By performing local projective measurements on a two-qubit entangled state one can certify in a device-independent way up to one bit of randomness. We show here that general measurements, defined by positive-operator-valued measures, can certify up to two bits of randomness, which is the optimal amount of randomness that can be certified from an entangled bit. General measurements thus provide an advantage over projective ones for device-independent randomness certification.
Quantum mechanical calculations of a modification of the X-ray scattering form factor of an atom/ion in an electric field using a three parameter wave function have been performed. These calculations are compared with the previous two parameter wave function calculations.
A short introduction is given about direct variational methods and their relation to Galerkin and moment methods, all flexible and powerful approaches for finding approximate solutions to difficult physicalequations. An application of these methods is given in the form of the variational problem of minimizing the discomfort experienced during different journeys, between two fixed horizontal points while keeping the travel time constant. The analysis is shown to provide simple, yet accurate, approximate solutions of the problem and illustrates the usefulness and the power of direct variational and moment methods. It also demonstrates the problem of a priori assessing the accuracy of the approximate solutions and illustrates that the variational solution does not necessarily provide a more accurate solution than that obtained by moment methods.
Direct variational methods are used to find simple approximate solutions of the Thomas–Fermi equations describing the properties of self-gravitating radially symmetric stellar objects both in the non-relativistic and ultra-relativistic cases. The approximate solutions are compared and shown to be in good agreement with exact and numerically obtained solutions.
Entanglement is one of the most studied properties of quantum mechanics for its application in quantum information protocols. Nevertheless, detecting the presence of entanglement in large multipartite sates keeps being a great challenge both from the theoretical and the experimental point of view. Most of the known methods either have computational costs that scale inefficiently with the number of parties or require more information on the state than what is attainable in every-day experiments. We introduce a new technique for entanglement detection that provides several important advantages in these respects. First, its scales efficiently with the number of parties, thus allowing for application to systems composed by up to few tens of parties. Second, it needs only the knowledge of a subset of all possible measurements on the state, therefore being apt for experimental implementation. Moreover, since it is based on the detection of nonlocality, our method is device-independent. We report several examples of its implementation for well-known multipartite states, showing that the introduced technique has a promising range of applications.
This paper is based on a curious observation about an equation related to the tracelessness constraints of higher spin gauge fields. A similar equation also occurs in the theory of continuous spin representations of the Poincaré group. Expressed in an oscillator basis for the higher spin fields, the equation becomes a non-linear partial differential operator of the Riccati type acting on the vertex functions. The consequences of the equation for the cubic vertex is investigated in the light-front formulation of higher spin theory. The vertex is fixed by the PDE up to a set of terms that can be considered as boundary data for the PDE. These terms can serve as off-shell quantum corrections. In order to set the present work in perspective, some comments and comparisons to recent research on higher spin interactions are made. A few particular cubic vertices are calculated explicitly and compared to similar results in the literature, in particular the interesting cases 2 ÿ 3 ÿ 3 and 3 ÿ 2 ÿ 2 involving spin 2 fields.
Some puzzling aspects of higher spin field theory in Minkowski space-time, such as the tracelessness constraints and the search for an underlying physical principle, are discussed. A connecting idea might be provided by the recently much researched continuous spin representations of the Poincaré group. The Wigner equations, treated as first class constraints, yields to a four-constraint BRST formulation. The resulting field theory, generalizing free higher spin field theory, is one among a set of higher spin theories that can be related to previous work on unconstrained formulations. In particular, it is conjectured that the unconstrained higher spin theory of Francia and Sagnotti is a limit of a continuous spin theory. Furthermore, a simple analysis of the constraint structure reveals a hint of a physical rationale behind the trace constraints.
In this paper we discuss gravity in the light-front formulation (light-cone gauge) and show how possible counterterms arise. We find that Poincaré invariance is not enough to find the three-point counterterms uniquely. Higher-spin fields can intrude and mimic three-point higher derivative gravity terms. To select the correct term we have to use the remaining reparametrization invariance that exists after the gauge choice. We finally sketch how the corresponding programme for N = 8 Supergravity should work.
