Quantum-JumpContinuous-Time QuantumError-Correction
Kung-Chuan Hsu, Todd A. Brun · 2013
• Continuous-time quantum error-correction (CTQEC) is a study of pro-tecting quantum information against decoherence, where both the decoher-ence and error-correction processes are considered continuous in time. • Quantum-jump CTQEC is a model for CTQEC that describes a quantum sys-tem with a continuous master equation. One important task in concerning this model is to find a protocol that realizes the quantum-jump CTQEC mapping ρ δt1−−−→ 1 − κδt ρ+ κδt R(ρ), (1) ε ε whereR(·) is a recovery mapping. Contribution • For any given quantum stabilizer code, we found a set of criterion that leads to a large family of protocols that realize the corresponding quantum-jump CTQEC mapping. • We propose a CTQEC protocol, based on any given [[n, k, d]] quantum stabilizer code, that requires only n − k + 1 ancillary qubits in the quantum measurement phase. This greatly reduces the number of ancillary qubits required from 2n−k as in [1]. • The comparison of existing CTQEC protocols. Typical Procedures in a CTQEC protocol • Step I: Couple an ancillary system of size sa, prepared in the state |A0 〉 = |+〉⊗sa =