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GATES ARE ROTATIONS
Turning the Bloch sphere
X, Y, Z
Half turns about the three axes.
H
Swaps |0⟩ and |+⟩.
S and T
Quarter and eighth turns: they change only the phase.
Every single-qubit gate is just a rotation.
PUZZLE
Steer the qubit
Goal
Rotate the arrow onto the target in as few gates as possible.
Why it matters
Fewer gates mean fewer chances for errors.
Compilers
Real software does this optimisation automatically.
Programming a quantum computer means choosing rotations.
TWO QUBITS
Two-qubit gates
CNOT
Flips B when A is 1.
CZ and SWAP
A sign flip on |11⟩, and an exchange.
Universal
One entangling gate plus rotations can build any program.
Two-qubit gates are the slowest and least accurate, and the most important.
FIDELITY
Why 99.9% isn't good enough
Fidelity
How close a gate comes to perfect.
It compounds
Success ≈ FN for N gates.
At 99.9%
A thousand gates leaves about a 37% chance of no error.
No physical qubit is good enough alone: hence error correction.
PULSES
How gates are really done
Microwave pulses
Tens of nanoseconds long.
Leakage
Sharp pulses can kick the qubit up to |2⟩.
Shaping
Smooth pulses (and designs like DRAG) keep it in its two levels.
Precise control electronics are as important as the qubits themselves.
UNIT 12 STUDY COMPLETE
🎛️
Ready for the Fab Challenge?
You've steered qubits with gates, entangled them with CNOT and seen why fidelity and pulse shape matter.