Recent progress implies that a crossover between machine learning and quantum information processing benefits both fields. Traditional machine learning has dramatically improved the benchmarking and control of experimental quantum computing systems, including adaptive quantum phase estimation and designing quantum computing gates. On the other hand, quantum mechanics offers tantalizing prospects to enhance machine learning, ranging from reduced computational complexity to improved generalization performance. The most notable examples include quantum enhanced algorithms for principal component analysis, quantum support vector machines, and quantum Boltzmann machines. Progress has been rapid, fostered by demonstrations of midsized quantum optimizers which are predicted to soon outperform their classical counterparts. Further, we are witnessing the emergence of a physical theory pinpointing the fundamental and natural limitations of learning. Here we survey the cutting edge of this merger and list several open problems.
This thesis report deals with the 1D Hubbard model and the quantum objects that diagonalize the normal ordered Hubbard hamiltonian, among those the so called PseudoFermions (PFs). These PFs have no residual energy interactions, are eta-spin and spin zero objects, and are the scatterers and the scattering centers of the theory. The S-matrix of this representation is a simple phase factor, involving the phase shifts of the zero energy forward momentum scattering events.
A PF dynamical theory is developed and applied to the one-electron removal and lower Hubbard band addition cases. For any value of the on-site effective Coloumb repulsion and electronic density, and in the limit of zero magnetization, we derive closed form expressions for these spectral functions, showing the emergence of the power-law type behavior of correlation functions of Luttinger liquids. However, our expressions are valid for the entire elementary excitation energy bandwidth.
The singular behavior of the theoretical spectral weight leads to a spectral weight distribution detectable by photo emission and photo absorption experiments. As an important contribution to the understanding of quasi 1D materials, we are able to reproduce for the whole energy bandwidth, the experimental spectral distributions recently found for the organic compound TTF-TCNQ. This confirms the validity of the PF dynamical theory, and provides a deeper understanding of low dimensional correlated systems.
A dynamical theory which accounts for all microscopic one-electron processes is used to study the spectral function of the 1D Hubbard model for the whole (k,ω)-plane, beyond previous studies which focused on the weight distribution in the vicinity of the singular branch lines only. While our predictions agree with those of the latter studies concerning the tetracyanoquinodimethane (TCNQ) related singular features in photoemission of the organic compound tetrathiafulvalene–tetracyanoquinodimethane (TTF–TCNQ) metallic phase, the generalized theory also leads to quantitative agreement concerning the tetrathiafulvalene (TTF) related finite-energy spectral features, which are found to correspond to a value of the on-site repulsion U larger than for TCNQ. Our study reveals the microscopic mechanisms behind the unusual spectral features of TTF–TCNQ and provides a good overall description of those features for the whole (k,ω)-plane.
Monte Carlo and molecular dynamics simulations were performed to calculate solubility, S, and diffusion, D, coefficients of oxygen and water in polyethylene, and to obtain a molecular-level understanding of the diffusion mechanism. The permeation coefficient, P, was calculated from the product of S and D. The AMBER force field, which yields the correct polymer densities under the conditions studied, was used for the simulations, and it was observed that the results were not sensitive to the inclusion of atomic charges in the force field. The simulated S for oxygen and water are higher and lower than experimental data, respectively. The calculated diffusion coefficients are in good agreement with experimental data. Possible reasons for the discrepancy in the simulated and experimental solubilities, which results in discrepancies in the permeation coefficients, are discussed. The diffusion of both penetrants occurs mainly by large amplitude, infrequent jumps of the molecules through the polymer matrix.
