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Can someone explain to me what a "fully connected transverse field Ising" is ?

I know what a classical Ising model is and I think the transverse term refers to the magnetic field being transverse to the spins am I right ?

But what exactly does fully connected means ? And how is it translated in term of hamiltonian ?

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I would guess that it means $$ H=\sum_{n=2}^N\sum_{m=1}^{n-1}Z_nZ_m+\lambda\sum_{n=1}^NX_n, $$ i.e. the Ising terms act between every pair of qubits.

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  • $\begingroup$ But how can two qubits which are on the x-axis or on the y-axis for instance interact if we only consider the Pauli Z for the interactions here ? $\endgroup$
    – Duen
    Jul 13, 2023 at 14:05
  • $\begingroup$ Have you ever tried taking a 2-qubit transverse Ising model and evolving s separable state in time? Does it stay separable for all time? (No) $\endgroup$
    – DaftWullie
    Jul 13, 2023 at 14:36
  • $\begingroup$ I lack understanding on those kind of things. Do you have some ressources to improve my knowledges on what you just said ? $\endgroup$
    – Duen
    Jul 13, 2023 at 14:39

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