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Traditional superconductors fall into two categories, type-I, expelling magnetic fields, and type-II, into which magnetic fields exceeding a lower critical field $H_{\rm c1}$ penetrate in form of Abrikosov vortices. Abrikosov vortices are characterized by two spatial scales, the size of the normal core, $\xi$, where the superconducting order parameter is suppressed and the London penetration depth $\lambda$, describing the scale at which circulating superconducting currents forming vortices start to noticeably drop. Here we demonstrate that a novel type-III superconductivity, realized in granular media in any dimension hosts a novel vortex physics. Type-III vortices have no cores, are logarithmically confined and carry only a gauge scale $\lambda$. Accordingly, in type-III superconductors $H_{\rm c1}=0$ at zero temperature and the Ginzburg-Landau theory must be replaced by a topological gauge theory. Type-III superconductivity is destroyed not by Cooper pair breaking but by vortex proliferation generalizing the Berezinskii-Kosterlitz-Thouless mechanism to any dimension.

With the rise of quantum technologies, data security increasingly relies on quantum cryptography and its most notable application, quantum key distribution (QKD). Yet, current technological limitations, in particular, the unavailability of quantum repeaters, cause relatively low key distribution rates in practical QKD implementations. Here, we demonstrate a remarkable improvement in the QKD performance using end-to-end line tomography for the wide class of relevant protocols. Our approach is based on the real-time detection of interventions in the transmission channel, enabling an adaptive response that modifies the QKD setup and post-processing parameters, leading, thereby, to a substantial increase in the key distribution rates. Our findings provide everlastingly secure efficient quantum cryptography deployment potentially overcoming the repeaterless rate-distance limit.

Quantum algorithms are getting extremely popular due to their potential to significantly outperform classical algorithms. Yet, applying quantum algorithms to optimization problems meets challenges related to the efficiency of quantum algorithms training, the shape of their cost landscape, the accuracy of their output, and their ability to scale to large-size problems. Here, we present an approximate gradient-based quantum algorithm for hardware-efficient circuits with amplitude encoding. We show how simple linear constraints can be directly incorporated into the circuit without additional modification of the objective function with penalty terms. We employ numerical simulations to test it on MaxCut problems with complete weighted graphs with thousands of nodes and run the algorithm on a superconducting quantum processor. We find that for unconstrained MaxCut problems with more than 1000 nodes, the hybrid approach combining our algorithm with a classical solver called CPLEX can find a better solution than CPLEX alone. This demonstrates that hybrid optimization is one of the leading use cases for modern quantum devices., Comment: Accepted for publication in Quantum

Superconductivity remains one of most fascinating quantum phenomena existing on a macroscopic scale. Its rich phenomenology is usually described by the Ginzburg-Landau (GL) theory in terms of the order parameter, representing the macroscopic wave function of the superconducting condensate. The GL theory addresses one of the prime superconducting properties, screening of the electromagnetic field because it becomes massive within a superconductor, the famous Anderson-Higgs mechanism. Here we describe another widely-spread type of superconductivity where the Anderson-Higgs mechanism does not work and must be replaced by the Deser-Jackiw-Templeton topological mass generation and, correspondingly, the GL effective field theory must be replaced by an effective topological gauge theory. These superconductors are inherently inhomogeneous granular superconductors, where electronic granularity is either fundamental or emerging. We show that the corresponding superconducting transition is a three-dimensional (3D) generalization of the 2D Berezinskii-Kosterlitz-Thouless (BKT) vortex binding-unbinding transition. The binding-unbinding of the line-like vortices in 3D results in the Vogel-Fulcher-Tamman (VFT) scaling of the resistance near the superconducting transition. We report experimental data fully confirming the VFT behavior of the resistance.

Quantum key distribution (QKD) is a revolutionary cryptography response to the rapidly growing cyberattacks threat posed by quantum computing. Yet, the roadblock limiting the vast expanse of secure quantum communication is the exponential decay of the transmitted quantum signal with the distance. Today's quantum cryptography is trying to solve this problem by focusing on quantum repeaters. However, efficient and secure quantum repetition at sufficient distances is still far beyond modern technology. Here, we shift the paradigm and build the long-distance security of the QKD upon the quantum foundations of the Second Law of Thermodynamics and end-to-end physical oversight over the transmitted optical quantum states. Our approach enables us to realize quantum states' repetition by optical amplifiers keeping states' wave properties and phase coherence. The unprecedented secure distance range attainable through our approach opens the door for the development of scalable quantum-resistant communication networks of the future., Comment: 27 pages (main text: 13 pages, supplement: 14 pages), 9 figures (main text: 4 figures, supplement: 5 figures)

