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Despite significant progress and efforts, lattice gauge theories remain to be challenging to be simulated on classical computers. A quantum simulator of U(1) lattice gauge theories can however be implemented with superconducting circuits. This allows, for instance, the investigation of confined and deconfined phases in quantum link models, and of valence bond solid and spin liquid phases in quantum dimer models.
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Superfluidity and superconductivity, are striking signatures of quantum mechanics at the macroscopic level, resulting in extraordinary features like the absence of viscosity or resistance in superconducting metals. In liquid helium and dilute gases, Bose and Fermi superfluidity has been observed separately, but producing a mixture in which both the fermionic and the bosonic components are superfluid is challenging.
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The quantum Hall effect has led to a deeper understanding of topological (or geometrical) effects in physics and has found generalizations in the spin quantum Hall effect and topological insulators. The plateaux in conductivity in this effect are attributed to the Chern numbers, a topological invariant characterizing the Bloch bands.
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While superconducting qubits represent a promising technological platform for quantum computation, a good enough control of the mechanisms of decoherence and dissipation in these systems is still an experimental challenge. In particular, Josephson’s key theoretical prediction that quasiparticle dissipation should vanish in transport through a junction when the phase difference across the junction is π has never been observed.
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