5 votes

On Cluster States: Measuring in $|+\rangle$ and $|-\rangle$ basis vs. some other computational basis

Welcome to the stack exchange! Based on your question, it feels as you might have some small misunderstandings, so allow me to (hopefully) clear them up. Quantum measurements? In its most simple form, ...
JSdJ's user avatar
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2 votes
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How does the stated Pauli decomposition for $\operatorname{CP\cdot A\cdot CP}$ arise?

When I talked about a controlled-phase gate, I meant the standard gate that has unitary matrix $$ \left(\begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 &...
DaftWullie's user avatar
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2 votes
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Possible applications for small photonic cluster-states

There are quite a few! In terms of quantum communications, anything that can generate two+ entangled photons can be used to implement quantum key distribution, which allows for two parties to ...
Chris E's user avatar
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1 vote

How to compute the state resulting from measuring a single photon in a cluster state?

I don't have access to the book you mentioned but I tried to understand and decipher what you are asking. Let's start with the state $$ a|0\rangle|0\rangle^{\otimes n} + b|1\rangle|1\rangle^{\otimes n}...
Yunzhe's user avatar
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1 vote
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Hadamard Gate on Cluster States

Your calculation shows that you are doing the right thing for a single step. You just don't seem to be carrying it through for a set of 4 steps. Overall, you should be getting $$ (X^{m_4}HS)(X^{m_3}HS)...
DaftWullie's user avatar
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1 vote

Is the topological cluster state a single-shot stabilizer code?

I believe this is just a matter of definition, in some sense the topological state is a single-shot code. One difference between the topological cluster state and single-shot 3D codes is that the size ...
Peter-Jan's user avatar
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1 vote
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Is this generalized 2D cluster state still a universal resource?

TLDR: Yes, it's universal. If you only measure on one of the two registers, No. Longer answer... Let's deal with the measuring just one register first. So we're doing nothing with the other register. ...
DaftWullie's user avatar
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1 vote

Distance of one dimensional quantum error correcting code

The distance of an $[[n, 0]]$ code is defined to be the smallest non-zero weight of any stabilizer.
esabo's user avatar
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1 vote

Limitations on the number of qubits for a $\mathrm{CNOT}$-gate in cluster states

In answer to your second question, remember that you can always add any extra vertices (with arbitrary edges) to your graph. You just have to remove those vertices by using a $Z$ measurement on those ...
DaftWullie's user avatar
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1 vote

How does the stated Pauli decomposition for $\operatorname{CP\cdot A\cdot CP}$ arise?

Yes if you work with general phase shift there would be $\phi$ in the final answer. In fact you would be able to take $\phi=0$ and just get $A$ back. Try $\phi=\frac{\pi}{4}$. Looks like notational ...
AHusain's user avatar
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