
C. Kokail, C. Maier, R. van Bijnen, T. Brydges, M. K. Joshi, P. Jurcevic, C. A. Muschik, P. Silvi, R. Blatt, C. F. Roos, P. Zoller Selfverifying variational quantum simulation of lattice models,
Nature 569 360 (20190515),
http://dx.doi.org/10.1038/s4158601911774 doi:10.1038/s4158601911774 (ID: 720076)
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Hybrid classicalquantum algorithms aim at variationally solving optimisation problems, using a feedback loop between a classical computer and a quantum coprocessor, while benefitting from quantum resources. Here we present experiments demonstrating selfverifying, hybrid, variational quantum simulation of lattice models in condensed matter and highenergy physics. Contrary to analog quantum simulation, this approach forgoes the requirement of realising the targeted Hamiltonian directly in the laboratory, thus allowing the study of a wide variety of previously intractable target models. Here, we focus on the Lattice Schwinger model, a gauge theory of 1D quantum electrodynamics. Our quantum coprocessor is a programmable, trappedion analog quantum simulator with up to 20 qubits, capable of generating families of entangled trial states respecting symmetries of the target Hamiltonian. We determine ground states, energy gaps and, by measuring variances of the Schwinger Hamiltonian, we provide algorithmic error bars for energies, thus addressing the longstanding challenge of verifying quantum simulation.

T. Brydges, A. Elben, P. Jurcevic, B. Vermersch, C. Maier, B. P. Lanyon, P. Zoller, R. Blatt, C. F. Roos Probing Renyi entanglement entropy via randomized measurements,
Science 364 260 (20190419),
http://dx.doi.org/10.1126/science.aau4963 doi:10.1126/science.aau4963 (ID: 720034)
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Entanglement is the key feature of manybody quantum systems, and the development of new tools to probe it in the laboratory is an outstanding challenge. Measuring the entropy of different partitions of a quantum system provides a way to probe its entanglement structure. Here, we present and experimentally demonstrate a new protocol for measuring entropy, based on statistical correlations between randomized measurements. Our experiments, carried out with a trappedion quantum simulator, prove the overall coherent character of the system dynamics and reveal the growth of entanglement between its parts  both in the absence and presence of disorder. Our protocol represents a universal tool for probing and characterizing engineered quantum systems in the laboratory, applicable to arbitrary quantum states of up to several tens of qubits.

C. Maier, T. Brydges, P. Jurcevic, N. Trautmann, C. Hempel, B. P. Lanyon, P. Hauke, R. Blatt, C. F. Roos Environmentassisted quantum transport in a 10qubit network,
Phys. Rev. Lett. 122 50501 (20190208),
http://dx.doi.org/10.1103/PhysRevLett.122.050501 doi:10.1103/PhysRevLett.122.050501 (ID: 720065)
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The way in which energy is transported through an interacting system governs fundamental properties in many areas of physics, chemistry, and biology. Remarkably, environmental noise can enhance the transport, an effect known as environmentassisted quantum transport (ENAQT). In this paper, we study ENAQT in a network of coupled spins subject to engineered static disorder and temporally varying dephasing noise. The interacting spin network is realized in a chain of trapped atomic ions and energy transport is represented by the transfer of electronic excitation between ions. With increasing noise strength, we observe a crossover from coherent dynamics and Anderson localization to ENAQT and finally a suppression of transport due to the quantum Zeno effect. We found that in the regime where ENAQT is most effective the transport is mainly diffusive, displaying coherences only at very short times. Further, we show that dephasing characterized by nonMarkovian noise can maintain coherences longer than white noise dephasing, with a strong influence of the spectral structure on the transport effciency. Our approach represents a controlled and scalable way to investigate quantum transport in manybody networks under static disorder and dynamic noise.