Magnetic systems governed by exchange interactions between magnetic moments harbor frustration that leads to ground state degeneracy and results in the new topological state often referred to as a frustrated state of matter (FSM). The frustration in the commonly discussed magnetic systems has a spatial origin. Here we demonstrate that an array of nanomagnets coupled by the real retarded exchange interactions develops a new state of matter, time frustrated matter (TFM). In a spin system with the time-dependent retarded exchange interaction, a single spin-flip influences other spins not instantly but after some delay. This implies that the sign of the exchange interaction changes, leading to either ferro- or antiferromagnetic interaction, depends on time. As a result, the system's temporal evolution is essentially non-Markovian. The emerging competition between different magnetic orders leads to a new kind of time-core frustration. To establish this paradigmatic shift, we focus on the exemplary system, a granular multiferroic, where the exchange transferring medium has a pronounced frequency dispersion and hence develops the TFM.

Room temperature superconductivity under normal conditions has been a major challenge of physics and material science since its very discovery. Here we report the global room-temperature superconductivity observed in cleaved highly oriented pyrolytic graphite carrying dense arrays of nearly parallel surface line defects. The multiterminal measurements performed at the ambient pressure in the temperature interval 4.5 K < T < 300 K and at magnetic fields 0 < B < 9 T applied perpendicular to the basal graphitic planes reveal that the superconducting critical current I_c(T,B) is governed by the normal state resistance RN(T, B) so that I_c(T,B) is proportional to 1/R_N(T, B). Magnetization M(T, B) measurements of superconducting screening and hysteresis loops together with the critical current oscillations with temperature that are characteristic for superconductor-ferromagnet-superconductor Josephson chains, provide strong support for occurrence of superconductivity at T > 300 K. We develop a theory of global superconductivity emerging in the array of linear structural defects which well describes the experimental findings and demonstrate that global superconductivity arises as a global phase coherence of superconducting granules in linear defects promoted by the stabilizing effect of underlying Bernal graphite via tunneling coupling to the three dimensional (3D) material., Comment: Published version

Superinsulators offer a unique laboratory realizing strong interaction phenomena like confinement and asymptotic freedom in quantum materials. Recent experiments evidenced that superinsulators are the mirror-twins of superconductors with reversed electric and magnetic field effects. Cooper pairs and Cooper holes in the superinsulator are confined into neutral electric pions by electric strings, with the Cooper pairs playing the role of quarks. Here we report the non-equilibrium relaxation of the electric pions in superinsulating films. We find that the time delay $t_{\mathrm{sh}}$ of the current passage in the superinsulator is related to the applied voltage $V$ via the power law, $t_{\mathrm{sh}}\propto (V-V_{\mathrm p})^{-\mu}$, where $V_{\mathrm p}$ is the effective threshold voltage. Two distinct critical exponents, $\mu=1/2$ and $\mu=3/4$, correspond to jumps from the electric Meissner state to the mixed state and to the superinsulating resistive state with broken charge confinement, respectively. The $\mu=1/2$ value establishes a direct experimental evidence for the electric strings' linear potential confining the charges of opposite signs in the electric Meissner state and effectively rules out disorder-induced localization as a mechanism for superinsulation. We further report the memory effects and their corresponding dynamic critical exponents arising upon the sudden reversal of the applied voltage. Our observations open routes for exploring fundamental strong interaction charge confinement via desktop experiments.

Planar superconductors, thin films with thickness comparable to the superconducting coherence length, differ crucially from their bulk counterparts. The Coulomb interaction is logarithmic up to distances exceeding typical sample sizes and the Anderson-Higgs mechanism is ineffective to screen the resulting infrared divergences of the resulting (2+1)-dimensional QED because the Pearl length is also typically larger than sample sizes. As a consequence, the system decomposes into superconducting droplets with the typical size of the coherence length. We show that the two possible phases of the system match the two known mechanisms by which (2+1)-dimensional QED cures its infrared divergences, either by generating a mixed topological Chern-Simons mass or by magnetic monopole instantons. The former is realized in superconductors, the latter governs mirror-dual superinsulators. Planar superconductors are thus described by a topological Chern-Simons gauge (TCSG) theory which replaces the Ginzburg-Landau model in two dimensions. In the TCSG model, the Higgs field is absent. Accordingly, in planar superconductors Abrikosov vortices do not form, and only Josephson vortices with no normal core can emerge.

