Quantum cicruits

Quantum cicruits

1. Unitary transformations

   • Linear
   • Length preserving

2. One-bit gates

   • X-gate flips amplitudes
   • Z-gate negates last amplitude
   • H-gate has property H^2=I
     • H=X+Z renormalized

3. Controlled gates

   • 1st bit -> preserve or apply unitary U
     • Can create any unitary transformation from small set of gates

4. Bell state = H + CNOT

   • Quantum teleportation
     • By doing local operations, transform joint state with recipient
       • Measure to collapse to one-of-four state
         • Send two qubits to indicate which one it is
           • Recover using controlled X and Z operations