affect the success rate and the number of iterations in optimized quantum random-walk search algorithm. Through geometric description of this algorithm, the model of the…

We present a quantum algorithm for solving perfect mazes by casting the pathfinding task as a structured search problem. Building on Grover's amplitude amplification, the algorithm encodes all candidate paths in superposition and evaluates…

In this work, we consider the spatial search for a general marked state on graphs by continuous time quantum walks. As a simplest case, we compute the amplitude expression of the search for the multi-vertex uniform superposition state on…

Quantum computing has advanced rapidly in recent years and has shown advantages in a variety of domains. In this paper, we investigate its potential for discrete simulation optimization in the fixed-confidence setting, a fundamental problem…

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…