In classical hydrodynamics with uniform density, vortices move with the local fluid velocity. This description is rewritten in terms of forces arising from the interaction with other vortices. Two such positive straight vortices experience a repulsive interaction and precess in a positive (anticlockwise) sense around their common centroid. A similar picture applies to vortices in a two-component two-dimensional uniform Bose-Einstein condensate (BEC) coherently coupled through rf Rabi fields. Unlike the classical case, however, the rf Rabi coupling induces an attractive interaction and two such vortices with positive signs now rotate in the negative (clockwise) sense. Pairs of counter-rotating vortices are instead found to translate with uniform velocity perpendicular to the line joining their cores. This picture is extended to a single vortex in a two-component trapped BEC. Although two uniform vortex-free components experience familiar Rabi oscillations of particle-number difference, such behavior is absent for a vortex in one component because of the nonuniform vortex phase. Instead the coherent Rabi coupling induces a periodic vorticity transfer between the two components.
The dynamical correlation functions in one-dimensional electronic systems show power-law behaviour at low energies and momenta close to integer multiples of the charge and spin Fermi momenta. These systems are usually referred to as Tomonaga–Luttinger liquids. However, near well defined lines of the (k,ω) plane the power-law behaviour extends beyond the low-energy cases mentioned above, and also appears at higher energies, leading to singular features in the photoemission spectra and other dynamical correlation functions. The general spectral-function expressions derived in this paper were used in recent theoretical studies of the finite-energy singular features in photoemission of the organic compound tetrathiafulvalene–tetracyanoquinodimethane (TTF-TCNQ) metallic phase. They are based on a so-called pseudofermion dynamical theory (PDT), which allows us to systematically enumerate and describe the excitations in the Hubbard model starting from the Bethe ansatz, as well as to calculate the charge and spin object phase shifts appearing as exponents of the power laws. In particular, we concentrate on the spin-density limit and on effects in the vicinity of the singular border lines, as well as close to half filling. Our studies take into account spectral contributions from types of microscopic processes that do not occur for finite values of the spin density. In addition, the specific processes involved in the spectral features of TTF-TCNQ are studied. Our results are useful for the further understanding of the unusual spectral properties observed in low-dimensional organic metals and also provide expressions for the one- and two-atom spectral functions of a correlated quantum system of ultracold fermionic atoms in a 1D optical lattice with on-site two-atom repulsion.
We derive general closed-form analytical expressions for the finite-energy one- and two-electron spectral-weight distributions of an one-dimensional correlated metal with on-site electronic repulsion. Our results also provide general expressions for the one- and two-atom spectral functions of a correlated quantum system of cold fermionic atoms in a one-dimensional optical lattice with onsite atomic repulsion. In the limit of zero spin density our spectral-function expressions provide the correct zero-spin density results. Our results reveal the dominant non-perturbative microscopic many-particle mechanisms behind the exotic spectral properties observed in quasi-one-dimensional metals and correlated systems of cold fermionic atoms in one-dimensional optical lattices. (c) 2005 Elsevier B.V. All rights reserved.
We review developments concerning the effect of correlations on the electronic properties of one-dimensional systems, focusing our analysis on the one-dimensional Hubbard model. We consider methods used to describe the exotic properties of these systems, ranging from bosonization associated with the Tomonaga and Luttinger liquid behavior, to the Bethe ansatz solution, referring to all energy scales of solvable quantum problems and the pseudoparticle description. We use that description to study the model energy spectrum and the low-energy quantities. In the ensuing companion chapter we discuss the relation of the electronic operators to these quantum objects.
This chapter follows its companion, chapter 1. Here we review different methods based on the Bethe ansatz solution of the one-dimensional Hubbard model, in order to study quantities related to charge transport and the momentum dependent conductivity. Moreover, we report recent developments on finite-energy dynamical properties. This is achieved by introducing new entities called pseudofermions which are basically free, in the sense that their energies are additive, and where the effect of the interactions appears through phase shifts that are absorbed by their discrete momentum values. The resulting pseudofermion dynamical theory enables the evaluation of matrix elements between energy eigen-states and hence the derivation of finite energy expressions for the one- and two-electron correlation and spectral functions. Comparison with experimental results is also discussed.
