Many important chemical and biochemical processes in the condensed phase are notoriously difficult to simulate numerically. Often this difficulty arises from the complexity of simulating dynamics resulting from coupling to structured, mesoscopic baths, for which no separation of time scales exists and statistical treatments fail. A prime example of such a process is vibrationally assisted charge or energy transfer. A quantum simulator, capable of implementing a realistic model of the system of interest, could provide insight into these processes in regimes where numerical treatments fail. We take a first step towards modeling such transfer processes using an ion trap quantum simulator. By implementing a minimal model, we observe vibrationally assisted energy transport between the electronic states of a donor and an acceptor ion augmented by coupling the donor ion to its vibration. We tune our simulator into several parameter regimes and, in particular, investigate the transfer dynamics in the nonperturbative regime often found in biochemical situations.

The detailed characterization of non-trivial coherence properties of composite quantum systems of increasing size is an indispensable prerequisite for scalable quantum computation, as well as for understanding non-equilibrium many-body physics. Here, we show how autocorrelation functions in an interacting system of phonons as well as the quantum discord between distinct degrees of freedoms can be extracted from a small controllable part of the system. As a benchmark, we show this in chains of up to 42 trapped ions, by tracing a single phonon excitation through interferometric measurements of only a single ion in the chain. We observe the spreading and partial refocusing of the excitation in the chain, even on a background of thermal excitations. We further show how this local observable reflects the dynamical evolution of quantum discord between the electronic state and the vibrational degrees of freedom of the probe ion.

We present an analysis of the relaxation dynamics of finite-size topological qubits in contact with a thermal bath. Using a continuous-time Monte Carlo method, we explicitly compute the low-temperature nonequilibrium dynamics of the toric code on finite lattices. In contrast to the size-independent bound predicted for the toric code in the thermodynamic limit, we identify a lowtemperature regime on finite lattices below a size-dependent crossover temperature with nontrivial finite-size and temperature scaling of the relaxation time. We demonstrate how this nontrivial finite-size scaling is governed by the scaling of topologically nontrivial two-dimensional classical random walks. The transition out of this low-temperature regime defines a dynamical finite-size crossover temperature that scales inversely with the log of the system size, in agreement with a crossover temperature defined from equilibrium properties. We find that both the finite-size and finite-temperature scaling are stronger in the low-temperature regime than above the crossover temperature. Since this finite-temperature scaling competes with the scaling of the robustness to unitary perturbations, this analysis may elucidate the scaling of memory lifetimes of possible physical realizations of topological qubits.

We describe a parametric frequency conversion scheme for trapped charged particles, which enables a coherent interface between atomic and solidstate quantum systems. The scheme uses geometric nonlinearities of the potential of coupling electrodes near a trapped particle, and can be implemented using standard charged-particle traps. Our scheme does not rely on actively driven solid-state devices, and is hence largely immune to noise in such devices. We present a toolbox which can be used to build electron-based quantum information processing platforms, as well as quantum hybrid platforms using trapped electrons and superconducting electronics.

Electric noise from metallic surfaces is a major obstacle towards quantum applications with trapped ions due to motional heating of the ions. Here, we discuss how the same noise source can also lead to pure dephasing of motional quantum states. The mechanism is particularly relevant at small ion-surface distances, thus imposing a new constraint on trap miniaturization. By means of a free induction decay experiment, we measure the dephasing time of the motion of a single ion trapped 50 µm above a Cu-Al surface. From the dephasing times we extract the integrated noise below the secular frequency of the ion. We find that none of the most commonly discussed surface noise models for ion traps describes both, the observed heating as well as the measured dephasing, satisfactorily. Thus, our measurements provide a benchmark for future models for the electric noise emitted by metallic surfaces.PACS numbers: 37.10. Ty, 73.50.Td, 05.40.Ca, 03.65.Yz Understanding decoherence constitutes an integral part in the development of any quantum technology. All present implementations of a quantum bit have to contend with the deleterious effects of decoherence [1][2][3][4][5]. It is usually identified with an irreversible loss of information from a quantum system when the system interacts with its environment. Decoherence manifests itself in a decay of the phase relationships between energyeigenstates, and can be characterized by the coherence time T 2 , when these relationships decay to 1/e of their original values. This decay is usually thought to be a combination of two processes, a population relaxation with time constant T 1 and pure phase relaxation with a characteristic time of T φ .Trapped ion technology is one of the most promising candidate platforms to host a scalable quantum information processor. Before it can attain this goal, key challenges from decohering noise processes have to be overcome [6]. In particular, motional heating of ions trapped above room temperature microfabricated surface traps has been discussed as a serious roadblock as it limits the miniaturization of ion traps due to the increased heating as the ion is trapped closer to the trap electrodes. It is now firmly established that the main obstacle in achieving low motional heating stems from electric field fluctuations emanating from the metallic surfaces [7][8][9]. Electric fields resonant with the secular frequency of the trapped ion excite the ion's secular motion and thus lead to motional heating. Some models attribute the electric field noise to fluctuating dipole-like sources on the trap electrode surfaces [10][11][12] while others to fluctuating potential patches [13,14] or surface diffusion of adatoms [7,15,16]. Electric field noise from surfaces has been found to span across a wide range of distance and frequency regimes, impacting diverse fields, including scanning probe microscopy [17], gravitational wave experiments [18], superconducting electronics [2], detection of Casimir forces [19], and studies of non-contact friction [20]. Investig...