RAINER BLATT (UNIVERSITÄT INNSBRUCK): Quantum Computation and Quantum Simulation with Strings of Trapped Ca+ Ions

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The state-of-the-art of the Innsbruck trapped-ion quantum computer is briefly reviewed. We present an overview on the available quantum toolbox and discuss the scalability of the approach. Fidelities of quantum gate operations are evaluated and optimized by means of cycle- benchmarking [1] and we show the generation of entangled states with fully controlled strings of 20 to 50 ions [2], which are used for quantum simulations.

In the second part, we present both the digital quantum simulation and a hybrid quantum- classical simulation of the Lattice Schwinger model, a gauge theory of 1D quantum electrodynamics. Employing universal quantum computations, we investigate the dynamics of the pair-creation [3] and using a hybrid-classical ansatz, we determine steady-state properties of the Hamiltonian. Hybrid classical-quantum algorithms aim at solving optimization problems variationally, using a feedback loop between a classical computer and a quantum co-processor, while benefitting from quantum resources [4]. With randomized measurements, we describe a protocol for cross-platform verification of quantum simulators and quantum computers [5].

[1] A. Erhard et al., Nat. Commun. 10, 5347 (2019)
[2] N. Friis et al., Phys Rev X 8, 021012 (2018)
[3] E. A. Martinez et al., Nature 534, 516 (2016)
[4] C. Kokail et al., Nature 569, 355–360 (2019)
[5] A. Elben et al., Phys. Rev. Lett. 124, 010504 (2020)