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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 central qubit is redundantly encoded in the two-qubit basis $|VV \rangle$, $|HH \rangle$.

Could someone explain this?

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  • $\begingroup$ Please link the relevant resources. $\endgroup$
    – FDGod
    Commented Jan 12 at 22:44
  • $\begingroup$ Here's the link arxiv.org/pdf/quant-ph/0702044.pdf (on page 3). I tried to locally apply the Hadamard gate to two qubits, but I'm not getting a state where the central qubit is redundantly encoding. Perhaps I just have to try and rewrite the state in that way so a logical qubit is encoded in two physical qubits $\endgroup$
    – physics22
    Commented Jan 13 at 9:04

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