Building GHZ States
A GHZ state puts n qubits into an equal superposition of all-zeros and all-ones: one Hadamard followed by a chain of CX gates builds it. The fan-out order matters — on five qubits a linear chain needs four sequential CX layers while a balanced tree needs only three — and a two-peak histogram alone does not prove the state is genuinely entangled.
What is a GHZ state?
A GHZ state — named after Greenberger, Horne and Zeilinger, who studied it in 1989 — is the n-qubit state (|00…0⟩ + |11…1⟩)/√2: an equal superposition of "all qubits read 0" and "all qubits read 1", with nothing in between.
It is the simplest example of multipartite entanglement — entanglement shared across more than two qubits, where the register behaves as one indivisible whole rather than a collection of pairs. Measure any single qubit and you instantly know what every other qubit will read.
The recipe extends the Bell pair you already know. One H on q0 creates the two-branch superposition; then CX gates fan out the branch choice — copy the 0-or-1 decision, in the computational basis, from qubits that have it to qubits that don't. Each CX recruits one more qubit into the correlated state.
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