julian / ghz
Public
GHZ State Generator
ghz_state(n) prepares the n-qubit GHZ state:
A Hadamard on qubit 0 creates the superposition, then a chain of CNOTs
propagates it down the register.
Parameters
- n (
int) — number of qubits.n = 0→ empty circuitn = 1→ single H (|+⟩ state)n = 2→ Bell staten ≥ 3→ GHZ state
Expected measurement statistics
Only the all-zeros and all-ones bitstrings occur, each with probability 1/2. Any other outcome beyond noise indicates decoherence or a broken entangling chain — GHZ fidelity degrades quickly with n, making this a useful hardware stress test.Notes
Circuit depth is O(n). For wide circuits on well-connected hardware, a fan-out variant achieves O(log n) depth with the same state.GHZ size:
┌───┐ ░ ┌─┐
q_0: ┤ H ├──■────────░─┤M├──────
└───┘┌─┴─┐ ░ └╥┘┌─┐
q_1: ─────┤ X ├──■───░──╫─┤M├───
└───┘┌─┴─┐ ░ ║ └╥┘┌─┐
q_2: ──────────┤ X ├─░──╫──╫─┤M├
└───┘ ░ ║ ║ └╥┘
meas: 3/═══════════════════╩══╩══╩═
0 1 2