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%.

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.

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.

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.

Superposition, entanglement and quantum computation

2002 ◽  
Vol 2 (2) ◽  
pp. 97-116
Author(s):  
T.M. Forcer ◽  
A.J.G. Hey ◽  
D.A. Ross ◽  
P.G.R. Smith
Keyword(s):  
Quantum Computing ◽  
Quantum Computation ◽  
Search Algorithm ◽  
Quantum Algorithms ◽  
Quantum Search ◽  
Quantum Search Algorithm ◽  
Electronic Implementation

The paper examines the roles played by superposition and entanglement in quantum computing. The analysis is illustrated by discussion of a "classical" electronic implementation of Grover's quantum search algorithm. It is shown explicitly that the absence of multi-particle entanglement leads to exponentially rising resources for implementing such quantum algorithms.

Optimization of 16-Element Quantum Search on IBMQ

SPIN ◽  
2021 ◽  
pp. 2140003
Author(s):  
Wei Zi ◽  
Shuai Yang ◽  
Cheng Guo ◽  
Xiaoming Sun
Keyword(s):  
Success Rate ◽  
Search Algorithm ◽  
Quantum Circuit ◽  
Experimental Results ◽  
Quantum Search ◽  
Quantum Devices ◽  
Grover Algorithm ◽  
Quantum Search Algorithm ◽  
Diffusion Operator ◽  
And Diffusion

Unstructured searching, which is to find the marked element from a given unstructured data set, is a widely studied problem in computer science. It is well known that Grover algorithm provides a quadratic speedup to solve unstructured search problem compared with the classical algorithm. This algorithm has received a lot of attention due to the strong versatility. In this manuscript, we report experimental results of searching a unique target from 16 elements on five different quantum devices of IBM quantum Experience (IBMQ). We first implement the original Grover algorithm on these devices. However, the experiment probability of success of finding the correct target is almost the same as random choice. We then optimize the quantum circuit size of the search algorithm. The oracle operator and diffusion operator are two of the most costly operators in Grover algorithm. For the 16-element quantum search algorithm, both the oracle operator and diffusion operator consist of a triple controlled [Formula: see text] gate ([Formula: see text]) and some single-qubit gates. So we optimize the implementation of the [Formula: see text] gate according to the qubits layout of different quantum devices. On the ibmq_santiago, the experimental success rate of the 16-element quantum search algorithm is increased to [Formula: see text] by the optimization, which is better than all the published experiments implemented on IBMQ devices. For other IBMQ devices, the experimental success rate of 16-element quantum search also has been significantly improved. We then try to further reduce the size of the quantum circuit by modifying the Grover algorithm, with a tolerable loss of the theoretical success probability. On ibmq_quito, the experimental success rate is further improved from 25.23% to 27.56% after optimization. These experimental results show the importance of circuit optimization and algorithm optimization in the Noisy-Intermediate-Scale Quantum (NISQ) era.

scholarly journals Search via quantum walks with intermediate measurements

2015 ◽  
Vol 29 (19) ◽  
pp. 1550127
Author(s):  
Efrain Buksman ◽  
André L. Fonseca de Oliveira ◽  
Jesús García López de Lacalle
Keyword(s):  
Close Relationships ◽  
Search Algorithm ◽  
Quantum Algorithms ◽  
Quantum Walks ◽  
Quantum Search ◽  
Brute Force ◽  
Correlation Measure ◽  
Quantum Search Algorithm ◽  
Control Qubit ◽  
Modified Algorithm

A modification of Tulsi's quantum search algorithm with intermediate measurements of the control qubit is presented. In order to analyze the effect of measurements in quantum searches, a different choice of the angular parameter is used. The study is performed for several values of time lapses between measurements, finding close relationships between probabilities and correlations (mutual information and cumulative correlation measure). The order of this modified algorithm is estimated, showing that for some time lapses the performance is improved, and becomes of order O(N) (classical brute-force search) when measurements are taken in every step. The results provide a possible way to analyze improvements to other quantum algorithms using one, or more, control qubits.

Success Rate Versus Finite Run Time in Local Adiabatic Quantum Search Algorithm

2017 ◽  
Vol 67 (4) ◽  
pp. 355 ◽  
Author(s):  
Feng-Guang Li ◽  
Wan-Su Bao ◽  
Xiang Wang ◽  
Xiang-Qun Fu ◽  
Shuo Zhang ◽  
...  
Keyword(s):  
Success Rate ◽  
Search Algorithm ◽  
Quantum Search ◽  
Quantum Search Algorithm ◽  
Rate Versus ◽  
Run Time

Nonadiabatic Quantum Search Algorithm with Analytical Success Rate

2018 ◽  
Vol 58 (3) ◽  
pp. 939-949
Author(s):  
Feng-Guang Li ◽  
Wan-Su Bao ◽  
Tan Li ◽  
He-liang Huang ◽  
Shuo Zhang ◽  
...  
Keyword(s):  
Success Rate ◽  
Search Algorithm ◽  
Quantum Search ◽  
Quantum Search Algorithm

scholarly journals A Little Bit of Classical Magic to Achieve (Super-)Quantum Speedup

2021 ◽  
Vol 51 (3) ◽  
Author(s):  
Dagomir Kaszlikowski ◽  
Paweł Kurzyński
Keyword(s):  
Random Walk ◽  
Probability Distribution ◽  
Search Algorithm ◽  
Quantum Algorithms ◽  
Quantum Search ◽  
Classical Dynamics ◽  
Quantum Search Algorithm ◽  
Operational Interpretation ◽  
Simple Dynamical Model ◽  
Quantum Speedup

AbstractWe introduce nebit, a classical bit with a signed probability distribution. We study its properties and basic transformations that can be applied to it. Then, we introduce a simple dynamical model – a classical random walk supplemented with nebits. We show that such a model exhibits some counterintuitive non-classical properties and that it can achieve or even exceed the speedup of Grover’s quantum search algorithm. The proposed classical dynamics never reveals negativity of nebits and thus we do not need any operational interpretation of negative probabilities. We argue that nebits can be useful as a measure of non-classicality as well as a tool to find new quantum algorithms.

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