Recursive encoding and decoding of the noiseless subsystem and decoherence-free subspace
Chi-Kwong Li, Mikio Nakahara, Yiu‐Tung Poon, Nung-Sing Sze, Hiroyuki Tomita · Physical Review A · 2011
When an environmental disturbance to a quantum system has a wavelength much larger than the system size, all qubits in the system are under the action of the same error operator. The noiseless subsystem and decoherence-free subspace are immune to such collective noise. We construct simple quantum circuits that implement these error-avoiding codes for a small number $n$ of physical qubits. A single logical qubit is encoded with $n=3$ and 4, while two and three logical qubits are encoded with $n=5$ and 7, respectively. Recursive relations among subspaces employed in these codes play essential roles in our implementation.