Digital quantum simulations and machine learning on near-term quantum processors

Quantum mechanics is the gateway towards novel and potentially disruptive approaches to scientific and technical computing. In this thesis we explore, from a number of different perspectives, the effects of such strong relationship between the physical nature of information and the informational side of physical processes, with a focus on the digital quantum computing paradigm. After an extensive introduction to the theory of universal quantum simulation techniques, we review the main achievements in the field and, in parallel, we outline the state of the art of near-term architectures for quantum information processing. We then move on to present novel and scalable procedures for the study of paradigmatic spin models on intermediate-scale noisy quantum processors. Through an innovative combination of quantum algorithms with classical post-processing and error mitigation protocols, we demonstrate in practice the full digital quantum simulation of spin-spin dynamical correlation functions, reporting experimental results obtained on superconducting cloud-accessible IBM Q devices. We also exhibit a practical use-case by successfully reproducing, from quantum computed data, cross section calculations for four-dimensional inelastic neutron scattering, a common tool employed in the analysis of molecular magnetic clusters. The central part of the thesis is dedicated to the exploration of perspective hardware solutions for quantum computing. As it is not yet clear whether the currently dominant platforms, namely trapped ions and superconducting circuits, will eventually allow to reach the final goal of a fully-fledged architecture for general-purpose quantum information processing, the search for alternative technologies is at least as urgent as the improvement of existing ones or the development of new algorithms. After providing an overview of some recent proposals, including hybrid set-ups, we introduce quantum electromechanics as a promising candidate platform for future realizations of digital quantum simulators and we predict competitive performances for an elementary building block featuring nanomechanical qubits integrated within superconducting circuitry. In the final part, we extend the reach of quantum information protocols beyond its traditional areas of application, and we account for the birth and rapid development of Quantum Machine Learning, a discipline aimed at establishing a productive interplay between the parallel revolutions brought about by quantum computing and artificial intelligence. In particular, we describe an original procedure for implementing, on a quantum architecture, the behavior of binary-valued artificial neurons. Formally exact and platform-independent, our data encoding and processing scheme guarantees in principle an exponential memory advantage over classical counterparts and is particularly well suited for pattern and image recognition purposes. We test our algorithm on IBM Q quantum processors, discussing possible training schemes for single nodes and reporting a proof-of-principle demonstration of a 2-layer, 3-neuron feed-forward neural network computation run on 7 active qubits. The latter is, in terms of the total size of the quantum register, one of the largest quantum neural network computation reported to date on real quantum hardware.