Real-time hybrid quantum-classical computations for trapped-ions with Python control-flow

In recent years, the number of hybrid algorithms that combine quantum and classical computations has been continuously increasing. These two approaches to computing can mutually enhance each others' performances thus bringing the promise of more advanced algorithms that can outmatch their pure counterparts. In order to accommodate this new class of codes, a proper environment has to be created, which enables the interplay between the quantum and classical hardware. For many of these hybrid processes the coherence time of the quantum computer arises as a natural time constraint, making it crucial to minimize the classical overhead. For ion-trap quantum computers however, this is a much less limiting factor than with superconducting technologies, since the relevant timescale is on the order of seconds instead of microseconds. In fact, this long coherence time enables us to develop a scheme for real-time control of quantum computations in an interpreted programming language like Python. In particular, compilation of all instructions in advance is not necessary, unlike with superconducting qubits. This keeps the implementation of hybrid algorithms simple and also lets users benefit from the rich environment of existing Python libraries. In order to show that this approach of interpreted quantum-classsical computations (IQCC) is feasible, we bring real-world examples and evaluate them in realistic benchmarks.