Simulation of Chemical Isomerization Reaction Dynamics on a NMR Quantum Simulator

Quantum simulation can beat current classical computers with minimally a few tens of qubits. Here we report an experimental demonstration that a small nuclear-magnetic-resonance quantum simulator is already able to simulate the dynamics of a prototype laser-driven isomerization reaction using engineered quantum control pulses. The experimental results agree well with classical simulations. We conclude that the quantum simulation of chemical reaction dynamics not computable on current classical computers is feasible in the near future.

Figure 1

(a) Isomerization reaction of nonsymmetric substituted malonaldehydes. (b) Left panel: Potential energy curve, together with the eigenfunctions of the ground (red) and the first excited (blue) states. The main system parameters [Eq. (2)] are taken from Ref. 24, with $V^{‡}=0.00625E_h$, $\Delta =0.000257E_h$, and $q_0=1a_0$. The potential values for $q$ approaching the left and right ends are increased to obtain rapid decay of wave function amplitudes. Right panel: Numerically exact time dependence of populations of the ground state (reactant state, denoted $P_0$) and the first excited state (product state, denoted $P_1$).

Figure 2

(a) Molecular structure of Diethyl-fluoromalonate and the system parameters. The ${}^1\mathrm{H}$, ${}^{13}\mathrm{C}$, and ${}^{19}\mathrm{F}$ nuclear spins marked by the oval are used as 3 qubits. The Larmor frequencies (Hz), the scalar coupling strength (Hz), the relaxation, and dephasing time scales (second) T1 and T2 are listed in the table. (b) The network of quantum operations to simulate the isomerization dynamics, with the reactant state $|{\varphi }_0⟩$. The whole process is divided into 25 loops. The operators $T_{\delta t}$, $V_{\delta t}$, and $E_{\delta t/2}$ are assumed to be in their diagonal representations.

Figure 3

(a),(b) Real part of the density matrix of the initial and final states of the simulated reaction. Upper panels show the theoretical results and lower panels show the experimental results. (c) The measured probabilities of the reactant and product states to give 25 snapshots of the reaction dynamics. The (red) plus symbols represent measured results of $C\mathbf{(}|\psi (t_j)⟩,|{\varphi }_0⟩\mathbf{)}$ and the (blue) circles represent measured results of $C\mathbf{(}|\psi (t_j)⟩,|{\varphi }_1⟩\mathbf{)}$, both in agreement with the theoretical smooth curves. Results here also agree qualitatively with the numerically exact dynamics shown in Fig. 1b.