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Author(s):  
François David ◽  
Thordur Jonsson

Abstract We study continuous time quantum random walk on a comb with infinite teeth and show that the return probability to the starting point decays with time t as t−1. We analyse the diffusion along the spine and into the teeth and show that the walk can escape into the teeth with a finite probability and goes to infinity along the spine with a finite probability. The walk along the spine and into the teeth behaves qualitatively as a quantum random walk on a line. This behaviour is quite different from that of classical random walk on the comb.


2022 ◽  
Vol 22 (1&2) ◽  
pp. 53-85
Author(s):  
Thomas G. Wong

The task of finding an entry in an unsorted list of $N$ elements famously takes $O(N)$ queries to an oracle for a classical computer and $O(\sqrt{N})$ queries for a quantum computer using Grover's algorithm. Reformulated as a spatial search problem, this corresponds to searching the complete graph, or all-to-all network, for a marked vertex by querying an oracle. In this tutorial, we derive how discrete- and continuous-time (classical) random walks and quantum walks solve this problem in a thorough and pedagogical manner, providing an accessible introduction to how random and quantum walks can be used to search spatial regions. Some of the results are already known, but many are new. For large $N$, the random walks converge to the same evolution, both taking $N \ln(1/\epsilon)$ time to reach a success probability of $1-\epsilon$. In contrast, the discrete-time quantum walk asymptotically takes $\pi\sqrt{N}/2\sqrt{2}$ timesteps to reach a success probability of $1/2$, while the continuous-time quantum walk takes $\pi\sqrt{N}/2$ time to reach a success probability of $1$.


2022 ◽  
Vol 41 (2) ◽  
pp. 461-477
Author(s):  
Sardar Zafar Iqbal ◽  
Hina Gull ◽  
Saqib Saeed ◽  
Madeeha Saqib ◽  
Mohammed Alqahtani ◽  
...  

2022 ◽  
Vol 31 (1) ◽  
pp. 581-590
Author(s):  
Raham Hashim Yosuf ◽  
Rania A. Mokhtar ◽  
Rashid A. Saeed ◽  
Hesham Alhumyani ◽  
S. Abdel-Khalek

Author(s):  
Christof Wetterich

A simple probabilistic cellular automaton is shown to be equivalent to a relativistic fermionic quantum field theory with interactions. Occupation numbers for fermions are classical bits or Ising spins. The automaton acts deterministically on bit configurations. The genuinely probabilistic character of quantum physics is realized by probabilistic initial conditions. In turn, the probabilistic automaton is equivalent to the classical statistical system of a generalized Ising model. For a description of the probabilistic information at any given time quantum concepts as wave functions and non-commuting operators for observables emerge naturally. Quantum mechanics can be understood as a particular case of classical statistics. This offers prospects to realize aspects of quantum computing in the form of probabilistic classical computing. This article is part of the theme issue ‘Quantum technologies in particle physics’.


2021 ◽  
Vol 104 (6) ◽  
Author(s):  
Shivani Singh ◽  
C. Huerta Alderete ◽  
Radhakrishnan Balu ◽  
Christopher Monroe ◽  
Norbert M. Linke ◽  
...  

2021 ◽  
Author(s):  
Pooja Hooda ◽  
V. B. Taxak ◽  
R. K. Malik ◽  
Savita Khatri ◽  
Poonam Kumari ◽  
...  

Abstract Six crimson samarium (III) complexes based on β-ketone carboxylic acid and ancillary ligands were synthesized by adopting grinding technique. All synthesized complexes were investigated via employing elemental analysis, infrared, UV-Vis, NMR, TG/DTG and photoluminescence studies. Optical properties of these photostimulated samarium (III) complexes exhibit reddish-orange luminescence due to 4G5/2→6H7/2 transition at 606 nm of samarium (III) ions. Further, energy band gap, color purity, CIE color coordinates, CCT and quantum yield of all complexes were determined accurately. Replacement of water molecules by ancillary ligands enriched the complexes (S2-S6) with decay time, quantum yield, luminescence, energy band gap and biological properties than parent complex (S1). Interestingly, these efficient properties of complexes may find their applications in optoelectronic and lighting systems. In addition to these the antioxidant and antimicrobial assays were also investigated to explore the application in biological assays.


Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2263
Author(s):  
Leo Matsuoka ◽  
Kenta Yuki ◽  
Hynek Lavička ◽  
Etsuo Segawa

Maze-solving by natural phenomena is a symbolic result of the autonomous optimization induced by a natural system. We present a method for finding the shortest path on a maze consisting of a bipartite graph using a discrete-time quantum walk, which is a toy model of many kinds of quantum systems. By evolving the amplitude distribution according to the quantum walk on a kind of network with sinks, which is the exit of the amplitude, the amplitude distribution remains eternally on the paths between two self-loops indicating the start and the goal of the maze. We performed a numerical analysis of some simple cases and found that the shortest paths were detected by the chain of the maximum trapped densities in most cases of bipartite graphs. The counterintuitive dependence of the convergence steps on the size of the structure of the network was observed in some cases, implying that the asymmetry of the network accelerates or decelerates the convergence process. The relation between the amplitude remaining and distance of the path is also discussed briefly.


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