Questions tagged [quantum-walk]

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Gate definitions for quantum random access codes

I would like to know how the gates are defined in quantum random access codes? Consider the $2 \to 1$ code described in Lemma 3.1 of this paper. The section defines the encoding and decoding circuits. ...
Omar Shehab's user avatar
2 votes
0 answers
154 views

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

Note: Cross-posted on Quantum Computing Stack Exchange. I am an undergraduate, reading about quantum information and quantum technology. For about some time, I have been interested in the ...
Nimish Mishra's user avatar
5 votes
0 answers
102 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 ...
Tyson Williams's user avatar
2 votes
0 answers
107 views

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 ...
Fleeep's user avatar
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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 ...
Omar Shehab's user avatar
7 votes
2 answers
3k 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 ...
csss's user avatar
  • 171
12 votes
1 answer
386 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 ...
Artem Kaznatcheev's user avatar
13 votes
2 answers
692 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 ...
Marcos Villagra's user avatar