High critical temperature nodal superconductors as building block for time-reversal invariant topological superconductivity

We study possible applications of high critical temperature nodal superconductors for the search for Majorana bound states in the DIII class. We propose a microscopic analysis of the proximity effect induced by d-wave superconductors on a semiconductor wire with strong spin-orbit coupling. We characterize the induced superconductivity on the wire employing a numerical self-consistent tight-binding Bogoliubov-de Gennes approach, and analytical considerations on the Green's function. The order parameter induced on the wire, the pair correlation function, and the renormalization of the Fermi points are analyzed in detail, as well as the topological phase diagram in the case of weak coupling. We highlight optimal Hamiltonian parameters to access the nontrivial topological phase which could display time-reversal invariant Majorana doublets at the boundaries of the wire

May a dissipative environment be beneficial for quantum annealing?

We discuss the quantum annealing of the fully-connected ferromagnetic $p$-spin model in a dissipative environment at low temperature. This model, in the large $p$ limit, encodes in its ground state the solution to the Grover's problem of searching in unsorted databases. In the framework of the quantum circuit model, a quantum algorithm is known for this task, providing a quadratic speed-up with respect to its best classical counterpart. This improvement is not recovered in adiabatic quantum computation for an isolated quantum processor. We analyze the same problem in the presence of a low-temperature reservoir, using a Markovian quantum master equation in Lindblad form, and we show that a thermal enhancement is achieved in the presence of a zero temperature environment moderately coupled to the quantum annealer.Comment: 4 pages, 1 figure, proceeding of IQIS 201

High-accuracy Hamiltonian learning via delocalized quantum state evolutions

In this Letter, we propose a method to learn the unknown Hamiltonian governing the dynamics of a quantum many-body system, using measurements on a single time-dependent state. We investigate the error scaling of our reconstruction with respect to the experiment duration, measuring an exponential decrease during the equilibration time. We prove that the accuracy of the learning process is maximised for states that are delocalized in the Hamiltonian eigenstates, capable of exploring a large sample of the Hilbert space. Finally, we provide examples of our algorithm on simulated quantum systems

Dissipative time crystals with long-range Lindbladians

Dissipative time crystals can appear in spin systems, when the $Z_2$ symmetry of the Hamiltonian is broken by the environment, and the square of total spin operator $S^2$ is conserved. In this manuscript, we relax the latter condition and show that time-translation-symmetry breaking collective oscillations persist, in the thermodynamic limit, even in the absence of spin symmetry. We engineer an ad hoc Lindbladian using power-law decaying spin operators and show that time-translation symmetry breaking appears when the decay exponent obeys $0<\eta\leq 1$. This model shows a surprisingly rich phase diagram, including the time-crystal phase as well as first-order, second-order, and continuous transitions of the fixed points. We study the phase diagram and the magnetization dynamics in the mean-field approximation, which we prove to be exact, in the thermodynamic limit, as the system does not develop sizable quantum fluctuations, up to the third order cumulant expansion.Comment: 13 pages, 11 figure

Andreev spin-noise detector

We investigate the possibility to employ magnetic Josephson junctions as magnetic-noise detectors. To illustrate our idea, we consider a system consisting of a quantum dot coupled to superconducting leads in the presence of an external magnetic field. Under appropriate assumptions, we relate the noise in the Josephson current to magnetization noise. At the magnetic field driven $0-\pi$ transition the junction sensitivity as magnetic noise detector is strongly enhanced and it diverges in the zero temperature limit. Moreover, we demonstrate that, if also dot energy is affected by fluctuations, only the magnetic noise channel contributes to Josephson current noise response when the quantum dot is tuned in resonance with superconducting leads.Comment: Review. 14 pages. 3 appendices. 14 figure

Suppression of Kondo-assisted co-tunneling in a spin-1 quantum dot with Spin-Orbit interaction

Kondo-type zero-bias anomalies have been frequently observed in quantum dots occupied by two electrons and attributed to a spin-triplet configuration that may become stable under particular circumstances. Conversely, zero-bias anomalies have been so far quite elusive when quantum dots are occupied by an even number of electrons greater than two, even though a spin-triplet configuration is more likely to be stabilized there than for two electrons. We propose as an origin of this phenomenon the spin-orbit interaction, and we show how it profoundly alters the conventional Kondo screening scenario in the simple case of a laterally confined quantum dot with four electrons.Comment: 5 pages, 3 figures, submitted 05May201

High-accuracy Hamiltonian learning via delocalized quantum state evolutions

Learning the unknown Hamiltonian governing the dynamics of a quantum many-body system is a challenging task. In this manuscript, we propose a possible strategy based on repeated measurements on a single time-dependent state. We prove that the accuracy of the learning process is maximized for states that are delocalized in the Hamiltonian eigenbasis. This implies that delocalization is a quantum resource for Hamiltonian learning, that can be exploited to select optimal initial states for learning algorithms. We investigate the error scaling of our reconstruction with respect to the number of measurements, and we provide examples of our learning algorithm on simulated quantum systems

Deep learning optimal quantum annealing schedules for random Ising models

A crucial step in the race towards quantum advantage is optimizing quantum annealing using ad-hoc annealing schedules. Motivated by recent progress in the field, we propose to employ long short term memory (LSTM) neural networks to automate the search for optimal annealing schedules for (random) weighted Max-Cut on regular graphs. By training our network using locally adiabatic annealing paths, we are able to predict optimal annealing schedules for unseen instances and even larger graphs than those used for training.Comment: 9 pages, 6 figure