Methods for single qubit gate teleportation

A method for applying a single-qubit gate to an arbitrary quantum state, wherein said arbitrary quantum state is initially on a data qubit, the method comprising:

• setting a state of a first and second ancillary qubit to an entangled initial state |I>;
• weakly measuring a state of said data qubit and said first ancillary qubit thereby performing said single qubit gate on said arbitrary quantum state with a probability;
• and
• determining a first result from said weakly measuring step.

A method for applying a single-qubit gate to an arbitrary quantum state that is initially present on a data qubit, the method comprising:

• setting a state of a first and second ancillary qubit to an entangled initial state |I>;
• performing a weak measurement on a state of said data qubit and said first ancillary qubit;
• determining whether said weak measurement indicates said data qubit and said first ancillary qubit were in a singlet or triplet state;
• wherein
• when the data qubit and said first ancillary qubit are in the singlet state, said single-qubit gate was applied on said arbitrary quantum state, and
• when the data qubit and said first ancillary qubit are in the triplet state, the Hermitian conjugate of said single-qubit gate was applied on said arbitrary quantum state;
• and
• performing a corrective operation when the data qubit and said first ancillary qubit are in the triplet state to convert the Hermitian conjugate of said single-qubit gate to said single-qubit gate.