Arbitrary Single-Qubit Gate (U3) | Euler Angle Parameterization
Quick Technical Answer:
The U3 gate is the most general single-qubit unitary operator, parameterized by three Euler angles (θ, φ, λ). It can transform any point on the Bloch sphere into any other arbitrary quantum state.
Formula / Unitary:
U_3(\theta, \phi, \lambda) = \begin{pmatrix} \cos(\theta/2) & -e^{i\lambda}\sin(\theta/2) \\ e^{i\phi}\sin(\theta/2) & e^{i(\phi+\lambda)}\cos(\theta/2) \end{pmatrix} = R_z(\phi) R_y(\theta) R_z(\lambda)
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Frequently Asked Questions
How do quantum compilers synthesize U3 gates?
Most superconducting compilers decompose U3 into frame-changes (virtual-Z gates with zero duration and zero error) surrounding calibrated physical π/2 pulses: Rz(φ) · X_{π/2} · Rz(θ + π) · X_{π/2} · Rz(λ).