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# Simulating the vibrational quantum dynamics of molecules using photonics

## Abstract

Advances in control techniques for vibrational quantum states in molecules present new challenges for modelling such systems, which could be amenable to quantum simulation methods. Here, by exploiting a natural mapping between vibrations in molecules and photons in waveguides, we demonstrate a reprogrammable photonic chip as a versatile simulation platform for a range of quantum dynamic behaviour in different molecules. We begin by simulating the time evolution of vibrational excitations in the harmonic approximation for several four-atom molecules, including H2CS, SO3, HNCO, HFHF, N4 and P4. We then simulate coherent and dephased energy transport in the simplest model of the peptide bond in proteins—N-methylacetamide—and simulate thermal relaxation and the effect of anharmonicities in H2O. Finally, we use multi-photon statistics with a feedback control algorithm to iteratively identify quantum states that increase a particular dissociation pathway of NH3. These methods point to powerful new simulation tools for molecular quantum dynamics and the field of femtochemistry.

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## Acknowledgements

We thank A. Orr-Ewing and R. Santagati for helpful conversations, and J. Barton for assistance with figures. This work was supported by the Engineering and Physical Sciences Research Council (EPSRC), European Commission QUCHIP (H2020-FETPROACT-3-2014: quantum simulation) and the European Research Council (ERC). A.N. is grateful for support from the Wilkinson Foundation. J.C. is supported by EU H2020 Marie Sklodowska-Curie grant number 751016. Y.N.J. was supported by NSF grant number DMR-1054020. J.L.O’B. acknowledges a Royal Society Wolfson Merit Award and a Royal Academy of Engineering Chair in Emerging Technologies. Fellowship support from EPSRC is acknowledged by A.L. (EP/N003470/1).

### Reviewer information

Nature thanks A. Aspuru-Guzik and F. Gatti for their contribution to the peer review of this work.

## Author information

All authors contributed to discussions and project development. The concept of simulating molecular vibrations with photonics was proposed by A.L. The methodology for simulating evolutions in localized bases was developed by E.M.-L. and D.P.T., with input from A.L. and C.S. Chemical calculations were done by D.P.T., based on which C.S. and E.M.-L. developed and simulated datasets. Methods for simulating open-system dynamics were developed by C.S. with input from Y.N.J. and A.L. The concept of simulating anharmonics with nonlinear gates was proposed by A.L., with the methodology for finding the nonlinear phase shift gates developed by C.S. and A.N.; A.N. also developed this code. The concept of incorporating AFC into simulations was proposed by A.L., with methodology by C.S., N.Mar., A.N. and A.L.; A.N. also developed this code. The photonic chip was developed by N.Mat. and T.H. with input from A.L. and J.L.O’B. The experiment was built by C.H., J.C., N. Mat., N.Mar. and A.L. Data were collected by N.Mar., C.H., E.M.-L. and J.C. Data were analysed by C.S., E.M.-L., N.Mar., A.N. and A.L. The manuscript was written by A.L., C.S. and E.M.-L. with input from D.P.T. and N.Mar. The project was conceived and managed by A.L.

### Competing interests

The authors declare no competing interests.

Correspondence to Anthony Laing.

## Supplementary information

1. ### Supplementary Information

This file contains Supplementary Text and Data, Supplementary Figures 1-7 and Supplementary References.

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• #### DOI

https://doi.org/10.1038/s41586-018-0152-9