Discovery of topological polarization textures has put ferroelectrics at the frontier of topological matter science. High-symmetry ferroelectric oxide materials allowing for freedom of the polarization vector rotation offer a fertile ground for emergent topological polar formations, like vortices, skyrmions, merons, and Hopfions. It has been commonly accepted that uniaxial ferroelectrics do not belong in the topological universe because strong anisotropy imposes insurmountable energy barriers for topological excitations. Here we show that uniaxial ferroelectrics provide unique opportunity for the formation of topological polarization networks comprising branching intertwined domains with opposite counterflowing polarization. We report that they host the topological state of matter: a crisscrossing structure of topologically protected colliding head-to-head and tail-to-tail polarization domains, which for decades has been considered impossible from the electrostatic viewpoint. The domain wall interfacing the counterflowing domains is a multiconnected surface, propagating through the whole volume of the ferroelectric.

Quantum key distribution (QKD) is a cornerstone of the secure quantum encryption. Building on the quantum irreversibility, we develop a technique reborning the existing QKDs into protocols that are unrestricted in distance and have unprecedented high rates enhanced up to the standard protocols communication speeds. The core of our method is the continuous end-to-end physical control of information leaks in the quantum channel. Contrary to the existing long-distance QKD offerings, our technique does not require any trust nodes.

Integrating ferroelectric negative capacitance (NC) into the field-effect transistor (FET) promises to break fundamental limits of power dissipation known as Boltzmann tyranny. However, realizing the stable static negative capacitance in the non-transient non-hysteretic regime remains a daunting task. The problem stems from the lack of understanding of how the fundamental origin of the NC due to the emergence of the domain state can be put in use for implementing the NC FET. Here we put forth an ingenious design for the ferroelectric domain-based field-effect transistor with the stable reversible static negative capacitance. Using dielectric coating of the ferroelectric capacitor enables the tunability of the negative capacitance improving tremendously the performance of the field-effect transistors.

Existing quantum cryptography is resistant against secrecy-breaking quantum computers but suffers fast decay of the signal at long distances. The various types of repeaters of propagating quantum states have been developed to meet the challenge, but the problem is far from being solved. We step in the breach and put forth long-distance high secrecy optical cryptography, creating the fast quantum key distribution over distances up to 40,000 kilometers. The key element of the proposed protocol is the physical control over the transmission line.

The ubiquitous presence of shot noise sets a fundamental limit to the measurement precision in classical metrology. Recent advances in quantum devices and novel quantum algorithms utilizing interference effects are opening new routes for overcoming the detrimental noise tyranny. However, further progress is limited by the restricted capability of existing algorithms to account for the decoherence pervading experimental implementations. Here, adopting a systematic approach to the evaluation of effectiveness of metrological procedures, we devise the Linear Ascending Metrological Algorithm (LAMA), which offers a remarkable increase in precision in the demanding situation where a decohering quantum system is used to measure a continuously distributed variable. We introduce our protocol in the context of magnetic field measurements, assuming superconducting transmon devices as sensors operated in a qudit mode. Our findings demonstrate a quantum-metrological procedure capable of mitigating detrimental dephasing and relaxation effects., Comment: 12 pages, 7 figures

The mechanism responsible for spatially localized, strong coupling electron pairing characteristic of high-temperature superconductors (HTS) remains elusive and is a subject of hot debate. Here we propose a new HTS pairing mechanism which is the binding of two electrons residing in adjacent conducting planes of layered HTS materials by effective magnetic monopoles forming between these planes. The pairs localized near the monopoles form real-space seeds for superconducting droplets and strong coupling is due to the topological Dirac quantization condition. The pairing occurs well above the superconducting transition temperature Tc. Localized electron pairing around effective monopoles promotes, upon cooling, the formation of superconducting droplets connected by Josephson links. Global superconductivity arises when strongly coupled granules form an infinite cluster, and global superconducting phase coherence sets in. The resulting Tc is estimated to fall in the range from hundred to thousand Kelvins. Our findings pave the way for tailoring materials with elevated superconducting transition temperatures.

