Non-Markovian dynamics of a qubit coupled to an Ising spin bath

2007/07/13 by Hari Krovi, Ognyan Oreshkov, Mikhail Ryazanov +1 · 4 citations
Computer Science · Physics and Astronomy · #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum and electron transport phenomena #quant-ph

paper · pdf · doi:10.1103/physreva.76.052117

published as Phys. Rev. A 76, 052117 (2007) · 17 pages, 16 figures

arxiv created 2007/07/13 · openalex publication_date 2007/11/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the analytically solvable Ising model of a single qubit system coupled to a spin bath. The purpose of this study is to analyze and elucidate the performance of Markovian and non-Markovian master equations describing the dynamics of the system qubit, in comparison to the exact solution. We find that the time-convolutionless master equation performs particularly well up to fourth order in the system-bath coupling constant, in comparison to the Nakajima-Zwanzig master equation. Markovian approaches fare poorly due to the infinite bath correlation time in this model. A recently proposed post-Markovian master equation performs comparably to the time-convolutionless master equation for a properly chosen memory kernel, and outperforms all the approximation methods considered here at long times. Our findings shed light on the applicability of master equations to the description of reduced system dynamics in the presence of spin baths.

Citations

• Optimal strategy for a single-qubit gate and the trade-off between opposite types of decoherence
• Non-Markovian dynamics in a spin star system: Exact solution and approximation techniques
• Completely positive post-Markovian master equation via a measurement approach

Cited by

• Bang-bang control of a qubit coupled to a quantum critical spin bath
• Measure for the non-Markovianity of quantum processes
• Quantum Metrology for Non-Markovian Processes
• On the conundrum of deriving exact solutions from approximate master equations

Related

• Non-Markovianity of qubit evolution under the action of spin environment
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• Non-Markovian master equation for interacting qubits coupled to a bosonic bath: analytic form and asymptotic approximation
• Abrupt transitions between Markovian and non-Markovian dynamics in open quantum systems
• Non-Markovian dynamics in a spin star system: Exact solution and approximation techniques