Compressed Qubit Noise Spectroscopy: Piecewise-Linear Modeling and Rademacher Measurements

2026-01-05

AI Summary

This work proposes a compressed sensing framework based on total generalized variation (TGV) regularization, combined with real-time-generated Rademacher random pulse sequences, to efficiently reconstruct non-sparse noise spectra exhibiting piecewise-linear structures. Conventional qubit noise spectroscopy methods struggle to accurately and efficiently recover such spectra while requiring complex experimental protocols. In contrast, the proposed approach significantly simplifies the experimental procedure without sacrificing reconstruction accuracy, enabling the resolution of finer spectral features. Moreover, it achieves an order-of-magnitude improvement in reconstruction speed compared to traditional techniques, thereby substantially expanding the applicability of compressed sensing–based noise spectroscopy in characterizing structured environmental noise.

Technology Category

• Search and Optimization: Non-convex Optimization
• Machine Learning: Quantum Machine Learning
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization

Abstract

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.

Problem

• qubit noise spectroscopy
• piecewise-linear noise spectra
• random pulse sequences
• noise characterization
• quantum systems

Innovation

• Compressed Qubit Noise Spectroscopy
• Piecewise-Linear Modeling
• Total Generalized Variation
• Rademacher Measurements
• Random Pulse Sequences