Applied Physics CSIE II: UNIT IV: Quantum Computing

Pauli Z Gate (Z GATE)

Definition, Action, Matrix form, Operation, Bloch Sphere action | Quantum gates

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The Pauli‒Z gate is a single‒qubit quantum gate that leaves the |0> state unchanged and adds a phase of ‒1 to the |1> state.

PAULI‒Z GATE (Z GATE)

Definition

The Pauli‒Z gate is a single‒qubit quantum gate that leaves the |0> state unchanged and adds a phase of ‒1 to the |1> state.

Action

Adds a phase flip (Changes the sign of |1>)

Matrix forms

The matrix for the Z gate is the same as Pauli matrix σ_Z and can be written as

Operation

Z |0> = |1>

Z |1> = -|1>

Thus for an input |0> the output of Z gate is not changed, that is, also |0> and for an input |1> the output is ‒|1>.

Bloch Sphere action

Rotation by π radians (180°) around the Z‒axis

Applied Physics CSIE II: UNIT IV: Quantum Computing : Tag: Applied Physics : Definition, Action, Matrix form, Operation, Bloch Sphere action | Quantum gates - Pauli Z Gate (Z GATE)

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Applied Physics CSIE II: UNIT IV: Quantum Computing

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