Quantum polyspectra for modeling and evaluating simultaneous quantum measurements

量子多谱最近出现作为一种新的不妥协的方法来连续量子测量。它们允许解决一个非常广泛的实验，包括量子电子学，自旋噪声光谱学和电路量子电动力学（cQED），使它们成为未来连续量子测量的瑞士军刀。多谱是众所周知的二阶谱的自然高阶推广，并且可以从实验的频率分辨噪声检测器输出z（t）直接计算。分析量子polyspectrum的模型主方程可以被安装到测量光谱获得系统参数，如耦合常数，隧穿率，进动频率等，在以前的方法，如n-分辨主方程（全计数统计）相比，新的方法工作在全制度之间的高斯主导的噪声和电报噪声中发现自旋噪声测量和量子输运，分别。我们于二零二一年成功将量子多光谱应用于量子点的输运测量。在这个项目中，我们将推广量子多谱框架的重要情况下，同时测量两个或两个以上的探测器与非交换测量算子。最近，在cQED的背景下，此类实验在超导量子比特上成为可能。 特别是（i）我们将推导出四阶量子多光谱的解析表达式，最多可达四个探测器;（ii）我们将开发并提供一个基于Python的工具箱，用于从数据中快速计算多元多光谱，使实验人员能够分析自己的数据;（iii）我们将提供一个基于QuTiP的工具箱，用于计算Liouvillians模型的解析多光谱（涵盖哈密顿动力学，测量反作用，环境阻尼，温度）（iv）我们将应用我们的框架，在cQED和新的多探测器方案在量子输运的非高斯环境噪声的紧迫的挑战性问题。我们期望量子多光谱对评估实际测量和量子限制测量的理论基础都有很大的影响。

Quantum polyspectra have recently appeared as a new uncompromising approach to continuous quantum measurements. They allow for addressing an extremely broad class of experiments covering quantum-electronics, spin noise spectroscopy, and circuit quantum electrodynamics (cQED) making them the future swiss army knife of continuous quantum measurements. Polyspectra are the natural higher-order generalization of the well-known second-order spectra and can be directly calculated from the frequency resolved noisy detector output z(t) of an experiment. Analytic quantum polyspectra of a model master equation can be fitted to measured spectra for obtaining system parameters like coupling constants, tunneling rates, precessing frequencies, etc. In contrast to previous approaches like the n-resolved master equation (full counting statistics), the new approach works in the full regime between Gaussian-dominated noise and telegraph noise as found in spin noise measurements and quantum transport, respectively. We successfully applied quantum polyspectra to transport measurements on quantum dots in 2021. In this project, we will generalize the quantum-polyspectra framework to the important case of simultaneous measurements of two or more detectors with non-commuting measurement operators. Such experiments have recently become possible on superconducting qubits in the context of cQED. In particular (i) we will derive analytical expression for quantum polyspectra up to fourth order for up to four detectors; (ii) we will develop and provide a Python-based toolbox for the fast calculation of multivariate polyspectra from data empowering experimentalist to analyze their own data; (iii) we will provide a toolbox based on QuTiP for the calculation of analytic polyspectra from model Liouvillians (covering Hamiltonian dynamics, measurement back-action, environmental damping, temperature) (iv) We will apply our framework to urgent challenging questions about the non-Gaussian environmental noise in cQED and new multi-detector schemes in quantum transport. We expect a high impact of quantum polyspectra both on evaluating actual measurements and on the theoretical foundations of quantum-limited measurements.