Experimental implementation of a continuous-time quantum random walk on a solid-state quantum information processor

2019 ◽  
Vol 28 (11) ◽  
pp. 110302
Author(s):  
Maimaitiyiming Tusun ◽  
Yang Wu ◽  
Wenquan Liu ◽  
Xing Rong ◽  
Jiangfeng Du
Keyword(s):  
Quantum Information ◽  
Random Walk ◽  
Solid State ◽  
Continuous Time ◽  
Quantum Random Walk ◽  
Experimental Implementation ◽  
Time Quantum

scholarly journals Quantum walk on a comb with infinite teeth

2022 ◽  
Author(s):  
François David ◽  
Thordur Jonsson
Keyword(s):  
Random Walk ◽  
Continuous Time ◽  
Quantum Walk ◽  
Quantum Random Walk ◽  
Return Probability ◽  
Starting Point ◽  
Time Quantum

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.

scholarly journals NON-UNIFORM MIXING OF QUANTUM WALK ON CYCLES

2007 ◽  
Vol 05 (06) ◽  
pp. 781-793 ◽  
Author(s):  
WILLIAM ADAMCZAK ◽  
KEVIN ANDREW ◽  
LEON BERGEN ◽  
DILLON ETHIER ◽  
PETER HERNBERG ◽  
...  
Keyword(s):  
Random Walk ◽  
Uniform Distribution ◽  
Continuous Time ◽  
Quantum Walk ◽  
Complete Graphs ◽  
Circulant Graph ◽  
Mixing Properties ◽  
Time Quantum ◽  
Average Distribution ◽  
Instantaneous Distribution

A classical lazy random walk on cycles is known to mix with the uniform distribution. In contrast, we show that a continuous-time quantum walk on cycles exhibits strong non-uniform mixing properties. First, we prove that the instantaneous distribution of a quantum walk on most even-length cycles is never uniform. More specifically, we prove that a quantum walk on a cycle Cnis not instantaneous uniform mixing, whenever n satisfies either: (a) n = 2u, for u ≥ 3; or (b) n = 2uq, for u ≥ 1 and q ≡ 3 (mod 4). Second, we prove that the average distribution of a quantum walk on any Abelian circulant graph is never uniform. As a corollary, the average distribution of a quantum walk on any standard circulant graph, such as the cycles, complete graphs, and even hypercubes, is never uniform. Nevertheless, we show that the average distribution of a quantum walk on the cycle Cnis O(1/n)-uniform.

Experimental implementation of a quantum random-walk search algorithm using strongly dipolar coupled spins

2010 ◽  
Vol 81 (2) ◽  
Author(s):  
Dawei Lu ◽  
Jing Zhu ◽  
Ping Zou ◽  
Xinhua Peng ◽  
Yihua Yu ◽  
...  
Keyword(s):  
Random Walk ◽  
Search Algorithm ◽  
Quantum Random Walk ◽  
Experimental Implementation

The passage from random walk to diffusion in quantum probability

1988 ◽  
Vol 25 (A) ◽  
pp. 151-166 ◽  
Author(s):  
K. R. Parthasarathy
Keyword(s):  
Random Walk ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Discrete Time ◽  
Continuous Time ◽  
Quantum Probability ◽  
Diffusion Limit ◽  
Quantum Random Walk

The notion of a quantum random walk in discrete time is formulated and the passage to a continuous time diffusion limit is established. The limiting diffusion is described in terms of solutions of certain quantum stochastic differential equations.

scholarly journals Experimental implementation of the quantum random-walk algorithm

2003 ◽  
Vol 67 (4) ◽  
Author(s):  
Jiangfeng Du ◽  
Hui Li ◽  
Xiaodong Xu ◽  
Mingjun Shi ◽  
Jihui Wu ◽  
...  
Keyword(s):  
Random Walk ◽  
Quantum Random Walk ◽  
Random Walk Algorithm ◽  
Experimental Implementation ◽  
Walk Algorithm

The passage from random walk to diffusion in quantum probability

1988 ◽  
Vol 25 (A) ◽  
pp. 151-166 ◽  
Author(s):  
K. R. Parthasarathy
Keyword(s):  
Random Walk ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Discrete Time ◽  
Continuous Time ◽  
Quantum Probability ◽  
Diffusion Limit ◽  
Quantum Random Walk

The notion of a quantum random walk in discrete time is formulated and the passage to a continuous time diffusion limit is established. The limiting diffusion is described in terms of solutions of certain quantum stochastic differential equations.

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