Machine learning algorithms utilizing gradient descent to identify concepts or more general learnables hint at a so-far ignored possibility, namely that local and global minima represent any vocabulary as a landscape against which evaluation of the results can take place. A simple example to illustrate this idea would be a potential surface underlying gravitation. However, to construct a gravitation-based representation of, e.g., word meaning, only the distance between localized items is a given in the vector space, whereas the equivalents of mass or charge are unknown in semantics. Clearly, the working hypothesis that physical fields could be a useful metaphor to study word and sentence meaning is an option but our current representations are incomplete in this respect.For a starter, consider that an RBF kernel has the capacity to generate a potential surface and hence create the impression of gravity, providing one with distance-based decay of interaction strength, plus a scalar scaling factor for the interaction, but of course no term masses. We are working on an experiment design to change that. Therefore, with certain mechanisms in neural networks that could host such quasi-physical fields, a novel approach to the modeling of mind content seems plausible, subject to scrutiny.Work in progress in another direction of the same idea indicates that by using certain algorithms, already emerged vs. still emerging content is clearly distinguishable, in line with Aristotle’s Metaphysics. The implications are that a model completed by “term mass” or “term charge” would enable the computation of the specific work equivalent of sentences or documents, and that via replacing semantics by other modalities, vector fields of more general symbolic content could exist as well. Also, the perceived hypersurface generated by the dynamics of language use may be a step toward more advanced models, for example addressing the Hamiltonian of expanding semantic systems, or the relationship between reaction paths in quantum chemistry vs. sentence construction by gradient descent.
Solutions of the nonlinear Schrodinger equation for initial conditions in the form of two separated sech-shaped in-phase pulsed,; are analyzed. It is found that; this initial condition, with appropriate amplitude, may give rise to, not; only stationary solitons, but also to symmetrically separating solitons, if the initial distance of separation is large enough. The condition for the generation of a separating soliton pair is derived from the Zakharov-Shabat eigenvalue problem using a variational approach.
The significant potential for so-called “smart textiles” in the design of the next generation of devices that measure pressure, tension, moisture, and heat at the humanehorse interface is discussed in this article. Research techniques from theoretical and experimental physics laboratories, combined with wireless technology, can be readily adapted to measure and store metrics for numerous variables in equine structure and function. Activities, such as breathing, the extension and flexion of joints, limb kinematics, and cardiac function, can be logged as indicators of physiological and behavioral conditioning (training). Such metrics may also, one day, support veterinary diagnostics but also play a role in safeguarding sporthorse welfare, especially in elite contexts where the horse may be pushed to its functional limits. As such, they are likely to emerge as an area of great interest to equitation and welfare scientists. It is important to note that smart textiles sense and react to exogenous stimuli via integrated sensors. So, beyond the equitation science laboratory, the emergence of polymers and smart materials may enhance the effectiveness of, or challenge us to completely rethink, traditional items of saddlery, thus improving equitation. The integration of smart textiles in all sorts of extant and emergent equipment for everyday equestrians could, in the future, lead to equipment that responds appropriately to the demands of equitation in its various forms. Rethinking equitation through physics and the use of smart textiles seems to have merit in that it is a novel means of both investigating and addressing problems that compromise the welfare and performance of horses. The purpose of this article is to envision the use of smart textiles in research, clinical, equestrian, and horse care contexts.
In supervised learning, an inductive learning algorithm extracts general rules from observed training instances, then the rules are applied to test instances. We show that this splitting of training and application arises naturally, in the classical setting, from a simple independence requirement with a physical interpretation of being non-signalling. Thus, two seemingly different definitions of inductive learning happen to coincide. This follows from very specific properties of classical information, which break down in the quantum setup. We prove a quantum de Finetti theorem for quantum channels, which shows that in the quantum case, the equivalence holds in the asymptotic setting (for large number of test instances). This reveals a natural analogy between classical learning protocols and their quantum counterparts, thus allowing to naturally enquire about standard elements in computational learning theory, such as structural risk minimization, model and sample complexity.
