To implement quantum computers on harmonic-oscillator-liked systems, the conventional approach is to: 1) Cool the system to the ground state; 2) Specify two physical states as the encoding basis of a qubit; 3) Implement logic gates by engineering encoding-specific interaction. In our recent works, we show that all of these procedures are sufficient but not necessary. Specifically, we find a unified operation that can implement logic gates for any encoding . The formalism permits a new class of encoding that a pure logical qubit is represented by a mixed physical state . Because the purity of quantum system is not essential, the requirement of ground-state cooling can be relaxed. Additionally, our formalism can reduce the initialisation energy, and protect the logical qubit against a wider class of noise.
 Hoi-Kwan Lau and Martin B. Plenio, arXiv:1608.03213
 Hoi-Kwan Lau and Martin B. Plenio, Physical Review Letters 117, 100501 (2016)