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Questions tagged [quantum-walk]

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What can be some bachelor thesis ideas in Quantum random walks?

I am an undergraduate, reading Quantum information and quantum technology. For about some time, I am interested in applications of Quantum walks to quantum algorithms. Can anybody suggest a start ...
6
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0answers
90 views

Improve analysis of quantum random walk

The paper Quantum Complexity of Testing Group Commutativity considers the problem of identifying if a given group is commutative. The group is given via a certain oracle and the complexity of the ...
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Claw finding using quantum walk: superposition for Szegedy's framework

Within Claw Finding Algorithms Using Quantum Walk there is the subroutine $claw_{detect}$ described. As in above paper: Let $J_f(N, l)$ and $J_G(M, m)$ be Johnson graphs. Let $F$ and $G$ be vertices ...
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0answers
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Coset state of $3$-node graph isomorphism problem

The hidden subgroup representation of a $3$-node graph isomorphism problem is defined over the symmetric group, $G = S_6$. So, any hidden subgroup algorithm that wishes to solve the problem should ...
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2answers
1k views

Applications of Quantum Walks?

Can someone explain to me what real world applications could potentially benefit from the study of quantum random walks? I have researched a fair amount on how quantum walks operate and their ...
12
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1answer
316 views

Transitioning from quantum to classical random walks on the line

Quick version Are there models of decoherence for the quantum walk on the line such that we can tune the walk to spread as $\Theta(t^k)$ for any $1/2 \leq k \leq 1$? Motivation Classical random ...
13
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2answers
571 views

One-shot quantum hitting times

In the paper Quantum Random Walks Hit Exponentially Faster (arXiv:quant-ph/0205083) Kempe gives a notion of hitting time for quantum walks (in the hypercube) that is not very popular in the quantum ...