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Trapped ions are a highly advanced platform for implementing quantum circuits. They provide standard pairs of magnetic field insensitive "atomic clock" states as qubits with unsurpassed coherence times and optical schemes for near-unity preparation and measurement, as well as strong Coulomb interactions to generate entanglement. 

We present a modular architecture comprised of a chain of trapped 171Yb+ ions with individual Raman beam addressing and individual readout. We employ a pulse-shaping scheme [1] to use the transverse modes of motion in the chain to produce entangling gates between any qubit pair. This creates a fully connected system which can be configured to run any sequence of single- and two-qubit gates, making it in effect an arbitrarily programmable quantum computer [2] with a powerful native gate set. 

To demonstrate the universality of this setup, we present experimental results from different quantum algorithms on five ions including the Deutsch-Jozsa algorithm and the Quantum Fourier Transform which we use to implement a Period Finding as well as a Phase Estimation protocol, the latter being a key ingredient in prime factorization. Additionally, recent results from an error detection experiment will be discussed which demonstrate fault-tolerance of a logical qubit. 

[1] T. Choi et al., Phys. Rev. Lett. 112, 19502 (2014)

[2] S. Debnath et al., Nature 536, 63 (2016)

ACKNOWLEDGEMENTS

This work is supported by the ARO with funding from the IARPA LogiQ program and the AFOSR MURI on Quantum Measurement and Verification.