Quantics Tensor Cross Interpolation for High-Resolution Parsimonious Representations of Multivariate Functions.

Multivariate functions of continuous variables arise in countless branches of science. Numerical computations with such functions typically involve a compromise between two contrary desiderata: accurate resolution of the functional dependence, versus parsimonious memory usage. Recently, two promising strategies have emerged for satisfying both requirements: (i) The quantics representation, which expresses functions as multi-index tensors, with each index representing one bit of a binary encoding of one of the variables; and (ii) tensor cross interpolation (TCI), which, if applicable, yields parsimonious interpolations for multi-index tensors. Here, we present a strategy, quantics TCI, which combines the advantages of both schemes. We illustrate its potential with an application from condensed matter physics: the computation of Brillouin zone integrals.

The quantum house of cards.

Quantum computers have been proposed to solve a number of important problems such as discovering new drugs, new catalysts for fertilizer production, breaking encryption protocols, optimizing financial portfolios, or implementing new artificial intelligence applications. Yet, to date, a simple task such as multiplying 3 by 5 is beyond existing quantum hardware. This article examines the difficulties that would need to be solved for quantum computers to live up to their promises. I discuss the whole stack of technologies that has been envisioned to build a quantum computer from the top layers (the actual algorithms and associated applications) down to the very bottom ones (the quantum hardware, its control electronics, cryogeny, etc.) while not forgetting the crucial intermediate layer of quantum error correction.

Coulomb-mediated antibunching of an electron pair surfing on sound.

Electron flying qubits are envisioned as potential information links within a quantum computer, but also promise-like photonic approaches-to serve as self-standing quantum processing units. In contrast to their photonic counterparts, electron-quantum-optics implementations are subject to Coulomb interactions, which provide a direct route to entangle the orbital or spin degree of freedom. However, controlled interaction of flying electrons at the single-particle level has not yet been established experimentally. Here we report antibunching of a pair of single electrons that is synchronously shuttled through a circuit of coupled quantum rails by means of a surface acoustic wave. The in-flight partitioning process exhibits a reciprocal gating effect which allows us to ascribe the observed repulsion predominantly to Coulomb interaction. Our single-shot experiment marks an important milestone on the route to realize a controlled-phase gate for in-flight quantum manipulations.

Quantum Quasi-Monte Carlo Technique for Many-Body Perturbative Expansions.

High order perturbation theory has seen an unexpected recent revival for controlled calculations of quantum many-body systems, even at strong coupling. We adapt integration methods using low-discrepancy sequences to this problem. They greatly outperform state-of-the-art diagrammatic Monte Carlo simulations. In practical applications, we show speed-ups of several orders of magnitude with scaling as fast as 1/N in sample number N; parametrically faster than 1/sqrt[N] in Monte Carlo simulations. We illustrate our technique with a solution of the Kondo ridge in quantum dots, where it allows large parameter sweeps.

Nonlocal Spin Dynamics in the Crossover from Diffusive to Ballistic Transport.

Improved fabrication techniques have enabled the possibility of ballistic transport and unprecedented spin manipulation in ultraclean graphene devices. Spin transport in graphene is typically probed in a nonlocal spin valve and is analyzed using spin diffusion theory, but this theory is not necessarily applicable when charge transport becomes ballistic or when the spin diffusion length is exceptionally long. Here, we study these regimes by performing quantum simulations of graphene nonlocal spin valves. We find that conventional spin diffusion theory fails to capture the crossover to the ballistic regime as well as the limit of long spin diffusion length. We show that the latter can be described by an extension of the current theoretical framework. Finally, by covering the whole range of spin dynamics, our study opens a new perspective to predict and scrutinize spin transport in graphene and other two-dimensional material-based ultraclean devices.

Canted Persistent Spin Texture and Quantum Spin Hall Effect in WTe_{2}.

