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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…

Unstructured search remains as one of the significant challenges in computer science, as classical search algorithms become increasingly impractical for large-scale systems due to their linear time complexity. Quantum algorithms, notably…

Quantum computers can execute algorithms that sometimes dramatically outperform classical computation. Undoubtedly the best-known example of this is Shor's discovery of an efficient quantum algorithm for factoring integers, whereas the same…

In former work, we showed that a quantum algorithm requires the number of operations (oracle's queries) of a classical algorithm that knows in advance 50% of the information that specifies the solution of the problem. We gave a preliminary…

A quantum algorithm is a set of instructions for a quantum computer, however, unlike algorithms in classical computer science their results cannot be guaranteed. A quantum system can undergo two types of operation, measurement and quantum…

We study the quantum walk search algorithm of Shenvi, Kempe and Whaley [PRA 67 052307 (2003)] on data structures of one to two spatial dimensions, on which the algorithm is thought to be less efficient than in three or more spatial…

It is questionable that Grover algorithm may be more valuable than a classical one, when a partial information is given in a unstructured database. In this letter, to consider quantum search when a partial information is given, we replace…

Let a classical algorithm be determined by sequential applications of a black box performing one step of this algorithm. If we consider this black box as an oracle which gives a value F(a) for any query a, we can compute T sequential…

Spatial search by discrete-time quantum walk can find a marked node on any ergodic, reversible Markov chain $P$ quadratically faster than its classical counterpart, i.e.\ in a time that is in the square root of the hitting time of $P$.…

In the field of quantum linear system algorithms, quantum computing has realized exponential computational advantages over classical computing. However, the focus has been on square coefficient matrices, with few quantum algorithms…

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…

We describe a quantum algorithm for finding the smallest eigenvalue of a Hermitian matrix. This algorithm combines Quantum Phase Estimation and Quantum Amplitude Estimation to achieve a quadratic speedup with respect to the best classical…

Detection of symmetry is vital to problem solving. Most of the problems of computer vision and computer graphics and machine intelligence in general, can be reduced to symmetry detection problem. Unstructured search problem can also be…

Quantum algorithm is constructed which verifies the formulas of predicate calculus in time $O(\sqrt N)$ with bounded error probability, where $N$ is the time required for classical algorithms. This algorithm uses the polynomial number of…

Quantum algorithms require less operations than classical algorithms. The exact reason of this has not been pinpointed until now. Our explanation is that quantum algorithms know in advance 50% of the solution of the problem they will find…

Many computational problems are subject to a quantum speed-up: one might find that a problem having an O(n^3)-time or O(n^2)-time classic algorithm can be solved by a known O(n^1.5)-time or O(n)-time quantum algorithm. The question…

We study quantum algorithms that learn properties of a matrix using queries that return its action on an input vector. We show that for various problems, including computing the trace, determinant, or rank of a matrix or solving a linear…

The driving force in the pursuit for quantum computation is the exciting possibility that quantum algorithms can be more efficient than their classical analogues. Research on the subject has unraveled several aspects of how that can happen.…

Quantum search is a quantum mechanical technique for searching N possibilities in only sqrt(N) steps. This paper gives a fresh perspective on the algorithm in terms of a resonance phenomenon which is implemented through classical coupled…

In this perspective, we discuss conditions under which it would be possible for a modest fault-tolerant quantum computer to realize a runtime advantage by executing a quantum algorithm with only a small polynomial speedup over the best…