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Simulating chemistry is likely to be among the earliest applications of quantum computing. However, existing digital quantum algorithms for chemical simulation require many logical qubits and gates, placing practical applications beyond existing technology. Here, we use an analog approach to carry out the first quantum simulations of chemical reactions. In particular, we simulate photoinduced non-adiabatic dynamics, one of the most challenging classes of problems in quantum chemistry because they involve strong coupling and entanglement between electronic and nuclear motions. We use a mixed-qudit-boson (MQB) analog simulator, which encodes information in both the electronic and vibrational degrees of freedom of a trapped ion. We demonstrate its programmability and versatility by simulating the dynamics of three different molecules as well as open-system dynamics in the condensed phase, all with the same quantum resources. Our approach requires orders of magnitude fewer resources than equivalent digital quantum simulations, demonstrating the potential of analog quantum simulators for near-term simulations of complex chemical reactions.

Interactions of molecules with their environment influence the course and outcome of almost all chemical reactions. However, classical computers struggle to accurately simulate complicated molecule-environment interactions because of the steep growth of computational resources with both molecule size and environment complexity. Therefore, many quantum-chemical simulations are restricted to isolated molecules, whose dynamics can dramatically differ from what happens in an environment. Here, we show that analog quantum simulators can simulate open molecular systems by using the native dissipation of the simulator and injecting additional controllable dissipation. By exploiting the native dissipation to simulate the molecular dissipation -- rather than seeing it as a limitation -- our approach enables longer simulations of open systems than are possible for closed systems. In particular, we show that trapped-ion simulators using a mixed qudit-boson (MQB) encoding could simulate molecules in a wide range of condensed phases by implementing widely used dissipative processes within the Lindblad formalism, including pure dephasing and both electronic and vibrational relaxation. The MQB open-system simulations require significantly fewer additional quantum resources compared to both classical and digital quantum approaches.

Quantum walks have a host of applications, ranging from quantum computing to the simulation of biological systems. We present an intrinsically stable, deterministic implementation of discrete quantum walks with single photons in space. The number of optical elements required scales linearly with the number of steps. We measure walks with up to 6 steps and explore the quantum-to-classical transition by introducing tunable decoherence. Finally, we also investigate the effect of absorbing boundaries and show that decoherence significantly affects the probability of absorption., Comment: Published version, 5 pages, 4 figures