Analytical technique for simplification of the encoder-decoder circuit for a perfect five-qubit error correction

Simpler encoding and decoding networks are necessary for more reliable quantum error correcting codes (QECCs). The simplification of the encoder-decoder circuit for a perfect five-qubit QECC can be derived analytically if the QECC is converted from its equivalent one-way entanglement purification protocol (1-EPP). In this work, the analytical method to simplify the encoder-decoder circuit is introduced and a circuit that is as simple as the existent simplest circuits is presented as an example. The encoder-decoder circuit presented here involves nine single- and two-qubit unitary operations, only six of which are controlled-NOT (CNOT) gates

A simplification of entanglement purification

An idea of hybrid maps is proposed to establish standard entanglement purification protocols which guarantee to purify any distillable state to a desired maximally entangled pure state all by the standard purification local operations and classical communications. The protocols proposed in this work, in which two state transformations are used, perform better than the IBM and Oxford protocols in the sense that they require fewer operation times in yielding a same amount of the desired pure state. One of the proposed protocol in this work can even lead to a higher improved output yield when it is combined with the hashing protocol, as compared with the combined algorithm consisting of the Oxford and the hashing protocol.Comment: 4 figures, 10 page