Generalised quantum computational spectroscopy on a quantum chip.

Spectroscopy underpins modern scientific discovery across diverse disciplines. While experimental spectroscopy probes material properties through scattering or radiation measurements, computational spectroscopy combines theoretical models with experimental data to predict spectral properties, essential for advancements in physics, chemistry, and materials science. However, quantum systems present unique challenges for computational spectroscopy due to their inherent complexity, and current quantum algorithms remain largely limited to static and closed quantum systems. Here, we present and demonstrate a generalised quantum computational spectroscopy that lifts these limitations by reconstructing the quantum autocorrelation function via an ancilla-assisted Hadamard test quantum circuit. Our method is applicable to a broad range of quantum systems, including closed, open, and time-dependent driven quantum systems. We experimentally validate this approach, which leverages arbitrary controlled quantum dynamics and efficient classical noise-mitigation strategy, on a programmable silicon-photonic quantum processing chip, capable of high-fidelity time-evolution simulations. The versatility of our method is demonstrated through spectroscopic computations for diverse quantum systems, revealing novel phenomena such as parity-time symmetry breaking and topological holonomy that are inaccessible to conventional spectroscopy or quantum eigenstate algorithms. This work establishes a noise-robust methodology for quantum spectral analysis.