Questions tagged [cluster-states]
For questions about cluster states, a class of entangled many-qubit systems that are especially useful in the context of measurement-based quantum computation schemes.
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Is the topological cluster state a single-shot stabilizer code?
I saw in the literature claims that no single-shot 3D stabilizer code is known and that only 3D subsystem codes are known to have this feature.
However, isn't the topological cluster state (also known ...
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Creating Three Qubit Cluster Linear Cluster State (maybe a phase issue) (Qiskit)
I am creating a three-qubit linear cluster state as defined in the following paper: paper link. This circuit is quite simple to implement using various libraries. I'm utilizing qiskit to construct the ...
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Capping in topological cluster state error correction simulation
In this paper: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.90.052316, section IX., it is written:
"...The logical error rate (p_L) of a
given error model is determined by a continuous ...
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Logical error rate of topological cluster state under erasure channel
Assume I use the topological cluster state (https://arxiv.org/abs/quant-ph/0703143) to protect against erasure. Assume also that the only noise or erasure that I have in my system is loss in the ...
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Possible applications for small photonic cluster-states
Assume I have a "resource state generator", enabling me to produce photonic cluster states in arbitrary shape with O(1-10) photons.
Are there any possible applications for such a device in ...
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Is this generalized 2D cluster state still a universal resource?
Let $G = (V,E)$ be a graph that defines the graph state
$$
|G\rangle = \prod_{(i,j)\in E} CZ_{i,j}|+\rangle^{\otimes |V|}.
$$
Alternatively, we can write
$$
| G \rangle = \sum_{x \in \{0,1\}^{|V|}} ...
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The effect of qubit loss/erasure on its neighbors in topological cluster state
I try to understand how to simulate the effect of heralded qubit loss (or erasure) in one of the gates during the creation a topological cluster state (as a part of an error-correction simulation).
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Time ordering in topological cluster state creation
When performing syndrome measurements of the surface code, the time ordering of the CNOT\CZ gates between data and ancilla qubits is important. Namely, not every time ordering is valid.
Is it the same ...
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Distance of one dimensional quantum error correcting code
Consider one dimensional quantum codes $[[ n,k=0]] $.
One way to describe them is using stabilizer framework with $n$ independent Pauli matrices.
Usually, one considers them in the graph state model ...
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What is the effect of measuring a node in a cluster state?
I'm still quite confused about the post-measurement state when a node of a cluster state is measured.
As far as I'm aware, for a cluster state, a given node $j$ will have a stabilizer
$$X_j\bigotimes_{...
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On Cluster States: Measuring in $|+\rangle$ and $|-\rangle$ basis vs. some other computational basis
I'm currently learning quantum information and I seem to miss some important points on cluster states.
My question is this:
If we want to get one qubit disentangled from the quantum cluster state we ...
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Limitations on the number of qubits for a $\mathrm{CNOT}$-gate in cluster states
I'm reading about cluster states using this online source. It is explained that a CNOT can be performed on cluster states using as little as $4$ qubits. However, the standard implementation is with $...
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How does the stated Pauli decomposition for $\operatorname{CP\cdot A\cdot CP}$ arise?
I'm having a bit of trouble understand @DaftWullie's answer here.
I understood that the $4\times 4$ matrix $A$
$$ \frac{1}{4} \left[\begin{matrix}
15 & 9 & 5 & -3 \\
9 & 15 & 3 &...
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