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.

scholarly journals Robust Quantum Search with Uncertain Number of Target States

Entropy ◽  
2021 ◽  
Vol 23 (12) ◽  
pp. 1649
Author(s):  
Yuanye Zhu ◽  
Zeguo Wang ◽  
Bao Yan ◽  
Shijie Wei
Keyword(s):  
Success Rate ◽  
Search Algorithm ◽  
Quantum Algorithms ◽  
Query Complexity ◽  
Quantum Search ◽  
Success Rates ◽  
Quantum Search Algorithm ◽  
Speed Up ◽  
Target States ◽  
Marked State

The quantum search algorithm is one of the milestones of quantum algorithms. Compared with classical algorithms, it shows quadratic speed-up when searching marked states in an unsorted database. However, the success rates of quantum search algorithms are sensitive to the number of marked states. In this paper, we study the relation between the success rate and the number of iterations in a quantum search algorithm of given λ=M/N, where M is the number of marked state and N is the number of items in the dataset. We develop a robust quantum search algorithm based on Grover–Long algorithm with some uncertainty in the number of marked states. The proposed algorithm has the same query complexity ON as the Grover’s algorithm, and shows high tolerance of the uncertainty in the ratio M/N. In particular, for a database with an uncertainty in the ratio M±MN, our algorithm will find the target states with a success rate no less than 96%.

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.

ENTANGLEMENT PROPERTIES OF ADIABATIC QUANTUM ALGORITHMS

2009 ◽  
Vol 07 (08) ◽  
pp. 1531-1539 ◽  
Author(s):  
JIAYAN WEN ◽  
YI HUANG ◽  
DAOWEN QIU
Keyword(s):  
Quantum System ◽  
Search Algorithm ◽  
Quantum Algorithms ◽  
The Other ◽  
Constant Time ◽  
Quantum Search ◽  
Adiabatic Evolution ◽  
Algorithm Performance ◽  
Quantum Search Algorithm ◽  
Speed Up

In this paper, by constructing a more entangled quantum system, we shorten the adiabatic quantum search algorithm to constant time. On the other hand, we show that the speed-up of adiabatic quantum algorithms by selecting particular adiabatic evolution paths or injecting energy into the quantum system can be explained as a form of entanglement enlargement. These findings suggest that entanglement plays a fundamental role for the efficiency of algorithm performance.

scholarly journals A framework for reducing the overhead of the quantum oracle for use with Grover’s algorithm with applications to cryptanalysis of SIKE

2020 ◽  
Vol 15 (1) ◽  
pp. 143-156
Author(s):  
Jean-François Biasse ◽  
Benjamin Pring
Keyword(s):  
Search Algorithm ◽  
Circuit Complexity ◽  
Quantum Circuit ◽  
Grover’S Algorithm ◽  
Search Problems ◽  
Trade Offs ◽  
Single Target ◽  
Grover's Algorithm ◽  
Quantum Oracle ◽  
The Cost

AbstractIn this paper we provide a framework for applying classical search and preprocessing to quantum oracles for use with Grover’s quantum search algorithm in order to lower the quantum circuit-complexity of Grover’s algorithm for single-target search problems. This has the effect (for certain problems) of reducing a portion of the polynomial overhead contributed by the implementation cost of quantum oracles and can be used to provide either strict improvements or advantageous trade-offs in circuit-complexity. Our results indicate that it is possible for quantum oracles for certain single-target preimage search problems to reduce the quantum circuit-size from $O\left(2^{n/2}\cdot mC\right)$ (where C originates from the cost of implementing the quantum oracle) to $O(2^{n/2} \cdot m\sqrt{C})$ without the use of quantum ram, whilst also slightly reducing the number of required qubits.This framework captures a previous optimisation of Grover’s algorithm using preprocessing [21] applied to cryptanalysis, providing new asymptotic analysis. We additionally provide insights and asymptotic improvements on recent cryptanalysis [16] of SIKE [14] via Grover’s algorithm, demonstrating that the speedup applies to this attack and impacting upon quantum security estimates [16] incorporated into the SIKE specification [14].

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.

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