Quantum Space Research Articles

Discrete phase space and continuous time relativistic quantum mechanics II: Peano circles, hyper-tori phase cells, and fiber bundles

The discrete phase space and continuous time representation of relativistic quantum mechanics are further investigated here as a continuation of paper I.1 The main mathematical construct used here will be that of an area filling Peano curve. We show that the limit of a sequence of a class of Peano curves is a Peano circle denoted as [Formula: see text], a circle of radius [Formula: see text] where [Formula: see text]. We interpret this two-dimensional (2D) Peano circle in our framework as a phase cell inside our 2D discrete phase plane. We postulate that a first quantized Planck oscillator, being very light, and small beyond current experimental detection, occupies this phase cell [Formula: see text]. The time evolution of this Peano circle sweeps out a 2D vertical cylinder analogous to the worldsheet of string theory. Extending this to 3D space, we introduce a [Formula: see text]-dimensional phase space hyper-tori [Formula: see text] as the appropriate phase cell in the physical dimensional discrete phase space. A geometric interpretation of this structure in state space is given in terms of product fiber bundles. We also study free scalar Bosons in the background [Formula: see text]-dimensional discrete phase space and continuous time state space using the relativistic partial difference-differential Klein–Gordon equation. The second quantized field quanta of this system can cohabit with the tiny Planck oscillators inside the [Formula: see text] phase cells for eternity. Finally, a generalized free second quantized Klein–Gordon equation in a higher [Formula: see text]-dimensional discrete state space is explored. The resulting discrete phase space dimension is compared to the significant spatial dimensions of some of the popular models of string theory.

Construction of Space Quantum Information System Based on Satellite Recognition

Satellite identification is a form of space quantum information, which refers to the use of artificial earth satellites as the transmitting station between earth communication stations to perform satellite identification to construct a space quantum information system. However, at this stage, a single form of identification cannot meet the needs of various aspects such as the development of the information society. And mobile broadband services. Based on this, this paper has carried out research on the construction of space quantum information system based on satellite recognition. This paper firstly introduces the research significance of space quantum information transmission based on satellite identification, and then analyzes the research status of space information system based on satellite identification and the research status of space quantum information system based on satellite identification at home and abroad. Aiming at the problem of asymmetrical transmission of space information, this paper proposes, a spatial asymmetric transmission scheme based on layered modulation and network coding, and in view of the low communication quality caused by the influence of weather and surrounding environment on the space-based communication channel, this paper proposes an adaptive transmission scheme of spatial information based on satellite cooperation. The survey results show that under the MNC strategy and the traditional zero-padded strategy, the end-to-end bit error rate performance of S2 is not much different. As the signal-to-noise ratio continues to increase to 30dB, the two are basically the same. In the whole range of k value, the access probability of the MNC strategy is equal to a constant 0.67 and remains unchanged. When k=1, under the OUS scheme, it shows that the two source nodes have the same probability of accessing the channel, and the access probability is 50%, which is 16.7% lower than that of the MNC scheme.

Equally Spaced Quantum States in van der Waals Epitaxy-Grown Nanoislands.

Pursuing the confinement of linearly dispersive relativistic Fermions is of interest in both fundamental physics and potential applications. Here, we report strong STM evidence for the equally spaced, strikingly sharp, and densely distributed quantum well states (QWSs) near Fermi energy in Pb(111) nanoislands, van der Waals epitaxially grown on graphitized 6H-SiC(0001). The observations can be explained as the quantized energies of confined linearly dispersive [111] electrons, which essentially "simulate" the out-of-plane relativistic quasiparticles. The equally spaced QWSs with an origin of confined relativistic electrons are supported by phenomenological simulations and Fabry-Pérot fittings based on the relativistic Fermions. First-principles calculations further reveal that the spin-orbit coupling strengthens the relativistic nature of electrons near Fermi energy. Our finding uncovers the unique equally spaced quantum states in electronic systems beyond Landau levels and may inspire future studies on confined relativistic quasiparticles in flourishing topological materials and applications in structurally simpler quantum cascade laser.

Real Space Quantum Cluster Formulation for the Typical Medium Theory of Anderson Localization

We develop a real space cluster extension of the typical medium theory (cluster-TMT) to study Anderson localization. By construction, the cluster-TMT approach is formally equivalent to the real space cluster extension of the dynamical mean field theory. Applying the developed method to the 3D Anderson model with a box disorder distribution, we demonstrate that cluster-TMT successfully captures the localization phenomena in all disorder regimes. As a function of the cluster size, our method obtains the correct critical disorder strength for the Anderson localization in 3D, and systematically recovers the re-entrance behavior of the mobility edge. From a general perspective, our developed methodology offers the potential to study Anderson localization at surfaces within quantum embedding theory. This opens the door to studying the interplay between topology and Anderson localization from first principles.

Thermal properties of the one-dimensional space quantum fractional Dirac Oscillator

In this paper, we investigate the fractional version of the one-dimensional relativistic oscillators. We apply some important definitions and properties of a new kind of fractional formalism on the Dirac oscillator (DO). By using a semiclassical approximation, the energy eigenvalues have been determined for the oscillator. The obtained results show a remarkable influence of the fractional parameter on the energy eigenvalues. By considering a unique energy spectrum, we present a simple numerical computation of the thermal properties of a defined energy spectrum of a system. the Euler–Maclaurin formula has been used to calculate the partition function and therefore the associated thermodynamics quantities. In addition, the eigensolutions of the fractional Dirac oscillator, based on the factorization method, have been determined.