We provide a microscopic-level derivation of earlier results showing that, in the critical vicinity of the superconductor-to-insulator transition (SIT), disorder and localization become negligible and the structure of the emergent phases is determined by topological effects arising from the competition between two quantum orders, superconductivity and superinsulation. We find that, around the critical point, the ground state is a composite incompressible quantum fluid of Cooper pairs and vortices coexisting with an intertwined Wigner crystal for the excess (with respect to integer filling) excitations of the two types., Comment: Published version

Anderson's orthogonality catastrophe (AOC) theorem establishes that the ground state of the many-body fermion system is asymptotically orthogonal to the ground state of the same system perturbed by a scattering potential, so that the overlap between the original and new ground states decays to zero with the system size. We adopt the AOC for a description of heat production in a complementary metal-oxide-semiconductor (CMOS) transistor. We find that the heat released in the transistor comprises two distinct components, contribution from the dissipation accompanying electron transmission under the applied voltage and purely quantum-mechanical AOC part due to the change in scattering matrix for electrons upon switching between high and low conductance regimes. We calculate the AOC-induced heat production, which we call switching heat., Comment: 9 pages, 5 figures

The key to unraveling the nature of high-temperature superconductivity (HTS) lies in resolving the enigma of the pseudogap state. The pseudogap state in the underdoped region is a distinct thermodynamic phase characterized by nematicity, temperature-quadratic resistive behavior, and magnetoelectric effects. Till present, a general description of the observed universal features of the pseudogap phase and their connection with HTS was lacking. The proposed work constructs a unifying effective field theory capturing all universal characteristics of HTS materials and explaining the observed phase diagram. The pseudogap state is established to be a phase where a charged magnetic monopole condensate confines Cooper pairs to form an oblique version of a superinsulator. The HTS phase diagram is dominated by a tricritical point (TCP) at which the first order transition between a fundamental Cooper pair condensate and a charged magnetic monopole condensate merges with the continuous superconductor-normal metal and superconductor-pseudogap state phase transitions. The universality of the HTS phase diagram reflects a unique topological mechanism of competition between the magnetic monopole condensate, inherent to antiferromagnetic-order-induced Mott insulators and the Cooper pair condensate. The obtained results establish the topological nature of the HTS and provide a platform for devising materials with the enhanced superconducting transition temperature.

Despite decades-long efforts, magnetic monopoles were never found as elementary particles. Monopoles and associated currents were directly measured in experiments and identified as topological quasiparticle excitations in emergent condensed matter systems. These monopoles and the related electric-magnetic symmetry were restricted to classical electrodynamics, with monopoles behaving as classical particles. Here we show that the electric-magnetic symmetry is most fundamental and extends to full quantum behavior. We demonstrate that at low temperatures magnetic monopoles can form a quantum Bose condensate dual to the charge Cooper pair condensate in superconductors. The monopole Bose condensate manifests as a superinsulating state with infinite resistance, dual to superconductivity. Monopole supercurrents result in the electric analog of the Meissner effect and lead to linear confinement of Cooper pairs by Polyakov electric strings in analogy to quarks in hadrons., Comment: 6 pages, 2 figures

Electric-magnetic duality or S-duality, extending the symmetry of Maxwell's equations by including the symmetry between Noether electric charges and topological magnetic monopoles, is one of the most fundamental concepts of modern physics. In two-dimensional systems harboring Cooper pairs, S-duality manifests in the emergence of superinsulation, a state dual to superconductivity, which exhibits an infinite resistance at finite temperatures. The mechanism behind this infinite resistance is the linear charge confinement by a magnetic monopole plasma. This plasma constricts electric field lines connecting the charge-anti-charge pairs into electric strings, in analogy to quarks within hadrons. Yet the origin of the monopole plasma remains an open question. Here we consider a two-dimensional Josephson junction array (JJA) and reveal that the magnetic monopole plasma arises as quantum instantons, thus establishing the underlying mechanism of superinsulation as two-dimensional quantum tunneling events. We calculate the string tension and the dimension of an electric pion determining the minimal size of a system capable of hosting superinsulation. Our findings pave the way for study of fundamental S-duality in desktop experiments on JJA and superconducting films., Comment: 10 pages, 1 figure

Thermoelectric effect generating electricity from thermal gradient and vice versa appears in numerous generic applications. Recently, an original prospect of thermoelectricity arising from the nonlocal Cooper pair splitting (CPS) and the elastic co-tunneling (EC) in hybrid normal metal-superconductor-normal metal (NSN) structures was foreseen. Here we demonstrate experimentally the existence of non-local Seebeck effect in a graphene-based CPS device comprising two quantum dots connected to an aluminum superconductor and theoretically validate the observations. This non-local Seebeck effect offers an efficient tool for producing entangled electrons., Comment: 27 pages (main text: 6 pages; supplement: 21 pages), 15 figures (main text: 4 figures; supplement: 11 figures)

We show that the change of the fluctuation spectrum near the quantum critical point (QCP) may result in the continuous change of critical exponents with temperature due to the increase in the effective dimensionality upon approach to QCP. The latter reflects the crossover from thermal fluctuations white noise mode to the quantum fluctuations regime. We investigate the critical dynamics of an exemplary system obeying the Bose-Einstein employing the Keldysh-Schwinger approach and develop the renormalization group technique that enables us to obtain analytical expressions for temperature dependencies of critical exponents.

