Simplified mixed-state encoding for quantum computation with continuous-variable systems

Recent development of mixed-state encoding (MSE) allows a pure-state logical qubit to be encoded by a continuous-variable system in mixed physical state. Despite interest due to its counter-intuitiveness, the utility of current MSE is limited due to several operational drawbacks, namely probabilistic initialisation, redundant information carrier, and requirement of discrete-variable measurement. In this work, we present a simplified MSE that does not suffer from any of these drawbacks. Specifically, our protocol encodes each qubit by only one mixed-state harmonic oscillator, and the logical basis can be deterministically initialised by displacing a thermal equlibirum state. By using measurement-based quantum computation formalism, logical operations can be performed by only continuous-variable interaction and measurement. Without the necessity of ground state cooling, our proposal could broaden the candidate for quantum computation, and reduce the re-initialisation time of measured qubits. Additionally, the noise tolerance of logical quantum information can be enhanced by treating conventional pure-state encoded qubits as MSE qubits.