Predicting open quantum dynamics with data-informed quantum-classical dynamics

Abstract

We introduce a data-informed quantum-classical dynamics (DIQCD) approach for predicting the evolution of an open quantum system. The equation of motion in DIQCD is a Lindblad equation with a flexible, time-dependent Hamiltonian that can be optimized to fit sparse and noisy data from local observations of an extensive open quantum system. We demonstrate the accuracy and efficiency of DIQCD for both experimental and simulated quantum devices. We show that DIQCD can predict entanglement dynamics of ultracold molecules (Calcium Fluoride) in optical tweezer arrays. DIQCD also successfully predicts carrier mobility in organic semiconductors (Rubrene) with accuracy comparable to nearly exact numerical methods.

Figures (4)

• Figure 1: (a) Optically trapped CaF molecule and three control schemes used in Ramsey experiments. Contour lines represent the equipotential surface of the trap, with energy levels indicated in the color map. (b) A pair of CaF molecules and the control scheme for Bell state generation. (c) The contrast $C(t)$ (scaled by $\varsigma$) as a function of circuit duration $t$. Circle, square, and triangle markers represent $C^{\text{EXP}}(t)$ data. (d) The top three panels show $P_{\uparrow\uparrow}$ (scaled by $\varsigma^2$) as a function of $t$. The bottom panel shows the rate of qubit loss as a function of $t$.
• Figure 2: (a) Rubrene crystal (left) and the effective model for carrier transport (right). (b) Comparison of data and DIQCD on average $\langle \hat{\sigma}_x(t) \rangle$ and $\langle \hat{\sigma}_y(t)\rangle$ for $T=300$K. (c) Carrier mobility as a function of temperature. The blue triangle is an experimental estimation of the intrinsic mobility takeya2007very. (d) The square root of site occupation on the $L=150$ molecular lattice. Snapshots are obtained from a DIQCD simulation lasting 100fs for $T=300$K. (e) The mean squared displacement (MSD=$\langle \mathrm{Tr}(\rho_{\boldsymbol{\epsilon}}(t)n^2) -\mathrm{Tr}^2(\rho_{\boldsymbol{\epsilon}}(t) n )\rangle_{\boldsymbol{\epsilon}}$) as a function of time for $T=300$K. The shades represent standard deviation.
• Figure 3: The structure of QEpsilon.
• Figure 4: The mean and standard deviation (concerning the ensemble of sampled trajectories) of $\langle\hat{\sigma}_x(t)\rangle$ and $\langle\hat{\sigma}_y(t)\rangle$ from the final DIQCD models and the data associated with exact unitary simulation.