Quantum Gate Calculator

Calculate quantum gate operations, output states, probabilities, and gate fidelity for quantum computing.

Gate Type

Input State

Rotation Angle

rad

Tab to move between fields

P(|0⟩)

P(|1⟩)

100%

Output |0⟩ Amplitude0

Output |1⟩ Amplitude1

Gate Fidelity1

Gate Error0%

How to Use This Calculator

Select Gate Type: Pauli-X flips |0⟩↔|1⟩, Hadamard creates superposition, Pauli-Y and Pauli-Z apply phase rotations.
Choose Input State: |0⟩ or |1⟩ as the single-qubit input to the gate operation.
For rotation gates, set the Rotation Angle (rad): π/2 ≈ 1.5708 is a quarter-turn, π ≈ 3.1416 is a half-turn.
Read P(|0⟩) and P(|1⟩) to see the measurement outcome probabilities after the gate transforms the input.
Gate Fidelity (0–1) and Gate Error (%) indicate how well the ideal unitary operation is implemented.

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Formula

|ψ_out⟩ = U|ψ_in⟩

Calculate quantum measurement probabilities, expectation values, variance, and wave function collapse.

Calculate quantum superposition states, interference effects, coherence, and phase relationships.

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