Related papers: Description of the Grover algorithm based on geome…
This paper introduces a quantum-classical hybrid algorithm for generalized pattern search (GPS) algorithms. We introduce a quantum search step algorithm using amplitude amplification, which reduces the number of oracle calls needed during…
Quantum counting is a key quantum algorithm that aims to determine the number of marked elements in a database. This algorithm is based on the quantum phase estimation algorithm and uses the evolution operator of Grover's algorithm because…
A simpler quantum counting algorithm based on amplitude amplification is presented. This algorithm is bounded by O(sqrt(N/M)) calls to the controlled-Grover operator where M is the number of marked states and N is the total number of states…
Grover's algorithm is normally presented as a method of searching a database, however it would be more accurately described as a method of identifying elements of an interval of the integers which satisfy some logical clause - an example…
It is suggested that the individual outcomes of a measurement process can be understood within standard quantum mechanics in terms of the measuring apparatus, treated as a quantum computer, executing Grover's search algorithm.
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…
We question whether the measurement based quantum computing algorithm is in fact Grover's algorithm or simply a similar oracular search method. The two algorithms share several qualitative features especially in the case of the trivial 4…
In the multitarget Grover algorithm, we are given an unstructured N-element list of objects S_i containing a T-element subset tau and function f, called an oracle, such that f(S_i)=1 if S_i is in tau, otherwise f(S_i) = 0. By using quantum…
We investigate the use of amplitude amplification on the gate-based model of quantum computing as a means for solving combinatorial optimization problems. This study focuses primarily on QUBO (quadratic unconstrained binary optimization)…
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…
Grover's quantum search algorithm is analyzed for the case in which the initial state is an arbitrary pure quantum state $|\phi>$ of $n$ qubits. It is shown that the optimal time to perform the measurement is independent of $| \phi>$,…
As the engineering endeavour to realise quantum computers progresses, we consider that such machines need not rely on binary as their de facto unit of information. We investigate Grover's algorithm under a generalised quantum circuit model,…
Sparse quantum state preparation is a common subroutine in quantum algorithms, where classical data with few nonzero entries must be loaded into a quantum state. In this work, we consider the Grover-Rudolph algorithm, which has recently…
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…
We present a quantum algorithmic routine that extends the realm of Grover-based heuristics for tackling combinatorial optimization problems with arbitrary efficiently computable objective and constraint functions. Building on previously…
In this paper we present a novel quantum algorithm, namely the quantum grid search algorithm, to solve a special search problem. Suppose $ k $ non-empty buckets are given, such that each bucket contains some marked and some unmarked items.…
We apply quantum homomorphic encryption (QHE) schemes suitable for circuits with a polynomial number of $T/T^{\dagger}$-gates to Grover's algorithm, performing a simulation in Qiskit of a Grover circuit that contains 3 qubits. The…
Despite intensive research, the physical origin of the speed-up offered by quantum algorithms remains mysterious. No general physical quantity, like, for instance, entanglement, can be singled out as the essential useful resource. Here we…
The rapid progress of computer science has been accompanied by a corresponding evolution of computation, from classical computation to quantum computation. As quantum computing is on its way to becoming an established discipline of…
There are major advantages in a newer version of Grover's quantum algorithm utilizing a general unitary transformation in the search of a single object in a large unsorted database. In this paper, we generalize this algorithm to multiobject…