Related papers: Performance of Uncoded Implementation of Grover's …
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…
The present era of quantum processors with hundreds to thousands of noisy qubits has sparked interest in understanding the computational power of these devices and how to leverage it to solve practically relevant problems. For applications…
Withdrawn by the author due to irreparable errors. We present a quantum algorithm that in the black-box model performs a search in an ordered list of N elements. Using 3/4 log N + O(1) queries, it achieves a success probability of at least…
We introduce the concepts of Grover operators and Grover kernels to systematically analyse Grover's searching algorithms. Then, we investigate a one-parameter family of quantum searching algorithms of Grover's type and we show that the…
Noisy Intermediate-Scale Quantum (NISQ) devices fail to produce outputs with sufficient fidelity for deep circuits with many gates today. Such devices suffer from read-out, multi-qubit gate and crosstalk noise combined with short…
Near-term hardware is constrained by high error rates, small qubit counts, and relatively low output fidelity, making the execution of large, high performance quantum circuits difficult. Circuit partitioning (or circuit cutting) has emerged…
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.…
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…
Cloud-accessible quantum processors enable direct execution of quantum algorithms on heterogeneous hardware platforms. Unlike classical systems, however, identical quantum circuits may exhibit substantially different behavior across devices…
We review Grover's algorithm by means of a detailed geometrical interpretation and a worked out example. Some basic concepts of Quantum Mechanics and quantum circuits are also reviewed. This work is intended for non-specialists which have…
We investigate the performance of Grover's quantum search algorithm on a register which is subject to loss of the particles that carry the qubit information. Under the assumption that the basic steps of the algorithm are applied correctly…
We present the implementation of Grover's algorithm in a quantum simulator to perform a quantum search for preimages of two scaled hash functions, whose design only uses modular addition, word rotation, and bitwise exclusive or. Our…
We demonstrated the detailed construction of the hybrid quantum-classical computer. Based on this architecture, the useful concept of amplitude interception is illustrated. It is then embedded into a combination of Depth-First Search and…
While limitations on quantum computation by Markovian environmental noise are well-understood in generality, their behavior for different quantum circuits and noise realizations can be less universal. Here we consider a canonical quantum…
Quantum computation has attracted much attention since it was shown by Shor and Grover the possibility to implement quantum algorithms able to realize, respectively, factoring and searching in a faster way than any other known classical…
Grover's search algorithm provides a quadratic speedup over classical brute-force search in terms of query complexity and is widely used as a versatile subroutine in numerous quantum algorithms, including those for combinatorial problems…
Understanding fault-tolerant properties of quantum circuits is important for the design of large-scale quantum information processors. In particular, simulating properties of encoded circuits is a crucial tool for investigating the…
The method of noisy multiqubit quantum circuits modeling is proposed. The analytical formulas for the dependence of quantum algorithms accuracy on qubits count and noise level are obtained for Grover algorithm and quantum Fourier transform.…
The search operation for a marked state by means of Grover's quantum searching algorithm is shown to be an element of group SU(2) which acts on a 2-dimensional space spanned by the marked state and the unmarked collective state. Based on…
The search problem is to find a state satisfying certain properties out of a given set. Grover's algorithm drives a quantum computer from a prepared initial state to the target state and solves the problem quadratically faster than a…