Fig. 3: Proof-of-concept quantum simulation of vibrational dynamics in H2O with a programmable nonlinear photonic quantum circuit.
a Illustration of molecular potential of vibrational degrees of freedom that, in general, is anharmonic (depicted as a solid line), i.e., a harmonic approximation (dashed line) is not sufficient. b The quantum vibrational dynamics of the molecule are mapped onto a photonic system by associating optical modes with vibrational modes, and single optical excitations (photons) with single vibrational excitations (phonons). The associated vibrational dynamics for an anharmonic Hamiltonian \({\hat{H}}_{a}\) (upper inset) can be described in the localised basis (depicted on left and right) by converting to the normal basis (shown in the middle) via a matrix transformation U, evolving in the normal basis for a time t, and then converting back to the localised basis via U†. In the photonic implementation, the linear parts of the circuit perform the basis changes and the harmonic evolution. Subsequently, the photonic nonlinear interactions (depicted as yellow boxes) implement the anharmonic part of the evolution. c Experimental results for the quantum simulation of the anharmonic dynamics of the H2O molecule initialised with two photons in the same localised stretch mode. The top and bottom panels report the output occupancy for configurations in which the excitations emerge in separate or the same localised stretch mode, respectively. The data are compared with the theoretical model (solid lines) and with predictions from the harmonic approximation (dashed lines). The data markers are colour-coded according to the strength of the nonlinear phase (scale bar as inset) associated with each evolution time step.