State-of-the-art noisy intermediate-scale quantum devices (NISQ), although imperfect, enable computational tasks that are manifestly beyond the capabilities of modern classical supercomputers. However, present quantum computations are restricted to exploring specific simplified protocols, whereas the implementation of full-scale quantum algorithms aimed at solving concrete large scale problems arising in data analysis and numerical modelling remains a challenge. Here we introduce and implement a hybrid quantum algorithm for solving linear systems of equations with exponential speedup, utilizing quantum phase estimation, one of the exemplary core protocols for quantum computing. We introduce theoretically classes of linear systems that are suitable for current generation quantum machines and solve experimentally a $2^{17}$-dimensional problem on superconducting IBMQ devices, a record for linear system solution on quantum computers. The considered large-scale algorithm shows superiority over conventional solutions, demonstrates advantages of quantum data processing via phase estimation and holds high promise for meeting practically relevant challenges., Comment: 8 pages, 6 figures

Chirality, an intrinsic handedness, is one of the most intriguing fundamental phenomena in nature. Materials composed of chiral molecules find broad applications in areas ranging from nonlinear optics and spintronics to biology and pharmaceuticals. However, chirality is usually an invariable inherent property of a given material that cannot be easily changed at will. Here, we demonstrate that ferroelectric nanodots support skyrmions the chirality of which can be controlled and switched. We devise protocols for realizing control and efficient manipulations of the different types of skyrmions. Our findings open the route for controlled chirality with potential applications in ferroelectric-based information technologies.

For decades, researchers have sought to understand how the irreversibility of the surrounding world emerges from the seemingly time symmetric, fundamental laws of physics. Quantum mechanics conjectured a clue that final irreversibility is set by the measurement procedure and that the time reversal requires complex conjugation of the wave function, which is overly complex to spontaneously appear in nature. Building on this Landau-Wigner conjecture, it became possible to demonstrate that time reversal is exponentially improbable in a virgin nature and to design an algorithm artificially reversing a time arrow for a given quantum state on the IBM quantum computer. However, the implemented arrow-of-time reversal embraced only the known states initially disentangled from the thermodynamic reservoir. Here we develop a procedure for reversing the temporal evolution of an arbitrary unknown quantum state. This opens the route for general universal algorithms sending temporal evolution of an arbitrary system backwards in time., Comment: 5 pages

Non-reciprocity of signal transmission enhances capacity of communication channels and protects transmission quality against possible signal instabilities, thus becoming an important component ensuring coherent information processing. However, non-reciprocal transmission requires breaking time-reversal symmetry (TRS) which poses challenges of both practical and fundamental character hindering the progress. Here we report a new scheme for achieving broadband non-reciprocity using a specially engineered hybrid microwave cavity. The TRS breaking is realized via strong coherent coupling between a selected chiral mode in the microwave cavity and a single collective spin excitation (magnon) in a ferromagnetic yttrium iron garnet (YIG) sphere. The non-reciprocity in transmission is observed spanning nearly a 0.5 GHz frequency band, which outperforms by two orders of magnitude the previously achieved bandwidths. Our findings open new directions for robust coherent information processing in a broad range of systems in both classical and quantum regimes., Comment: 11 pages, 7 figures

The suppression of superconductivity in disordered systems is a fundamental problem of condensed matter physics. Here we investigate the superconducting niobium-titanium-nitride (Nb_{1-x}Ti_{x}N) thin films grown by atomic layer deposition (ALD) where disorder is controlled by the slight tuning of the ALD process parameters. We observe the smooth crossover from the disorder-driven superconductor-normal metal transition (often reffered to as fermionic mechanism) to the case where bosonic mechanism dominates and increasing disorder leads to formation of metal with Cooper pairing. We show that, in moderately disordered films, the transition to zero-resistance state occurs in a full agreement with the conventional theories of superconducting fluctuations and Berezinskii-Kosterlitz-Thouless transition. However, the critically disordered films violate this accord showing low-temperature features possibly indicating the Bose metal phase. We show that it is the interrelation between film's sheet resistance in the maximum, R_{max}, of the resistive curve R(T) and R_q = h/4e^2 that distinguishes between these two behaviors. We reveal the characteristic features in magnetoresistance of the critically disordered films with R_{max} > R_q, Comment: 8 pages, 3 figures

