从相干性到纵向极化的方向性转移及具有马尔可夫退相和玻璃态环境的transmon中的代数存储：一个非马尔可夫分数更新模型
Directional transfer from coherence to longitudinal polarization and algebraic storage in a transmon with Markovian dephasing and a glassy environment: A non-Markovian fractional renewal model
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中文总结 AI 辅助
提出非马尔可夫分数更新transmon模型，实现相干性到纵向极化的方向性转移和代数存储，优于泊松参考。
中文摘要 AI 辅助
我们开发了一个完全正且迹保持的非马尔可夫transmon模型，该模型包含纵向马尔可夫退相和横向更新事件，其动机源于玻璃态二能级系统环境。一个微观哈密顿量识别出耦合子空间；一个归一化的Prabhakar等待时间定律对慢缺陷重构进行了唯象粗粒化。前向时间顺序的更新历史产生了精确的映射级Volterra方程、一个非对易核- resolvent主方程，以及一个等价的漂移共轭Caputo型表示及其所需的初值项。在没有能量弛豫的情况下，Pauli空间动力学分裂为两个一维子空间和一个耦合的$(\sigma_y,\sigma_z)$子空间，该子空间支持相干性和纵向极化之间的方向性转移；$\sigma_x$极化对更新不敏感。对于重尾等待时间，当$0<\alpha<1$时，支割分析给出了纵向极化中由初始相干性产生的通用$t^{-\alpha}$存储尾和$O(t^{-1-\alpha})$反向转移；常数速率泊松更新产生极点生成的指数衰减。在有限$T_1$下，独立的零温度弛豫在其速率低于纯退相速率两倍时，会指数截断这些尾部。我们比较了等待时间密度、记忆核和选定量子比特响应分量的独立逆拉普拉斯重构，以评估数值精度。对于所研究的参数，Prabhakar更新在指定读出时间给出的前向转移幅度大于尺度匹配的常数速率泊松参考和匹配完整期望计数分布的非齐次泊松参考，包括有限$T_1$测试。两种泊松参考都产生更大的评估有限窗口峰值。无序驱动的更新记忆按状态和方向选择性地重塑transmon退相干。
英文摘要
We develop a completely positive and trace-preserving non-Markovian transmon model with longitudinal Markovian dephasing and transverse renewal events motivated by a glassy two-level-system environment. A microscopic Hamiltonian identifies coupling subspaces; a normalized Prabhakar waiting-time law phenomenologically coarse grains slow defect reconfigurations. Forward chronological renewal histories yield an exact map-level Volterra equation, a noncommuting kernel--resolvent master equation, and an equivalent drift-conjugated Caputo-type representation with its required initial-value term. Without energy relaxation, Pauli-space dynamics splits into two one-dimensional subspaces and a coupled $(σ_y,σ_z)$ subspace supporting directional transfer between coherence and longitudinal polarization; $σ_x$ polarization is renewal-insensitive. For heavy-tailed waiting times with $0<α<1$, branch-cut analysis gives a generic $t^{-α}$ storage tail in longitudinal polarization generated from initial coherence and $O(t^{-1-α})$ reverse transfer; constant-rate Poisson renewal yields pole-generated exponential decay. Independent zero-temperature relaxation at finite $T_1$ exponentially cuts off these tails when its rate is below twice the pure-dephasing rate. We compare independent inverse-Laplace reconstructions of the waiting-time density, memory kernel, and selected qubit-response components to assess numerical accuracy. For the studied parameters, Prabhakar renewal gives larger forward-transfer magnitudes at the prescribed readout than both a scale-matched constant-rate Poisson reference and an inhomogeneous Poisson reference matching the full expected-count profile, including finite-$T_1$ tests. Both Poisson references yield larger evaluated finite-window peaks. Disorder-motivated renewal memory reshapes transmon decoherence selectively by state and direction.
发表机构
- Dokuz Eylul University（德格埃尤尔大学）
- Izmir Institute of Technology（伊兹密尔理工学院）
机构由 AI 辅助整理，请以论文原文为准。
