Random pulse sequences are a powerful method for qubit noise spectroscopy, enabling efficient reconstruction of sparse noise spectra. Here, we advance this method in two complementary directions. First, we extend the method using a regularizer based on the total generalized variation (TGV) norm, in order to reconstruct a larger class of noise spectra, namely piecewise-linear noise spectra, which more realistically model many physical systems. We show through numerical simulations that the new method resolves finer spectral features, while maintaining an order-of-magnitude speedup over conventional approaches to noise spectroscopy. Second, we simplify the experimental implementation of the method, by introducing Rademacher measurements for reconstructing sparse noise spectra. These measurements use pseudorandom pulse sequences that can be generated in real time from a short random seed, reducing experimental complexity without compromising reconstruction accuracy. Together, these developments broaden the reach of random pulse sequences for accurate and efficient noise characterization in realistic quantum systems.

翻译：随机脉冲序列是一种强大的量子比特噪声谱学方法，能够高效重构稀疏噪声谱。本文从两个互补方向推进该方法。首先，我们基于总广义变分（TGV）范数引入正则化器，以扩展该方法对更广泛噪声谱类别的重构能力，即分段线性噪声谱，这种谱能更真实地模拟许多物理系统。数值模拟表明，新方法在保持比传统噪声谱学方法快一个数量级的速度的同时，能解析更精细的谱特征。其次，我们通过引入用于重构稀疏噪声谱的拉德马赫测量，简化了该方法的实验实现。这些测量使用伪随机脉冲序列，可通过短随机种子实时生成，在保持重构精度的同时降低了实验复杂度。这些进展共同拓展了随机脉冲序列在真实量子系统中实现精确高效噪声表征的应用范围。