Quantum walks are the quantum mechanical counterpart of classical random walks. This tag should be used for any question related to quantum walk models.
Questions tagged [quantum-walks]
43 questions
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Why can quantum walks not approach a stationary distribution
In Child's notes on quantum walks, he claims (section 16.6) "Since a quantum walk is a unitary process, we should not expect it to approach a limiting quantum state, no matter how long we wait."
But why should this be true? I understand that quantum…
SescoMath
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Angular spectral gap in Szegedy's quantum walk
I'm trying to understand how the Szegedy quantum walk operator is useful. I understand that given a reducible ergodic Markov chain with transition matrix $P\in\mathbb{R}^{2^n\times 2^n}$, implemented as an oracle $O$, we can implement a unitary…
zjs
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Why is discrete time quantum walks applicable only for undirected graphs?
I don't understand how this property of discrete-time quantum walk relates to the property that the transition operator SC is unitary. Many papers mention this and continue without explaining.
Suppose we have a directed graph, Let us give separate…
Adithya Bharath
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Why, in a discrete-time quantum walk,we first apply the tensor product of the coin operation with the identity?
When we apply coin step in the quantum walk, for example considering the H gate, we first do it's tensor product with Identity vector of the position Hilbert space. Why is this so? Please see below statement for more details:
Binshumesh sachan
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Quantum Walk Study Resource for Non-regular Graph
Does anyone know any good resource where I can study about how quantum walk is performed on non-regular graph?
Most of the papers I read, talks about only quantum walk on regular graphs containing cycles. For non-regular graph as each node have…
Binshumesh sachan
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quantum coin walk on a regular 3D grid graph
I am trying to apply the quantum coin walk on a 3D grid, with 3 Hadamard coins. So there would be 6 different directions at each steps and there is 8 possible coin outcomes.
I can't seem to get symmetric results after 3 steps. Is it simply not…
Trieu Jo
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Why is the *Absorbing* Quantum Walk (of Belov/ Montanaro) possible?
[Belovs] and [Montanaro1] define quantum walk search in the electric network framework, that share common property: A single step of the quantum walk is defined, such that its the identity on marked nodes. [ACRSZ] uses a similar quantum walker(, and…
Fleeep
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How to make a Node dependent coin operator?
In a non-regular graph the degree of each node is different.
So, the dimension of the coin operator also needs to be changed (as the number of options the walker has to hop to adjacent nodes will be different) as opposed to for example a 2-d regular…
Binshumesh sachan
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-1
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Use of Position Hilbert Space in Quantum Walk
To perform quantum walk first we need to define combine hilbert space for the position and coin, which is represented by: $H=H_p\bigotimes H_c$
Now, my question is what is the use of above representation, if all the operation are defined on initial…
Binshumesh sachan
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