We report an unconventional quantum spin Hall phase in the monolayer WTe_{2}, which exhibits hitherto unknown features in other topological materials. The low symmetry of the structure induces a canted spin texture in the yz plane, which dictates the spin polarization of topologically protected boundary states. Additionally, the spin Hall conductivity gets quantized (2e^{2}/h) with a spin quantization axis parallel to the canting direction. These findings are based on large-scale quantum simulations of the spin Hall conductivity tensor and nonlocal resistances in multiprobe geometries using a realistic tight-binding model elaborated from first-principle methods. The observation of this canted quantum spin Hall effect, related to the formation of topological edge states with nontrivial spin polarization, demands for specific experimental design and suggests interesting alternatives for manipulating spin information in topological materials.

Sound-driven single-electron transfer in a circuit of coupled quantum rails.

Surface acoustic waves (SAWs) strongly modulate the shallow electric potential in piezoelectric materials. In semiconductor heterostructures such as GaAs/AlGaAs, SAWs can thus be employed to transfer individual electrons between distant quantum dots. This transfer mechanism makes SAW technologies a promising candidate to convey quantum information through a circuit of quantum logic gates. Here we present two essential building blocks of such a SAW-driven quantum circuit. First, we implement a directional coupler allowing to partition a flying electron arbitrarily into two paths of transportation. Second, we demonstrate a triggered single-electron source enabling synchronisation of the SAW-driven sending process. Exceeding a single-shot transfer efficiency of 99%, we show that a SAW-driven integrated circuit is feasible with single electrons on a large scale. Our results pave the way to perform quantum logic operations with flying electron qubits.

Role of Quasiparticles in an Electric Circuit with Josephson Junctions.

Although Josephson junctions can be viewed as highly nonlinear impedances for superconducting quantum technologies, they also possess internal dynamics that may strongly affect their behavior. Here, we construct a computational framework that includes a microscopic description of the junction (full fledged treatment of both the superconducting condensate and the quasiparticles) in the presence of a surrounding electrical circuit. Our approach generalizes the standard resistor capacitor Josephson model to arbitrary junctions (including, e.g., multiterminal geometries and/or junctions that embed topological or magnetic elements) and arbitrary electric circuits treated at the classical level. By treating the superconducting condensate and quasiparticles on equal footings, we capture nonequilibrium phenomena such as multiple Andreev reflection. We show that the interplay between the quasiparticle dynamics and the electrical environment leads to the emergence of new phenomena. In a RC circuit connected to single channel Josephson junction, we find out-of-equilibrium current-phase relations that are strongly distorted with respect to the (almost sinusoidal) equilibrium one, revealing the presence of the high harmonic ac Josephson effect. In an RLC circuit connected to a junction, we find that the shape of the resonance is strongly modified by the quasiparticle dynamics: close to resonance, the current can be smaller than without the resonator. Our approach provides a route for the quantitative modeling of superconducting-based circuits.

Unveiling the bosonic nature of an ultrashort few-electron pulse.

Quantum dynamics is very sensitive to dimensionality. While two-dimensional electronic systems form Fermi liquids, one-dimensional systems-Tomonaga-Luttinger liquids-are described by purely bosonic excitations, even though they are initially made of fermions. With the advent of coherent single-electron sources, the quantum dynamics of such a liquid is now accessible at the single-electron level. Here, we report on time-of-flight measurements of ultrashort few-electron charge pulses injected into a quasi one-dimensional quantum conductor. By changing the confinement potential we can tune the system from the one-dimensional Tomonaga-Luttinger liquid limit to the multi-channel Fermi liquid and show that the plasmon velocity can be varied over almost an order of magnitude. These results are in quantitative agreement with a parameter-free theory and demonstrate a powerful probe for directly investigating real-time dynamics of fractionalisation phenomena in low-dimensional conductors.

Coherent control of single electrons: a review of current progress.

In this report we review the present state of the art of the control of propagating quantum states at the single-electron level and its potential application to quantum information processing. We give an overview of the different approaches that have been developed over the last few years in order to gain full control over a propagating single-electron in a solid-state system. After a brief introduction of the basic concepts, we present experiments on flying qubit circuits for ensemble of electrons measured in the low frequency (DC) limit. We then present the basic ingredients necessary to realise such experiments at the single-electron level. This includes a review of the various single-electron sources that have been developed over the last years and which are compatible with integrated single-electron circuits. This is followed by a review of recent key experiments on electron quantum optics with single electrons. Finally we will present recent developments in the new physics that has emerged using ultrashort voltage pulses. We conclude our review with an outlook and future challenges in the field.

