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arXiv:quant-ph/9905006 · Physics Letters A

Post-Markov master equation for the dynamics of open quantum systems

Ting Yu, Lajos Diósi, Nicolas Gisin, Walter T. Strunz

Published Feb 1, 2000• 49 citations
arXivHTMLPDF
DOI
10.1016/s0375-9601(00)00014-1

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Based on the exact non-Markovian system dynamic equation about the reduced density matrix of quantum system,which is a non-closed,unequal in time,integral-differential equation,a closed,equal in time,differential Markovian master equation was derived about the reduced density matrix of quantum system by means of Born approximation and Markov approximation.The Lindblad form of the Markovian master equation,GKS expression for the convenience of testing positivity,Bloch sphere expression for single qubit system,Kraus expression describing dissipative quantum system without specific information of environment were analyzed respectively.Four kinds of Markov approximations that can remove the non-Markovian property were compared.The post-Markovian master equation was analyzed that can meet the perfect requirements of dissipative dynamic when the Markov approximation is not suitable to the open quantum system.When energy exchange existed between the heat bath and quantum system,and the total system composed of the bath and the quantum system has a conservation of energy,the dynamic equation of open quantum system was presented when the bath does not have a constant state,and the Markovian master equation was derived by the Markov approximation.
We introduce the NCA and NCA-Markov dynamical maps for open quantum systems, which go beyond weak-coupling master equations replacing the Born approximation with a non-crossing approximation (NCA). We apply these NCA maps on a prototype model of open quantum systems, the Ohmic spin-boson model at zero temperature, showing that they can qualitatively reproduce its non-perturbative behaviour, including its crossover from a coherent to an incoherent dynamics and its localization quantum phase transition, which are entirely missed by perturbative master equations. Remarkably, the time-local NCA-Markov map qualitatively captures this physics entirely, opening up the possibility to address strong-coupling effects at a numerical cost comparable to standard Markovian master equations.
The research on open quantum systems is important for both quantum computing and quantum sensing. So far, we can only use the main equation to make an approximate description. The dynamics of a single Fluxonium qubit under Markovian environment satisfied Lindblad Master Equation. In experiments, pulse sequence dynamic decoupling (DD) can enhance the coherence of qubits and effectively suppress noise. Two Fluxonium qubits sensitive to two-level systems (TLS) noise. TLS formed by material defects results in noise with significant non-Markovian characteristics. The dynamics of non-Markovian noise satisfied the post Markov Master Equation (PMME). The TLS noise spectrum is mainly concentrated in low frequencies, so traditional DD cannot effectively suppress TLS noise. The relaxation and dephasing behavior with a complex dynamic characteristics. Based on Ornstein-Uhlenbeck process, we put forward a novel DD sequence and design a TLS-tailored dynamical decoupling protocol by optimizing pulse locations to minimize noise power spectral overlap with the Lorentzian shape. Using PMME-consistent framework, we can obtain a stronger low frequency suppression and significantly prolong both Bell-based fidelity and entanglement. We explore specific DD design and precise modeling of entanglement dynamics under non-Markovian TLS noise. Our dynamical decoupling protocol can effectively improve entanglement gates fidelity in NISQ quantum devices.