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

A General Phase Matching Condition for Quantum Searching Algorithm

A general consideration on the phase rotations in quantum searching algorithm is taken in this work. As four phase rotations on the initial state, the marked states, and the states orthogonal to them are taken account, we deduce a phase matching condition for a successful search. The optimal options for these phase are obtained consequently.Comment: 3 pages, 3 figure

A General SU(2) Formulation for Quantum Searching with Certainty

A general quantum search algorithm with arbitrary unitary transformations and an arbitrary initial state is considered in this work. To serach a marked state with certainty, we have derived, using an SU(2) representation: (1) the matching condition relating the phase rotations in the algorithm, (2) a concise formula for evaluating the required number of iterations for the search, and (3) the final state after the search, with a phase angle in its amplitude of unity modulus. Moreover, the optimal choices and modifications of the phase angles in the Grover kernel is also studied.Comment: 8 pages, 2 figure

A microsecond-response polymer-stabilized blue phase liquid crystal

A polymer-stabilized blue-phase liquid crystal (BPLC) with microsecond response time is demonstrated using a vertical field switching cell. The measured decay time is 39 mu s at room temperature (21 degrees C) and then decreases to 9.6 mu s at 44.3 degrees C. Such a response time is 1-2 orders of magnitude faster than that of a typical BPLC device. The responsible physical mechanisms are the collective effects of short pitch length, strong polymer network, and low viscosity through temperature effect. The on-state voltage of our BPLC device is 44.2 V, hysteresis is below 0.7%, and contrast ratio is over 1300:1