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Most of the quantum algorithms have been developed using a finite set of universal quantum gates, which allows for an easy decomposition of any unitary transformation. However, this set of gates includes entangling two-body gates. In the current context of faulty devices, the near-term noisy intermediate-scale quantum era, implementing these gates is deemed costly, both because the time requirement to implement these operations is much larger than for the single-qubit gates, and because they are more susceptible to errors. In contrast to the digital paradigm, analog quantum computers do not allow for arbitrary operations. But in turn of its lack of flexibility, analog devices excel in their robustness and resilience against noise.

In this context, digital-analog quantum computing (DAQC) was proposed as a way of taking advantage of the robustness of analog quantum computers while maintaining the flexibility of digital quantum computing. For this, this paradigm employs the natural interaction Hamiltonian of the devices as a resource for the entangling operations. Then, universality can be reached by the application of arbitrary single qubit gates. This allows us to implement any desired operation without the need of employing expensive and noisy two-qubit gates.

Here I present the contributions to the state of the art made during my PhD. In particular, I will describe the solution to one of the main challenges of DAQC, that was achieving universality employing efficient constructive methods. While optimal DAQC protocols require tackling an NP-Hard problem, we have proposed suboptimal protocols which only require polynomial classical resources to be calculated. In addition to this, we further studied its noise resilience, and introduced error mitigation techniques specifically designed for this paradigm. We further continued on the implementation of various algorithms and simulation tasks, showing the possibility that DAQC offers a valid alternative which in some cases might provide advantages in their run-time or fidelity.

https://combalgo.labri.fr/pmwiki.php/Groupe/Info-Quantique

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