Quantum gate teleportation

Quantum gate teleportation is a variant of the one-way quantum computer where quantum gates are applied to quantum states via quantum teleportation.[1] It proves that universal quantum computation can be performed using only single qubit gates, Bell measurements and GHZ states. This makes it convenient for implementations where gates can't be applied directly; like in Linear Optical Quantum Computing where two qubit gates are difficult to implement. For example, the figure on the right shows how a CNOT gate can be applied to states ${\displaystyle |\alpha \rangle }$ and ${\displaystyle |\beta \rangle }$ with a state ${\displaystyle |\chi \rangle =}$${\displaystyle (|00\rangle +|11\rangle )|00\rangle +(|01\rangle +|10\rangle )|11\rangle \over {\sqrt {2}}}$(${\displaystyle |\chi \rangle }$ is created before the dashed lines). Since universal fault tolerant quantum computation can be implemented with this protocol, quantum gate teleportation can be used to circumvent the Eastin-Knill theorem.[2] Quantum gate teleportation has been experimentally demonstrated in Linear optical quantum computing,[3] Superconducting quantum computing,[4] and Ion trap quantum computing.[5]