Standard projective measurements represent a subset of all possible measurements in quantum physics. In fact, non-projective measurements are relevant for many applications, e.g. for estimation problems or transformations among entangled states. In this work we study what quantum measurements can be simulated by using only projective measurements and classical randomness. We first prove that every measurement on a given quantum system can be realised by a projective-simulable measurement on a system enlarged by an ancilla of the same dimension. Then, given a general measurement in dimension two or three, we show that deciding whether it is projective-simulable can be solved by means of semi-definite programming. We also establish conditions for the simulation of measurements using projective ones valid for any dimension. As an application of our formalism, we improve the range of visibilities for which two-qubit Werner states do not violate any Bell inequality for all measurements. From an implementation point of view, our results provide bounds on the amount of noise a general measurement tolerates before losing any advantage over projective ones.
We develop a reinforcement-learning algorithm to construct a feedback policy that delivers quantum-enhanced interferometric-phase estimation up to 100 photons in a noisy environment. We ensure scalability of the calculations by distributing the workload in a cluster and by vectorizing time-critical operations. We also improve running time by introducing accept-reject criteria to terminate calculation when a successful result is reached. Furthermore, we make the learning algorithm robust to noise by fine-tuning how the objective function is evaluated. The results show the importance and relevance of well-designed classical machine learning algorithms in quantum physics problems.
Quantum-enhanced metrology aims to estimate an unknown parameter such that the precision scales better than the shot-noise bound. Single-shot adaptive quantum-enhanced metrology (AQEM) is a promising approach that uses feedback to tweak the quantum process according to previous measurement outcomes. Techniques and formalism for the adaptive case are quite different from the usual non-adaptive quantum metrology approach due to the causal relationship between measurements and outcomes. We construct a formal framework for AQEM by modeling the procedure as a decision-making process, and we derive the imprecision and the Cram´er- Rao lower bound with explicit dependence on the feedback policy. We also explain the reinforcement learning approach for generating quantum control policies, which is adopted due to the optimal policy being non-trivial to devise. Applying a learning algorithm based on differential evolution enables us to attain imprecision for adaptive interferometric phase estimation, which turns out to be SQL when non-entangled particles are used in the scheme.
Quantum control is valuable for various quantum technologies such as high-fidelity gates for universal quantum computing, adaptive quantum-enhanced metrology, and ultra-cold atom manipulation. Although supervised machine learning and reinforcement learning are widely used for optimizing control parameters in classical systems, quantum control for parameter optimization is mainly pursued via gradient-based greedy algorithms. Although the quantum fitness landscape is often compatible for greedy algorithms, sometimes greedy algorithms yield poor results, especially for large-dimensional quantum systems. We employ differential evolution algorithms to circumvent the stagnation problem of non-convex optimization, and we average over the objective function to improve quantum control fidelity for noisy systems. To reduce computational cost, we introduce heuristics for early termination of runs and for adaptive selection of search subspaces. Our implementation is massively parallel and vectorized to reduce run time even further. We demonstrate our methods with two examples, namely quantum phase estimation and quantum gate design, for which we achieve superior fidelity and scalability than obtained using greedy algorithms.
We discuss the magnetic phases of the Hubbard model for the honeycomb lattice both in two and three spatial dimensions. A ground state phase diagram is obtained depending on the interaction strength U and electronic density n. We find a first order phase transition between ferromagnetic regions where the spin is maximally polarized (Nagaoka ferromagnetism) and regions with smaller magnetization (weak ferromagnetism). When taking into account the possibility of spiral states, we find that the lowest critical U is obtained for an ordering momentum different from zero. The evolution of the ordering momentum with doping is discussed. The magnetic excitations (spin waves) in the antiferromagnetic insulating phase are calculated from the random-phase approximation for the spin susceptibility. We also compute the spin fluctuation correction to the mean field magnetization by virtual emission/absorption of spin waves. In the large U limit, the renormalized magnetization agrees qualitatively with the Holstein-Primakoff theory of the Heisenberg antiferromagnet, although the latter approach produces a larger renormalization.
