|ψ⟩
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|ψ⟩ = α|0⟩ + β|1⟩  •  iℏ ∂|ψ⟩/∂t = Ĥ|ψ⟩
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Controlled-Z Gate (CZ) | Symmetric Phase Entangler

Quick Technical Answer: The Controlled-Z (CZ) gate is a symmetric 2-qubit entangling gate that inverts the phase of the |11⟩ state by π radians while leaving |00⟩, |01⟩, and |10⟩ unaltered. Because it is symmetric, either qubit can act as the control.
Formula / Unitary: CZ = \text{diag}(1, 1, 1, -1) = (I \otimes H) \cdot CX \cdot (I \otimes H)
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Frequently Asked Questions

Why is the CZ gate naturally preferred on superconducting chips?

In tunable transmon architectures, fast flux pulsing brings the |11⟩ and |02⟩ states into near-resonance to accumulate a geometric π phase, making CZ the native two-qubit hardware gate.

Related Topics & Quantum Guides:

CNOT Gate (CX)Pauli-Z Gate (Phase-Flip)Superconducting Transmon Qubits