Cooperative Charge Pumping and Enhanced Skyrmion Mobility.

It is well known that moving magnetic textures may pump spin and charge currents along the direction of motion, a phenomenon called electronic pumping. Here, the electronic pumping arising from the steady motion of ferromagnetic skyrmions is investigated by solving the time evolution of the Schrödinger equation implemented on a tight-binding model with the statistical physics of the many-body problem. In contrast with rigid one-dimensional magnetic textures, we show that steadily moving magnetic skyrmions are able to pump large dc currents. This ability arises from their nontrivial magnetic topology, i.e., the coexistence of the spin-motive force and the topological Hall effect. Based on an adiabatic scattering theory, we compute the pumped current and demonstrate that it scales with the reflection coefficient of the conduction electrons against the skyrmion. In other words, in the semiclassical limit, reducing the size of the skyrmion and the width of the nanowire enhances this effect, making it scalable. We propose that such a phenomenon can be exploited in the context of racetrack devices, where the electronic pumping enhances the collective motion of the train of skyrmions.

Control of the Oscillatory Interlayer Exchange Interaction with Terahertz Radiation.

The oscillatory interlayer exchange interaction between two magnetic layers separated by a metallic spacer is one of the few coherent quantum phenomena that persists at room temperature. Here, we show that this interaction can be controlled dynamically by illuminating the sample (e.g., a spin valve) with radiation in the 10-100 THz range. We predict that the exchange interaction can be changed from ferromagnetic to antiferromagnetic (and vice versa) by tuning the amplitude and/or the frequency of the radiation. Our chief theoretical result is an expression that relates the dynamical exchange interaction to the static one that has already been extensively measured.

The a.c. Josephson effect without superconductivity.

Superconductivity derives its most salient features from the coherence of the associated macroscopic wave function. The related physical phenomena have now moved from exotic subjects to fundamental building blocks for quantum circuits such as qubits or single photonic modes. Here we predict that the a.c. Josephson effect-which transforms a d.c. voltage Vb into an oscillating signal cos (2eVbt/h)-has a mesoscopic counterpart in normal conductors. We show that when a d.c. voltage Vb is applied to an electronic interferometer, there exists a universal transient regime where the current oscillates at frequency eVb/h. This effect is not limited by a superconducting gap and could, in principle, be used to produce tunable a.c. signals in the elusive 0.1-10-THz 'terahertz gap'.

Dynamical control of interference using voltage pulses in the quantum regime.

As a general trend, nanoelectronics experiments are shifting towards frequencies so high that they become comparable to the device's internal characteristic time scales, resulting in new opportunities for studying the dynamical aspects of quantum mechanics. Here we theoretically study how a voltage pulse (in the quantum regime) propagates through an electronic interferometer (Fabry-Perot or Mach-Zehnder). We show that extremely fast pulses provide a conceptually new tool for manipulating quantum information: the possibility to dynamically engineer the interference pattern of a quantum system. Striking physical signatures are associated with this new regime: restoration of the interference in presence of large bias voltages; negative currents with respect to the direction of propagation of the voltage pulse; and oscillation of the total transmitted charge with the total number of injected electrons. The present findings have been made possible by the recent unlocking of our capability for simulating time-resolved quantum nanoelectronics of large systems.

Unified drift-diffusion theory for transverse spin currents in spin valves, domain walls, and other textured magnets.

