Nonlinear Spectroscopy via Generalized Quantum Phase Estimation

Ignacio Loaiza; Danial Motlagh; Kasra Hejazi; Modjtaba Shokrian Zini; Alain Delgado; Juan Miguel Arrazola

doi:10.22331/q-2025-08-07-1822

Nonlinear Spectroscopy via Generalized Quantum Phase Estimation

Ignacio Loaiza, Danial Motlagh, Kasra Hejazi, Modjtaba Shokrian Zini, Alain Delgado, and Juan Miguel Arrazola

Xanadu. Toronto, ON. M5G 2C8. Canada

Published:	2025-08-07, volume 9, page 1822
Editor:	Luis A. Correa
Eprint:	arXiv:2405.13885v3
Doi:	https://doi.org/10.22331/q-2025-08-07-1822
Citation:	Quantum 9, 1822 (2025).

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Abstract

Response theory has a successful history of connecting experimental observations with theoretical predictions. Of particular interest is the optical response of matter, from which spectroscopy experiments can be modelled. However, the calculation of response properties for quantum systems is often prohibitively expensive, especially for nonlinear spectroscopy, as it requires access to either the time evolution of the system or to excited states. In this work, we introduce a generalized quantum phase estimation framework designed for multi-variate phase estimation. This allows the treatment of general correlation functions enabling the recovery of response properties of arbitrary orders. The generalized quantum phase estimation circuit has an intuitive construction that is linked with a physical process of interest, and can directly sample frequencies from the distribution that would be obtained experimentally. In addition, we provide a single-ancilla modification of the new framework for early fault-tolerant quantum computers. Overall, our framework enables the efficient simulation of spectroscopy experiments beyond the linear regime, such as Raman spectroscopy, having that the circuit cost grows linearly with respect to the order of the target nonlinear response. This opens up an exciting new field of applications for quantum computers with potential technological impact.

► BibTeX data

@article{Loaiza2025nonlinear,
  doi = {10.22331/q-2025-08-07-1822},
  url = {https://doi.org/10.22331/q-2025-08-07-1822},
  title = {Nonlinear {S}pectroscopy via {G}eneralized {Q}uantum {P}hase {E}stimation},
  author = {Loaiza, Ignacio and Motlagh, Danial and Hejazi, Kasra and Zini, Modjtaba Shokrian and Delgado, Alain and Arrazola, Juan Miguel},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {9},
  pages = {1822},
  month = aug,
  year = {2025}
}

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