Why is entanglement creation difficult?

Question

No matter from the true physical realization to date or from some papers, it seems that multipartite entanglement creation is difficult. However, the circuit showing below can easily create entanglement at least from the perspective of gates:

The H in the picture above means the Hardmard gate, and the other four blue items are the control-x gate. The circuit can change $\mid 0\rangle^{\otimes n}$ into GHZ state.

So since the circuit realization of entanglement is clearly easy, why the entanglement creation in practice become a hard thing? Does it mean that the control-x gate or Hardmard gate is hard to realize, or there are some other reasons which make the realization of the circuit above very difficult?

Answer 1

Like you said, one reason why it's hard to do this in practice is simply due to the number of gates. Each gate comes with limited fidelity (never exactly 100%), so needing to do many of them will compound the total gate error. Moreover, for the GHZ state, notice that the whole state will dephase if even a single qubit dephases. Generally, the larger the state, the more noise channels it is subject to. If each qubit undergoes an open evolution described by four noise (Kraus) operators, then a state of $n$ qubits will have $4^n$ possible noise operators, and for a highly entangled state, if any of these noise channels occurs, then the whole state could be affected (though this of course depends on the actual entangled state in question, the particular noise channels of the device and their timescales, etc.)