Spins transverse to the magnetization of a ferromagnet only survive over a short distance. We develop a drift-diffusion approach that captures the main features of transverse spin effects in systems with arbitrary spin textures (e.g., vortices and domain walls) and generalizes the Valet-Fert theory. In addition to the standard characteristic lengths (mean free path for majority and minority electrons, and spin diffusion length), the theory introduces two length scales, the transverse spin coherence length ℓ(⊥) and the (Larmor) spin precession length ℓ(L). We show how ℓ(L) and ℓ(⊥) can be extracted from ab initio calculations or measured with giant magnetoresistance experiments. In long (adiabatic) domain walls, we provide an analytic formula that expresses the so-called "nonadiabatic" (or fieldlike) torque in terms of these length scales. However, this nonadiabatic torque is no longer a simple material parameter but depends on the actual spin texture: in thin (<10 nm) domain walls, we observe very significant deviations from the adiabatic limit.

Interplay between nonequilibrium and equilibrium spin torque using synthetic ferrimagnets.

We discuss the current induced magnetization dynamics of spin valves F(0)|N|SyF where the free layer is a synthetic ferrimagnet SyF made of two ferromagnetic layers F(1) and F(2) coupled by RKKY exchange coupling. When the magnetic moment of the outer layer F(2) dominates the magnetization of the SyF, the sign of the effective spin torque exerted on the layer F(1) is controlled by the coupling's strength: for weak coupling the spin torque tends to antialign F(1)'s magnetization with respect to the pinned layer F(0). At large coupling the situation is reversed and tends to align F(1) with respect to F(0). At intermediate coupling, numerical simulations reveal that the competition between these two incompatible limits leads generically to spin torque oscillator (STO) behavior. The STO is found at zero magnetic field, with very significant amplitude of oscillations and frequencies up to 50 GHz or higher.

Effective magnetic monopoles and universal conductance fluctuations.

The observation of isolated positive and negative charges, but not isolated magnetic north and south poles, is an old puzzle. Instead, evidence of effective magnetic monopoles has been found in the abstract momentum space. Apart from Hall-related effects, few observable consequences of these abstract monopoles are known. Here, we show that it is possible to manipulate the monopoles by external magnetic fields and probe them by universal conductance fluctuation measurements in ferromagnets with strong spin-orbit coupling. The observed fluctuations are not noise, but reproducible quasiperiodic oscillations as a function of magnetization direction, a novel Berry phase fingerprint of the magnetic monopoles.

Spin torque and waviness in magnetic multilayers: a bridge between Valet-Fert theory and quantum approaches.

We develop a simple theoretical framework for transport in magnetic multilayers, based on the Landauer-Buttiker scattering formalism and random matrix theory. A simple transformation allows one to go from the scattering point of view to theories expressed in terms of local currents and the electromagnetic potential. In particular, our theory can be mapped onto the well-established classical Valet-Fert theory for collinear systems. For noncollinear systems, in the absence of spin-flip scattering, our theory can be mapped onto the generalized circuit theory. We apply our theory to the angular dependence of spin accumulation and spin torque in noncollinear spin valves.

Many-body localization study in low-density electron gases: do metals exist in two dimensions?

Using a combination of ground state quantum Monte Carlo and finite size scaling techniques, we perform a systematic study of the effect of Coulomb interaction on the localization length of a disordered two-dimensional electron gas. We find that correlations delocalize the 2D system. In the absence of valley degeneracy (as in GaAs heterostructures), this delocalization effect corresponds to a finite increase of the localization length. The delocalization is much more dramatic in the presence of valley degeneracy [as in Si metal-oxide-semiconductor field-effect transistors], where the localization length increases drastically. We find that a simple mechanism accounts for the main features of the metallic behavior observed in two-dimensional gases. Our findings support the claim that this behavior is a genuine effect of the presence of interactions, yet that the system is not a "true" metal in the thermodynamic sense.

Persistent currents in one dimension: the counterpart of Leggett's theorem.

We discuss the sign of the persistent current of N electrons in one dimensional rings. Using a topology argument, we establish lower bounds for the free energy in the presence of arbitrary electron-electron interactions and external potentials. Those bounds are the counterparts of upper bounds derived by Leggett. Rings with odd (even) numbers of polarized electrons are always diamagnetic (paramagnetic). We show that unpolarized electrons with N being a multiple of four exhibit either paramagnetic behavior or a superconductorlike current-phase relation.