Bell inequalities have traditionally been used to demonstrate that quantum theory is nonlocal, in the sense that there exist correlations generated from composite quantum states that cannot be explained by means of local hidden variables. With the advent of device-independent quantum information processing, Bell inequalities have gained an additional role as certificates of relevant quantum properties. In this work we consider the problem of designing Bell inequalities that are tailored to detect the presence of maximally entangled states. We introduce a class of Bell inequalities valid for an arbitrary number of measurements and results, derive analytically their maximal violation and prove that it is attained by maximally entangled states. Our inequalities can therefore find an application in device-independent protocols requiring maximally entangled states.
We extended a parallel and distributed implementation of the Trotter-Suzuki algorithm for simulating quantum systems to study a wider range of physical problems and to make the library easier to use. The new release allows periodic boundary conditions, many-body simulations of non-interacting particles, arbitrary stationary potential functions, and imaginary time evolution to approximate the ground state energy. The new release is more resilient to the computational environment: a wider range of compiler chains and more platforms are supported. To ease development, we provide a more extensive command-line interface, an application programming interface, and wrappers from high-level languages.
Information representation is an important but neglected aspect of building text information retrieval models. In order to be efficient, the mathematical objects of a formal model, like vectors, have to reasonably reproduce language-related phenomena such as word meaning inherent in index terms. On the other hand, the classical vector space model, when it comes to the representation of word meaning, is approximative only, whereas it exactly localizes term, query and document content. It can be shown that by replacing vectors by continuous functions, information retrieval in Hilbert space yields comparable or better results. This is because according to the non-classical or continuous vector space model, content cannot be exactly localized. At the same time, the model relies on a richer representation of word meaning than the VSM can offer.
Markov logic networks (MLNs) reconcile two opposing schools in machine learning and artificial intelligence: causal networks, which account for uncertainty extremely well, and first-order logic, which allows for formal deduction. An MLN is essentially a first-order logic template to generate Markov networks. Inference in MLNs is probabilistic and it is often performed by approximate methods such as Markov chain Monte Carlo (MCMC) Gibbs sampling. An MLN has many regular, symmetric structures that can be exploited at both first-order level and in the generated Markov network. We analyze the graph structures that are produced by various lifting methods and investigate the extent to which quantum protocols can be used to speed up Gibbs sampling with state preparation and measurement schemes. We review different such approaches, discuss their advantages, theoretical limitations, and their appeal to implementations. We find that a straightforward application of a recent result yields exponential speedup compared to classical heuristics in approximate probabilistic inference, thereby demonstrating another example where advanced quantum resources can potentially prove useful in machine learning.
It is well known that the structure information through the use of Spin Polarised LowEnergy Electron Diffraction (SPLEED) is highly sensitive to the interaction potentialbetween the primary electrons and the electrons of the target, especially to the exchangeinteraction. Since the electrons in SPLEED penetrate the surface only a few latticespacing, it is extremely sensitive to the spin structure of a magnetic surface. The earlystudy of Feder [1] on Fe(110) provides a strong indication in this direction. The mainobjective of this work is to use the insights of our recent work [2,3] to study the spinpolarisation of the exchange-correlation potential. The differential cross sections for electronscattering from atoms with net spin, namely nickel and iron, have been calculated togetherwith studying the energy/wave vector dependence of the exchange scattering from surfacesof nickel and iron in glasses by calculating differential cross sections and the spin asymmetryusing Dirac equation. Comparison of predictions with observed spin dependent scattering intensities in amorphous magnetic alloys will give insight into surface magnetisation in these systems[4].