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