Curriculum / Quantum Foundations / Rotation Gate Challenge
Rotation Gate Challenge
Use RX, RY, and RZ to prepare arbitrary single-qubit states.
Rotation Gate Challenge
Now that you understand rotations, let's put them into practice. Using RX, RY, and RZ gates, you can prepare any single-qubit state.
Target States
State 1: The |+⟩ state = (|0⟩ + |1⟩)/√2
- •This is an RY(π/2) rotation from |0⟩
State 2: The |i−⟩ state = (|0⟩ − i|1⟩)/√2
- •Apply RX(π/2) from |0⟩
State 3: An equator state. Note that applying RZ(π/4) first (while the qubit is still |0⟩) only adds an unobservable global phase, so RZ(π/4) then RY(π/2) lands on |+⟩ at azimuth 0°. To actually reach azimuth 45°, you would apply RY(π/2) first to get onto the equator, then RZ(π/4) to rotate the azimuth.
- •Apply RZ(π/4) then RY(π/2)
Your challenge: prepare each state and verify by measuring with and without a basis change.
How this lesson works
A hands-on coding challenge. You write Qiskit-compatible Python in the browser editor, run it instantly via WebAssembly, watch the circuit and Bloch sphere react, and pass automatic output checks. The AI tutor Qubitus gives Socratic hints if you get stuck.
Part of: Quantum Foundations
Learn the basics: qubits, gates, superposition, and measurement.
Take this lesson free
Create a free account and start this lesson in your browser. No credit card, no installation.