#Quantum error correction slides presentation code#

Measurement Destroys Superpositions? Let us apply the classical repetition code to a quantum state to try to correct a single bit flip error: 0 + 1  000 + 111 Bit flip error (X) on 2nd qubit: 010 + 101 2nd qubit is now different from 1st and 3rd.

How can we correct continuous errors and decoherence? Must correct multiple types of errors (e.g., bit flip and phase errors). No-Cloning Theorem There is no device that will copy an unknown quantum state: 0  00, 1  11 By linearity, 0 + 1  00 + 11 (0 + 1)(0 + 1) (Related to Heisenberg Uncertainty Principle)īarriers to Quantum Error Correction Measurement of error destroys superpositions. When errors are rare, one error is more likely than two. Quantum Errors A general quantum error is a superoperator:    Ak  Ak† Examples of single-qubit errors: Bit Flip X: X0 = 1, X1 = 0 Phase Flip Z: Z0 = 0, Z1 = -1 Complete dephasing:   ( + ZZ†)/2 (decoherence) Rotation: R0 = 0, R1 = ei1Ĭlassical Repetition Code To correct a single bit-flip error for classical data, we can use the repetition code: 0  000 1  111 If there is a single bit flip error, we can correct the state by choosing the majority of the three bits, e.g.

Quantum Error Correction Daniel Gottesman Perimeter Institute