Implementation of QECC with NMR quantum computer

We propose an implementation of a 3-qubit bit-flip QECC proposed in [1] using an NMRquantum computer. A qubit state ∣ ⟩ = a∣0⟩+ b∣1⟩ is encoded as ∣Ψ⟩ = a∣000⟩+ b∣111⟩ andsent through a noisy channel. It is assumed that the bit-flip operator X acts on one of thequbits during transmission.We show that the recovery operation can be implemented with a unitary quantumcircuit, which contains several CNOT gates. The rank 2 projection operator P required forQECC is effectively implemented by a permutation of the qubit basis vectors and ignoring(i.e., filter out) unnecessary NMR signals from the free induction decay signal.We also suggest a new non-unitary process, which replaces the projection operator, withwhich our technique can be applied to 9-qubit and 5-qubit QECC.Co-authors Hiroyuki Tomita (Kinki University) and Yasushi Kondo (Kinki University) References[1] Chi-Kwong Li, Yiu-Tung Poon and Nung-Sing Sze, Recovery Operator for Mixed UnitaryChannel, unpublished note (2010). January 4-5, 2011, Hong Kong