Paradigmatic knotted solitons, Hopfions, that are characterized by topological Hopf invariant, are widely investigated in the diverse areas ranging from high energy physics, cosmology and astrophysics to biology, magneto- and hydrodynamics and condensed matter physics. Yet, while holding high promise for applications, they remain elusive and under-explored. Here we demonstrate that Hopfions emerge as a basic configuration of polarization field in confined ferroelectric nanoparticles. Our findings establish that Hopfions govern a wealth of novel functionalities in the electromagnetic response of composite nanomaterials opening route to unprecedented technological applications.

The nature of hadrons is one of the most fundamental mysteries of physics. It is generally agreed that they are made of "colored" quarks, which move nearly free at short scales but are confined inside hadrons by strong interactions at large distances. Because of confinement, quarks are never directly observable and, experimentally, their properties can be tested only indirectly, via high energy collisions. Here we show that superinsulating films realize a complete, one-color model system of hadron physics with Cooper pairs playing the role of quarks. We report measurements on highly controlled NbTiN films that provide a window into the interior of "Cooper pair mesons" and present the first direct evidence of asymptotic freedom, `t Hooft's dual superconductivity confinement mechanism, and magnetic monopoles.

A low-temperature intervening metallic regime arising in the two-dimensional superconductor-insulator transition challenges our understanding of electronic fluids. Here we develop a gauge theory revealing that this emergent anomalous metal is a bosonic topological insulator where bulk transport is suppressed by mutual statistics interactions between out-of-condensate Cooper pairs and vortices and the longitudinal conductivity is mediated by symmetry-protected gapless edge modes. We explore the magnetic-field-driven superconductor-insulator transition in a niobium titanium nitride device and find marked signatures of a bosonic topological insulator behavior of the intervening regime with the saturating resistance. The observed superconductor-anomalous metal and insulator-anomalous metal dual phase transitions exhibit quantum Berezinskii-Kosterlitz-Thouless criticality in accord with the gauge theory., Comment: 10 pages, 5 figures

We realize Landau-Streater (LS) and Werner-Holevo (WH) quantum channels for qutrits on the IBM quantum computers. These channels correspond to interaction between the qutrit and its environment that result in the globally unitarily covariant qutrit transformation violating multiplicativity of the maximal $p$-norm. Our realization of LS and WH channels is based on embedding qutrit states into states of two qubits and using single-qubit and two-qubit CNOT gates to implement the specific interaction. We employ the standard quantum gates hence the developed algorithm suits any quantum computer. We run our algorithm on a 5-qubit and a 20-qubit computer as well as on a simulator. We quantify the quality of the implemented channels comparing their action on different input states with theoretical predictions. The overall efficiency is quantified by fidelity between the theoretical and experimental Choi states implemented on the 20-qubit computer.

The pressing quest for overcoming Boltzmann tyranny in low-power nanoscale electronics revived the thoughts of engineers of early 1930-s on the possibility of negative circuit constants. The concept of the ferroelectric-based negative capacitance (NC) devices triggered explosive activity in the field. However, most of the research addressed transient NC, leaving the basic question of the existence of the steady-state NC unresolved. Here we demonstrate that the ferroelectric nanodot capacitor hosts a stable two-domain state realizing the static reversible NC device thus opening routes for the extensive use of the NC in domain wall-based nanoelectronics.

A quantum Maxwell demon is a device that can lower the entropy of a quantum system by providing it with purity. The functionality of such a quantum demon is rooted in a quantum mechanical SWAP operation exchanging mixed and pure states. We describe the setup and performance of a quantum Maxwell demon that purifies an energy-isolated system from a distance. Our cQED-based design involves two transmon qubits, where the mixed-state target qubit is purified by a pure-state demon qubit connected via an off-resonant transmission line; this configuration naturally generates an iSWAP gate. Although less powerful than a full SWAP gate, we show that assuming present-day performance characteristics of a cQED implementation, such an extended quantum Maxwell demon can purify the target qubit over macroscopic distances on the order of meters and tolerates elevated temperatures of the order of a few Kelvin in the transmission line., Comment: 10 pages, 4 figures

