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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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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 ...
physics22's user avatar
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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 ...
physics22's user avatar
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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 ...
Taylan Fırat's user avatar
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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 ...
Yaron Jarach's user avatar
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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 ...
quest's user avatar
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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 ...
Yaron Jarach's user avatar
1 vote
1 answer
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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 ...
Yaron Jarach's user avatar
1 vote
1 answer
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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|}} ...
trillianhaze's user avatar
2 votes
1 answer
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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 ...
Root's user avatar
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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_{...
wigglywinks's user avatar
2 votes
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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 ...
pantinah93's user avatar
3 votes
1 answer
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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 $...
nippon's user avatar
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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 &...
Sanchayan Dutta's user avatar