In Situ Quantum Analog Pulse Characterization via Structured Signal Processing

TL;DR

This paper introduces a novel in situ pulse characterization method for analog quantum simulators, extending Quantum Signal Processing to accurately reconstruct time-dependent control pulses without mid-circuit measurements.

Contribution

It develops a new algorithm combining QSP with an analog-digital mapping to directly learn smooth pulse trajectories from propagator queries, avoiding unscalable Trotterization errors.

Findings

Achieves high accuracy in pulse reconstruction

Demonstrates robustness against SPAM and depolarizing errors

Provides an efficient validation protocol for quantum hardware

Abstract

Analog quantum simulators can directly emulate time-dependent Hamiltonian dynamics, enabling the exploration of diverse physical phenomena such as phase transitions, quench dynamics, and non-equilibrium processes. Realizing accurate analog simulations requires high-fidelity time-dependent pulse control, yet existing calibration schemes are tailored to digital gate characterization and cannot be readily extended to learn continuous pulse trajectories. We present a characterization algorithm for in situ learning of pulse trajectories by extending the Quantum Signal Processing (QSP) framework to analyze time-dependent pulses. By combining QSP with a logical-level analog-digital mapping paradigm, our method reconstructs a smooth pulse directly from queries of the time-ordered propagator, without requiring mid-circuit measurements or additional evolution. Unlike conventional Trotterization-based methods, our approach avoids unscalable performance degradation arising from accumulated local truncation errors as the logical-level segmentation increases. Through rigorous theoretical analysis and extensive numerical simulations, we demonstrate that our method achieves high accuracy with strong efficiency and robustness against SPAM as well as depolarizing errors, providing a lightweight and optimal validation protocol for analog quantum simulators capable of detecting major hardware faults.