Parametric Quantum Search Algorithm as Quantum Walk: A Quantum Simulation

Ellinas, Demosthenes; Konstandakis, Christos

doi:10.1016/s0034-4877(16)30008-8

Cited by 5 publications

(5 citation statements)

References 23 publications

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“…Can the accelerated period of entanglement is valid for other measures of correlation like the ones mentioned previously? How the fast counting procedure is modified in the case of open, dissipative extensions of quantum search as those analysed in [25] and the more complicated ones as in [15,17] as well?…”

Section: Discussionmentioning

confidence: 99%

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Entanglement in Quantum Search Database: Periodicity Variations and Counting

Ellinas

Konstandakis

2022

Quantum Reports

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Employing the single item search algorithm of N dimensional database it is shown that: First, the entanglement developed between two any-size parts of database space varies periodically during the course of searching. The periodic entanglement of the associated reduced density matrix quantified by several entanglement measures (linear entropy, von Neumann, Renyi), is found to vanish with period O(sqrt(N)). Second, functions of equal entanglement are shown to vary also with equal period. Both those phenomena, based on size-independent database bi-partition, manifest a general scale invariant property of entanglement in quantum search. Third, measuring the entanglement periodicity via the number of searching steps between successive canceling out, determines N, the database set cardinality, quadratically faster than ordinary counting. An operational setting that includes an Entropy observable and its quantum circuits realization is also provided for implementing fast counting. Rigging the marked item initial probability, either by initial advice or by guessing, improves hyper-quadratically the performance of those phenomena.

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Section: Discussionmentioning

confidence: 99%

“…], N = 2 n } → {0, 1}, c.f. [14][15][16][17]. The work proceeds by treating a set S of cardinality N as a search-able database with no additional structure.…”

Section: Introductionmentioning

confidence: 99%

Entanglement in Quantum Search Database: Periodicity Variations and Counting

Ellinas

Konstandakis

2022

Quantum Reports

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“…Unlike the classical random walk, the process of the quantum walk is not a Markov chain [33]. The evolution of state vector |ϕ(k) with time T k is realized by the following unitary transformation:…”

Section: Quantum Walk Simulation Of Random Exit Selectionmentioning

confidence: 99%

“…With efficient matrix algorithms [31], a quantum walk can converge much faster than the classical random walk [32]. Due to the advantages of the quantum walk, there are already many applications of the quantum walk in algorithm construction [33], decision-making simulation [34], and data analysis [35].…”

Section: Introductionmentioning

confidence: 99%

Modeling Random Exit Selection in Intercity Expressway Traffic with Quantum Walk

Zhou

et al. 2022

Applied Sciences

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In intercity expressway traffic, the multiplicity of available routes leads to randomness in exit selection. Random exit selection by drivers is hard to observe, and thus it is a challenge to model intercity expressway traffic sufficiently. In this paper, we developed a Random Quantum Traffic Model (RQTM), which modeled the stochastic traffic fluctuation caused by random exit selection and the residual regularity fluctuation with the quantum walk and autoregressive moving average model (ARMA), respectively. The RQTM considered the random exit selection of a driver as a quantum stochastic process with a dynamic probability function. A quantum walk was applied to update the probability function, which simulated when and where a driver will leave the expressway. We validated our model with hourly traffic data from seven exits from the Nanjing–Changzhou expressway in eastern China. For the seven exits, the coefficients of determination of the RQTM ranged from 0.5 to 0.85. Compared with the classical random walk and the ARMA model, the coefficients of determination were increased by 21.28% to 104.98%, and the relative mean square error decreased by 11.61% to 32.92%. We conclude that the RQTM provides new potential for modeling traffic dynamics with consideration of unobservable random driver decision making.

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“…This appears to be a favorite context for implementing and applying the idea of merging. In particular quantum search by merging as outlined here could also be applied in applications where quantum simulation of quantum searching is carried out by multi-particle Hamiltonian models (see e.g., [17] and references therein). These prospects will be taken up elsewhere.…”

Section: Rowmentioning

confidence: 99%

Faster Together: Collective Quantum Search

Ellinas

Konstandakis

2015

Entropy

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Joining independent quantum searches provides novel collective modes of quantum search (merging) by utilizing the algorithm's underlying algebraic structure. If n quantum searches, each targeting a single item, join the domains of their classical oracle functions and sum their Hilbert spaces (merging), instead of acting independently (concatenation), then they achieve a reduction of the search complexity by factor O( √ n).

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Parametric Quantum Search Algorithm as Quantum Walk: A Quantum Simulation

Cited by 5 publications

References 23 publications

Entanglement in Quantum Search Database: Periodicity Variations and Counting

Entanglement in Quantum Search Database: Periodicity Variations and Counting

Modeling Random Exit Selection in Intercity Expressway Traffic with Quantum Walk

Faster Together: Collective Quantum Search

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