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Recently, digitized-counterdiabatic (CD) corrections to the quantum approximate optimization algorithm (QAOA) have been proposed, yielding faster convergence within the desired accuracy than standard QAOA. In this manuscript, we apply this approach to a fully-connected spin model with random couplings. We show that the performances of the algorithm are related to the spectral properties of the instances analyzed. In particular, the larger the gap between the ground state and the first excited states, the better the convergence to the exact solution.

Twisted bilayer structures have emerged as a fascinating arena in condensed matter thanks to their highly tunable physics. The role of spin-orbit coupling (SOC) in twisted bilayers has gained increasing attention due to its potential for spintronics. Thus, it is appealing to propose new materials for constructing twisted bilayers with substantial SOC. In this work, the intriguing effects induced by twisting two layers of two-dimensional bismuthene are unraveled from large-scale first-principles calculations. We show that spin-orbit coupling significantly affects the electronic properties of twisted bilayer bismuthene, even more than in its untwisted counterpart. We carefully investigate how the interplay between the spin-orbit coupling and the twist angle impacts the band structure and spin textures of twisted bilayer bismuthene. We find that the twist angle can be deemed a control knob to switch from a small-gap semiconductor to a metallic behavior. Most crucially, the accurate analysis of the energy bands close to Fermi energy reveals a twist-tunable splitting in the mexican-hat shape of the bands that can otherwise be obtained only by applying enormous electric fields. Our predictions provide insight into innovative bismuth-based technologies for future spintronic devices., Comment: Unrevised first version of the manuscript

Recently, Digitized-Counterdiabatic (CD) Quantum Approximate Optimization Algorithm (QAOA) has been proposed to make QAOA converge to the solution of an optimization problem in fewer steps, inspired by Trotterized counterdiabatic driving in continuous-time quantum annealing. In this paper, we critically revisit this approach by focusing on the paradigmatic weighted and unweighted one-dimensional MaxCut problem. We study two variants of QAOA with first and second-order CD corrections. Our results show that, indeed, higher order CD corrections allow for a quicker convergence to the exact solution of the problem at hand by increasing the complexity of the variational cost function. Remarkably, however, the total number of free parameters needed to achieve this result is independent of the particular QAOA variant analyzed.

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 Ising models 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: 10 pages, 8 figures

The study of novel 2D platforms implementing magnetism in tunable van der Waals (vdW) homo- and hetero-structures paves the way to innovative spintronics and magnetic devices. In this study, we unravel the intriguing properties of few-layer Nb$_3$I$_8$ vdW nanofilms from first principles, showing how and to what extent specific magnetic orderings can be tuned using several degrees of freedom, such as film thickness, stacking geometry, and strain or even a combination of them. All these aspects are explored here, giving a comprehensive view of this novel and promising magnetic material.

The interlayer van der Waals interaction in twisted bilayer graphene (tBLG) induces both in-plane and out-of-plane atomic displacements showing complex patterns that depend on the twist angle. In particular, for small twist angles, within each graphene layer, the relaxations give rise to a vortex-like displacement pattern which is known to affect the dispersion of the flat bands. Here, we focus on yet another structural property, the chirality of the twisted bilayer. We perform first-principles calculations based on density functional theory to investigate the properties induced by twist chirality in both real and momentum space. In real space, we study the interplay between twist chirality and atomic relaxation patterns. In momentum space, we investigate the spin textures around the $K$ points of the Brillouin zone, showing that alternating vortex-like textures are correlated with the chirality of tBLG. Interestingly, the helicity of each vortex is inverted by changing the chirality while the different twist angles also modify the spin textures. We discuss the origin of the spin textures by calculating the layer weights and using plot regression models., Comment: 12 pages and 7 figures in main text, 11 pages and 12 figures in supplemental material; revised according to referees' suggestions; Accepted in Phys. Rev. B

We combine state-of-the-art large-scale first principles calculations with a low-energy continuum model to describe the nearly flat bands of twisted bilayer graphene at the first magic angle $\theta =1.08^\circ$. We show that the energy width of the flat band manifold, as well as the energy gap separating it from the valence and conduction bands, can be obtained only if the out-of-plane relaxations are fully taken into account. The results agree both qualitatively and quantitatively with recent experimental outcomes., Comment: Published in Phys. Rev. B 99, 195419 (2019)

We show that the central finite difference formula for the first and the second derivative of a function can be derived, in the context of quantum mechanics, as matrix elements of the momentum and kinetic energy operators using, as a basis set, the discrete coordinate eigenkets $\vert x_n\rangle$ defined on the uniform grid $x_n=na$. Simple closed form expressions of the matrix elements are obtained starting from integrals involving the canonical commutation rule. A detailed analysis of the convergence toward the continuum limit with respect to both the grid spacing and the approximation order is presented. It is shown that the convergence from below of the eigenvalues in electronic structure calculations is an intrinsic feature of the finite difference method.

We characterize the transport properties of functionalized graphene nanoribbons using extensive first-principles calculations based on density functional theory (DFT) that encompass both monovalent and divalent ligands, hydrogenated defects and vacancies. We find that the edge metallic states are preserved under a variety of chemical environments, while bulk conducting channels can be easily destroyed by either hydrogenation or ion or electron beams, resulting in devices that can exhibit spin conductance polarization close to unity., Comment: 14 pages, 5 figures