Unitary Fourier transform lies at the core of the multitudinous computational and metrological algorithms. Here we show experimentally how the unitary Fourier transform-based phase estimation protocol, used namely in quantum metrology, can be translated into the classical linear optical framework. The developed setup made of beam splitters, mirrors and phase shifters demonstrates how the classical coherence, similarly to the quantum coherence, poses a resource for obtaining information about the measurable physical quantities. Our study opens route to the reliable implementation of the small-scale unitary algorithms on path-encoded qudits, thus establishing an easily accessible platform for unitary computation., Comment: 17 pages (main text: 9 pages, supplement: 8 pages), 7 figures (main text: 5 figures, supplement: 2 figures)

We develop a theory of the reversible switching of the magnetic state of the ferromagnet-insulator-normal metalferromagnet (FINF) nanostructure. The switching is controlled by tuning the Coulomb blockade strength via the gate voltage on the normal metal granule. The proposed mechanism allows for realizing the switching without passing a dissipative current through the structure., Comment: 17 pages, 3 figures

The Second Law of Thermodynamics states that temporal evolution of an isolated system occurs with non-diminishing entropy. In quantum realm, this holds for energy-isolated systems the evolution of which is described by the so-called unital quantum channel. The entropy of a system evolving in a non-unital quantum channel can, in principle, decrease. We formulate a general criterion of unitality for the evolution of a quantum system, enabling a simple and rigorous approach for finding and identifying the processes accompanied by decreasing entropy in energy-isolated systems. We discuss two examples illustrating our findings, the quantum Maxwell demon and heating-cooling process within a two-qubit system., Comment: 7 pages, 2 figures, IV International Conference on Quantum Technologies

The classical Second Law of Thermodynamics demands that an isolated system evolves with a non-diminishing entropy. This holds as well in quantum mechanics if the evolution of the energy-isolated system can be described by a unital quantum channel. At the same time, the entropy of a system evolving via a non-unital channel can, in principle, decrease. Here, we analyze the behavior of the entropy in the context of the H-theorem. As exemplary phenomena, we discuss the action of a Maxwell demon (MD) operating a qubit and the processes of heating and cooling in a two-qubit system. We further discuss how small initial correlations between a quantum system and a reservoir affect the increase in the entropy under the evolution of the quantum system., Comment: 8 pages

Uncovering the origin of the arrow of time remains a fundamental scientific challenge. Within the framework of statistical physics, this problem was inextricably associated with the second law of thermodynamics, which declares that entropy growth proceeds from the system's entanglement with the environment. It remains to be seen, however, whether the irreversibility of time is a fundamental law of nature or whether, on the contrary, it might be circumvented. Here we show that, while in nature the complex conjugation needed for time reversal is exponentially improbable, one can design a quantum algorithm that includes complex conjugation and thus reverses a given quantum state. Using this algorithm on an IBM quantum computer enables us to experimentally demonstrate a backward time dynamics for an electron scattered on a two-level impurity., Comment: 14 pages, 3 figures

We develop a gauge theory of the critical behavior of the topological excitations-driven Berezinskii-Kosterlitz-Thouless (BKT) phase transition in the XY model with weak quenched disorder. We find that while in two-dimensions the liquid of topological defects exhibits the BKT critical behavior, the three-dimensional system shows more singular Vogel-Fulcher-Tamman criticality heralding its freezing into a spin glass. Our findings provide insights into the topological origin of spin glass formation., Comment: 7 figures

It has long been believed that, at absolute zero, electrons can form only one quantum coherent state, a superconductor. Yet, several two dimensional superconducting systems were found to harbor the superinsulating state with infinite resistance, a mirror image of superconductivity, and a metallic state often referred to as Bose metal, characterized by finite longitudinal and vanishing Hall resistances. The nature of these novel and mysterious quantum coherent states is the subject of intense study.Here, we propose a topological gauge description of the superconductor-insulator transition (SIT) that enables us to identify the underlying mechanism of superinsulation as Polyakov's linear confinement of Cooper pairs via instantons. We find a criterion defining conditions for either a direct SIT or for the SIT via the intermediate Bose metal and demonstrate that this Bose metal phase is a Mott topological insulator in which the Cooper pair-vortex liquid is frozen by Aharonov-Bohm interactions.

