Phase gate
The Z gate is a single-qubit Pauli quantum operation that leaves |0⟩ unchanged and multiplies |1⟩ by −1.
Building Quantum Software with Python
The Z gate is a single-qubit quantum gate that multiplies the amplitude of the one basis state by negative one.
- How it is used
- Uses a single-qubit state transformation to reverse the |1⟩ amplitude direction without changing measurement probabilities.
- How deep it goes
- Explains amplitude signs, geometric direction, probability preservation, and a direct state-list implementation.
- Examples
- Demonstrates negating the second state-list entry and transforming [sqrt(0.3), sqrt(0.7)].
- What you can do after
- Apply the gate via a two-entry state-list transformation and verify direction reversal while preserving probabilities.
Read how Building Quantum Software with Python explains phase gate →
Quantum Programming in Depth
The Z gate is the single-qubit Pauli gate that leaves ket zero unchanged and multiplies ket one by negative one.
- How it is used
- Distinguishes candidate unitaries and extracts eigenvalues through controlled-Z phase kickback.
- How deep it goes
- Develops basis-state action, discrimination by measurement, eigenvectors, eigenvalues, and controlled phase kickback, stopping at the ±1 case.
- Examples
- Uses X-versus-Z identification on |0⟩ and controlled-Z experiments with target eigenstates |0⟩ and |1⟩.
- What you can do after
- Apply it to distinguish X from Z and read ±1 eigenvalues through a controlled-Z experiment.
Related concepts
- quantum gatekind of · A quantum gate is an operation that transforms the state of one or more qubits, typically represented by a unitary transformation.
- target qubitconfigures · A target qubit is the qubit designated to receive or participate in the action of a quantum operation.
- phase kickbackused by · Phase kickback is a quantum effect in which a controlled operation transfers a phase associated with its target to the relative phase of the control-qubit state.
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