Realization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices.

We demonstrate the experimental implementation of an optical lattice that allows for the generation of large homogeneous and tunable artificial magnetic fields with ultracold atoms. Using laser-assisted tunneling in a tilted optical potential, we engineer spatially dependent complex tunneling amplitudes. Thereby, atoms hopping in the lattice accumulate a phase shift equivalent to the Aharonov-Bohm phase of charged particles in a magnetic field. We determine the local distribution of fluxes through the observation of cyclotron orbits of the atoms on lattice plaquettes, showing that the system is described by the Hofstadter model. Furthermore, we show that for two atomic spin states with opposite magnetic moments, our system naturally realizes the time-reversal-symmetric Hamiltonian underlying the quantum spin Hall effect; i.e., two different spin components experience opposite directions of the magnetic field.

Hyperentanglement-enabled direct characterization of quantum dynamics.

We use hyperentangled photons to experimentally implement an entanglement-assisted quantum process tomography technique known as direct characterization of quantum dynamics. Specifically, hyperentanglement-assisted Bell-state analysis enabled us to characterize a variety of single-qubit quantum processes using far fewer experimental configurations than are required by standard quantum process tomography. Furthermore, we demonstrate how known errors in Bell-state measurement may be compensated for in the data analysis. Using these techniques, we have obtained single-qubit process fidelities over 98% but with one-third the number of experimental configurations required for standard quantum process tomography. Extensions of these techniques to multiqubit quantum processes are discussed.

Universal digital quantum simulation with trapped ions.

A digital quantum simulator is an envisioned quantum device that can be programmed to efficiently simulate any other local system. We demonstrate and investigate the digital approach to quantum simulation in a system of trapped ions. With sequences of up to 100 gates and 6 qubits, the full time dynamics of a range of spin systems are digitally simulated. Interactions beyond those naturally present in our simulator are accurately reproduced, and quantitative bounds are provided for the overall simulation quality. Our results demonstrate the key principles of digital quantum simulation and provide evidence that the level of control required for a full-scale device is within reach.