Although the overwhelming majority of natural processes occurs far from the equilibrium, general theoretical approaches to non-equilibrium phase transitions remain scarce. Recent breakthroughs introducing description of open dissipative systems in terms of non-Hermitian quantum mechanics allowed to identify a class of non-equilibrium phase transitions associated with the loss of combined parity (reflection) and time-reversal symmetries. Here we report that time evolution of a single classical spin (e.g. monodomain ferromagnet) governed by the Landau-Lifshitz-Gilbert-Slonczewski equation in absence of higher-order anisotropy terms is described by a M\"{o}bius transformation in complex stereographic coordinates. We identify the \textit{parity-time} symmetry-breaking phase transition occurring in spin-transfer torque-driven linear spin systems as a transition between hyperbolic and loxodromic classes of M\"{o}bius transformations, with the critical point of the transition corresponding to the parabolic transformation. This establishes the understanding of non-equilibrium phase transitions as topological transitions in configuration space., Comment: 4 pages, 2 figures

One of the most promising approaches of generating spin- and energy-entangled electron pairs is splitting a Cooper pair into the metal through spatially separated terminals. Utilizing hybrid systems with the energy-dependent barriers at the superconductor-normal metal interfaces, one can achieve practically 100% efficiency outcome of entangled electrons. We investigate minimalistic one-dimensional model comprising a superconductor and two metallic leads and derive an expression for an electron-to-hole transmission probability as a measure of splitting efficiency. We find the conditions for achieving 100% efficiency and present analytical results for the differential conductance and differential noise., Comment: 8 pages, 6 figures; minor corrections

Superconducting fluctuations have proved to be an irreplaceable source of information about microscopic and macroscopic material parameters that could be inferred from the experiment. According to common wisdom, the effect of thermodynamic fluctuations in the vicinity of the superconducting transition temperature, Tc, is to round off all of the sharp corners and discontinuities, which otherwise would have been expected to occur at Tc. Here we report the current spikes due to radiation-induced resonant tunneling of fluctuation Cooper pairs between two superconductors which grow even sharper and more pronounced upon approach to Tc. This striking effect offers an unprecedented tool for direct measurements of fluctuation Cooper pairs' lifetime, which is key to our understanding of the fluctuation regime. Our finding marks a radical departure from the conventional view of superconducting fluctuations as blurring and rounding phenomenon., Comment: 6 pages, 5 figures

We study electric properties of random resistor networks consisting of resistors of two kinds numerically, focusing on the power loss across each bond. Tuning the ratio of the resistances $r$ and their respective fraction $\alpha$ we find that at large $r$ the conductance of the network is dominated by a few optimal, percolation-like, conducting paths. We demonstrate that the distribution of the local power losses $P$ is exponential, $\propto\exp(-P/\langle P\rangle)$, and reveal the spatial distribution of hotspots concentrating the main part of the dissipated power., Comment: 7 pages, 7 figures

Remarkable progress of quantum information theory (QIT) allowed to formulate mathematical theorems for conditions that data-transmitting or data-processing occurs with a non-negative entropy gain. However, relation of these results formulated in terms of entropy gain in quantum channels to temporal evolution of real physical systems is not thoroughly understood. Here we build on the mathematical formalism provided by QIT to formulate the quantum H-theorem in terms of physical observables. We discuss the manifestation of the second law of thermodynamics in quantum physics and uncover special situations where the second law can be violated. We further demonstrate that the typical evolution of energy-isolated quantum systems occurs with non-diminishing entropy., Comment: 8 pages, 4 figures

We investigate the complex conductivity of a highly disordered MoC superconducting film with $k_Fl\approx 1$, where $k_F$ is the Fermi wavenumber and $l$ is the mean free path, derived from experimental transmission characteristics of coplanar waveguide resonators in a wide temperature range below the superconducting transition temperature $T_c$. We find that the original Mattis-Bardeen model with a finite quasiparticle lifetime, $\tau$, offers a perfect description of the experimentally observed complex conductivity. We show that $\tau$ is appreciably reduced by scattering effects. Characteristics of the scattering centers are independently found by the scanning tunneling spectroscopy and agree with those determined from the complex conductivity., Comment: 8 pages, 10 figures

We investigate temporal evolution of von Neumann's entropy in exemplary quantum mechanical systems and show that it grows in systems evolving with incrementally increasing decoherence during scattering processes. We demonstrate that the origin of irreversibility lies in complexity of preparing time-reversed quantum states due to entanglement and in partitioning of the wave function of the evolving system., Comment: 11 pages, 14 figures