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Quantum computing is an emerging research area which promises to offer a revolution in the computing performance. The world’s first commercially available quantum computer has been the D-Wave machine which aims at solving complex problems by representing them in terms of Ising Hamiltonians. This formulation allows addressing several combinatorial optimization problems since generally it is possible to map any problem to the Hamiltonian of the Ising model. However, D-Wave’s architecture restricts the Ising Hamiltonian to the case with only 2-body interactions. Therefore, in order to face problems mapped on systems with p -body interactions ( p ≥ 2 ), it is necessary to implement a procedure to compute 2-body effective Hamiltonians of p -body interacting systems. Due to the complexity of this task, recently, meta-heuristic methods have been applied with promising results. The aim of this paper is to implement a procedure to convert from p -body to 2-body Hamiltonians by means of memetic algorithms. As shown in the experimental session involving the ferromagnetic p -spin model as a case study, the proposed approach improves by 60% on average over the state-of-the-art meta-heuristic approaches.

The edge states of Topological Insulators (TI) are protected against backscattering, thanks to the topological properties arising from their band structure. Coupling a TI to a superconductor (S) can induce unconventional effects, including the creation of Majorana bound states (MBS). The fabrication of coplanar hybrid devices is a fundamental step to pave the way to the understanding of proximity effects in topologically non-trivial systems, and to a large variety of experiments aimed at the possible detection of MBS. We discuss the feasibility and some relevant properties of Al-Bi2Se3-Al coplanar proximity devices. Special attention is devoted to the design of the junction, aimed at enhancing the coupling between the electrodes and the TI.

Self-assembled nanoscale channels may naturally arise in the growth process of grain boundaries (GBs) in high critical temperature superconductor (HTS) systems, and deeply influence the transport properties of the GB Josephson junctions (JJs). By isolating nano-channels in YBCO biepitaxial JJs and studying their properties, we sort out specific fingerprints of the mesoscopic nature of the contacts. The size of the channels combined to the characteristic properties of HTS favors a special regime of the proximity effect, where normal state coherence prevails on the superconducting coherence in the barrier region. Resistance oscillations from the current–voltage characteristic encode mesoscopic information on the junction and more specifically on the minigap induced in the barrier. Thouless energy emerges as a characteristic energy of these types of Josephson junctions. Possible implications on the understanding of coherent transport of quasiparticles in HTS and of the dissipation mechanisms are discussed, along with elements to take into account when designing HTS nanostructures.