scholarly journals Grover's algorithm in natural settings

2021 ◽  
Vol 21 (11-12) ◽  
pp. 945-954
Author(s):  
Apoorva D. Patel
Keyword(s):  
Search Algorithm ◽  
Fine Tuning ◽  
Limited Resources ◽  
Quantum Search ◽  
Grover’S Algorithm ◽  
Quantum Search Algorithm ◽  
Wave Dynamics ◽  
Universal Structure ◽  
Natural Settings ◽  
Selection Of

The execution of Grover's quantum search algorithm needs rather limited resources without much fine tuning. Consequently, the algorithm can be implemented in a variety of physical set-ups, which involve wave dynamics but may not need other quantum features. Several of these set-ups are described, pointing out that some of them occur quite naturally. In particular, it is entirely possible that the algorithm played a key role in the selection of the universal structure of genetic languages.

Speed-up and entanglement in quantum Searching

2002 ◽  
Vol 2 (5) ◽  
pp. 399-409
Author(s):  
S.L. Braunstein ◽  
A.K. Pati
Keyword(s):  
Pure State ◽  
Search Algorithm ◽  
Quantum Search ◽  
Grover’S Algorithm ◽  
Active Molecule ◽  
Quantum Search Algorithm ◽  
Grover's Algorithm ◽  
Speed Up ◽  
Target States

We investigate the issue of speed-up and the necessity of entanglement in Grover's quantum search algorithm. We find that in a pure state implementation of Grover's algorithm entanglement is present even though the initial and target states are product states. In pseudo-pure state implementations, the separability of the states involved defines an entanglement boundary in terms of a bound on the purity parameter. Using this bound we investigate the necessity of entanglement in quantum searching for these pseudo-pure state implementations. If every active molecule involved in the ensemble is `charged for' then in existing machines speed-up without entanglement is not possible.

A quantum search algorithm for future spacecraft attitude determination

2011 ◽  
Vol 68 (7-8) ◽  
pp. 1208-1218 ◽  
Author(s):  
Jack Tsai ◽  
Fu-Yuen Hsiao ◽  
Yi-Ju Li ◽  
Jen-Fu Shen
Keyword(s):  
Attitude Determination ◽  
Search Algorithm ◽  
Spacecraft Attitude ◽  
Quantum Search ◽  
Quantum Search Algorithm

How significant are the known collision and element distinctness quantum algorithms?

2004 ◽  
Vol 4 (3) ◽  
pp. 201-206
Author(s):  
L. Grover ◽  
T. Rudolph
Keyword(s):  
Search Algorithm ◽  
Quantum Algorithms ◽  
Search Space ◽  
Space Complexity ◽  
Quantum Search ◽  
Quantum Search Algorithm ◽  
Time Space ◽  
Simple Quantum ◽  
Structured Problems ◽  
Better Than

Quantum search is a technique for searching $N$ possibilities for a desired target in $O(\sqrt{N})$ steps. It has been applied in the design of quantum algorithms for several structured problems. Many of these algorithms require significant amount of quantum hardware. In this paper we propose the criterion that an algorithm which requires $O(S)$ hardware should be considered significant if it produces a speedup of better than $O\left(\sqrt{S}\right)$ over a simple quantum search algorithm. This is because a speedup of $O\left(\sqrt{S}\right)$ can be trivially obtained by dividing the search space into $S$ separate parts and handing the problem to $S$ independent processors that do a quantum search (in this paper we drop all logarithmic factors when discussing time/space complexity). Known algorithms for collision and element distinctness exactly saturate the criterion.

scholarly journals Implementation of Grover’s Quantum Search Algorithm using Rigetti Forest

2019 ◽  
Vol 8 (6S3) ◽  
pp. 110-114
Keyword(s):  
Quantum Computing ◽  
Search Algorithm ◽  
Search Problem ◽  
Quantum Search ◽  
Quantum Search Algorithm ◽  
Search Result ◽  
Amplitude Amplification ◽  
Testing And Evaluation

Grover’s quantum search algorithm allows quadratic speedup in unsorted search problem by utilizing amplitude amplification trick in quantum computing. In this paper, an approach to implement Grover’s quantum search algorithm is proposed. The implementation is done using Rigetti Forest and Python. The testing and evaluation processes are carried on in two computers with different hardware specifications to derive more information from the result. The results are measured in user time and compared with implementation from Quantum Computing Playground. The user time of this implementation for 10 qubits and 1024 data is slower compared to Quantum Computing Playground’s implementation. The proposed implementation can be improved by calculating the probability of Grover’s quantum search algorithm in finding the appropriate search result.

scholarly journals A new algorithm for fixed point quantum search

2006 ◽  
Vol 6 (6) ◽  
pp. 483-494
Author(s):  
T. Tulsi ◽  
L.K. Grover ◽  
A. Patel
Keyword(s):  
Fixed Point ◽  
Error Probability ◽  
Search Algorithm ◽  
Quantum Search ◽  
Worst Case ◽  
Average Case ◽  
Standard Quantum ◽  
Quantum Search Algorithm ◽  
Monotonic Convergence ◽  
Worst Case Behavior

The standard quantum search lacks a feature, enjoyed by many classical algorithms, of having a fixed point, i.e. monotonic convergence towards the solution. Recently a fixed point quantum search algorithm has been discovered, referred to as the Phase-\pi/3 search algorithm, which gets around this limitation. While searching a database for a target state, this algorithm reduces the error probability from \epsilon to \epsilon^{2q+1} using q oracle queries, which has since been proved to be asymptotically optimal. A different algorithm is presented here, which has the same worst-case behavior as the Phase-\pi/3 search algorithm but much better average-case behavior. Furthermore the new algorithm gives \epsilon^{2q+1} convergence for all integral q, whereas the Phase-\pi/3 search algorithm requires q to be (3^{n}-1)/2 with n a positive integer. In the new algorithm, the operations are controlled by two ancilla qubits, and fixed point behavior is achieved by irreversible measurement operations applied to these ancillas. It is an example of how measurement can allow us to bypass some restrictions imposed by unitarity on quantum computing.

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