Quantum Computing Stack Exchange
Quantum Computing Stack Exchange

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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Hadamard Gate on Cluster States

In measurement based quantum computing, according to R. Raussendorf, Hadamard Gate can be realized by five qubit cluster state, where the first qubit is measured in X basis and the following three are measured in Y basis. However, even though I…
Taylan Fırat
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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 $15$ qubits. Why is that the case? Is it also…
nippon
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Performing gates and measurements on 2D cluster states in MBQC

I've been going through various papers on MBQC for a while now, and I am still not clear on how we perform gates on 2D cluster states. On 1D clusters it's very clear, just a series of measurements in either the $X$ or a rotated basis $\{|0\rangle +…
GaussStrife
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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 as well. If you use the distance definition by…
Root
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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 measure it in the$\vert\pm\rangle$ computational…
pantinah93
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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 $A$ $$ \frac{1}{4} \left[\begin{matrix} 15 & 9 & 5 & -3 \\ 9 & 15 & 3 & -5 \\ 5 & 3 & 15 & -9 \\ -3 & -5 & -9 & 15 \end{matrix}\right]$$ can…
Sanchayan Dutta
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Difference between Cluster states and Gaussian Boson Sampling- Discussion

Let me share my understanding first, the two key terms are Gaussian Boson Sampling and Cluster State. So far from my understanding, Gaussian Boson Sampling is a resonant state generator. I can generate this by sending a quantum emission ( I believe…
SakibulIslamSazzad
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Creation of cluster states using type I fusions

I recently asked this question regarding type I and II fusions on polarization photons. To be honest, I am still not really clear how this operation generates cluster states, as the output at the end of the answer I was given was not an cluster…
GaussStrife
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How does a local Hadamard gate change the cluster state?

I was reading a paper on a fault-tolerant quantum computation protocol based on tree cluster states. The author said that by applying a local Hadamard gate to two of the qubits in a 4 GHZ state, we create a three-qubit tree-cluster state where the…
physics22
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How to compute the state resulting from measuring a single photon in a cluster state?

I was reading the book ''Introduction to Optical Quantum Information Processing" by Pieter Kok and Brendon Lovett and on page 199 they talk about cluster states and the circuit model of Quantum Computation and I didn't understand the…
physics22
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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 as Raussendorf's cube or RHG cube) a single-shot…
Yaron Jarach
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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 quantum technologies besides quantum computing, e.g.,…
Yaron Jarach
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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 $$ | G \rangle = \sum_{x \in \{0,1\}^{|V|}} f_G(x)|x\rangle, $$ for some function $f_G$ that…
trillianhaze
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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 $$X_j\bigotimes_{k\in N_j}Z_k$$ for the set of nodes $N_j$ around…
wigglywinks
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