Reduced phase space approach to the U(1)3 model for Euclidean quantum gravity

If one replaces the constraints of the Ashtekar–Barbero SU(2) gauge theory formulation of Euclidean gravity by their U(1)3 version, one arrives at a consistent model which captures significant structure of its SU(2) version. In particular, it displays a non trivial realisation of the hypersurface deformation algebra which makes it an interesting testing ground for (Euclidean) quantum gravity as has been emphasised in a recent series of papers due to Varadarajan et al. In this paper we consider a reduced phase space approach to this model. This is especially attractive because, after a canonical transformation, the constraints are at most linear in the momenta. In suitable gauges, it is therefore possible to find a closed and explicit formula for the physical Hamiltonian which depends only on the physical observables. The corresponding reduced phase space quantisation can be confronted with the constraint quantisation due to Varadarajan et al to gain further insights into the quantum realisation of the hypersurface deformation algebra.

Arc Spaces and Chiral Symplectic Cores

We introduce the notion of chiral symplectic cores in a vertex Poisson variety, which can be viewed as analogs of symplectic leaves in Poisson varieties. As an application we show that any quasi-lisse vertex algebra is a quantization of the arc space of its associated variety, in the sense that its reduced singular support coincides with the reduced arc space of its associated variety. We also show that the coordinate ring of the arc space of Slodowy slices is free over its vertex Poisson center, and the latter coincides with the vertex Poisson center of the coordinate ring of the arc space of the dual of the corresponding simple Lie algebra.

Machine Learning-Assisted Selection of Active Spaces for Strongly Correlated Transition Metal Systems.

Active space quantum chemical methods could provide very accurate description of strongly correlated electronic systems, which is of tremendous value for natural sciences. The proper choice of the active space is crucial but a nontrivial task. In this article, we present a neural network-based approach for automatic selection of active spaces, focused on transition metal systems. The training set has been formed from artificial systems composed of one transition metal and various ligands, on which we have performed the density matrix renormalization group and calculated the single-site entropy. On the selected set of systems, ranging from small benchmark molecules up to larger challenging systems involving two metallic centers, we demonstrate that our machine learning models could predict the active space orbitals with reasonable accuracy. We also tested the transferability on out-of-the-model systems, including bimetallic complexes and complexes with ligands, which were not involved in the training set. Also, we tested the correctness of the automatically selected active spaces on a Fe(II)-porphyrin model, where we studied the lowest states at the DMRG level and compared the energy difference between spin states or the energy difference between conformations of ferrocene with recent studies.

Quantum space, quantum time, and relativistic quantum mechanics

We treat space and time as bona fide quantum degrees of freedom on an equal footing in Hilbert space. Motivated by considerations in quantum gravity, we focus on a paradigm dealing with linear, first-order Hamiltonian and momentum constraints that lead to emergent features of temporal and spatial translations. Unlike the conventional treatment, we show that Klein-Gordon and Dirac equations in relativistic quantum mechanics can be unified in our paradigm by applying relativistic dispersion relations to eigenvalues rather than treating them as operator-valued equations. With time and space being treated on an equal footing in Hilbert space, we show symmetry transformations to be implemented by unitary basis changes in Hilbert space, giving them a stronger quantum mechanical footing. Global symmetries, such as Lorentz transformations, modify the decomposition of Hilbert space; and local symmetries, such as $U(1)$ gauge symmetry are diagonal in coordinate basis and do not alter the decomposition of Hilbert space. We briefly discuss extensions of this paradigm to quantum field theory and quantum gravity.

Universal quantum state preparation via revised greedy algorithm

Preparation of quantum state lies at the heart of quantum information processing. The greedy algorithm provides a potential method to effectively prepare quantum state. However, the standard greedy (SG) algorithm, in general, cannot take the global maxima and instead becomes stuck on a local maxima. Based on the SG algorithm, in this paper we propose a revised version to design dynamic pulses to realize universal quantum state preparation, i.e. preparing an arbitrary state from another arbitrary one. As applications, we implement this scheme to the universal preparation of single- and two-qubit state in the context of semiconductor quantum dots and superconducting circuits. Evaluation results show that our scheme outperforms the alternative numerical optimizations with higher preparation quality while possesses the comparable high efficiency. Compared with the emerging machine learning, it shows better accessibility and does not require any training. Moreover, the numerical results show that the pulse sequences generated by our scheme are robust against various errors and noises. Our scheme opens a new avenue of optimization in few-level system and limited action space quantum control problems.

Quantization of Distributed Data for Learning

We consider machine learning applications that train a model by leveraging data distributed over a trusted network, where communication constraints can create a performance bottleneck. A number of recent approaches propose to overcome this bottleneck through compression of gradient updates. However, as models become larger, so does the size of the gradient updates. In this paper, we propose an alternate approach to learn from distributed data that quantizes data instead of gradients, and can support learning over applications where the size of gradient updates is prohibitive. Our approach leverages the dependency of the computed gradient on data samples, which lie in a much smaller space in order to perform the quantization in the smaller dimension data space. At the cost of an extra gradient computation, the gradient estimate can be refined by conveying the difference between the gradient at the quantized data point and the original gradient using a small number of bits. Lastly, in order to save communication, our approach adds a layer that decides whether to transmit a quantized data sample or not based on its importance for learning. We analyze the convergence of the proposed approach for smooth convex and non-convex objective functions and show that we can achieve order optimal convergence rates with communication that mostly depends on the data rather than the model (gradient) dimension. We use our proposed algorithm to train ResNet models on the CIFAR-10 and ImageNet datasets, and show that we can achieve an order of magnitude savings over gradient compression methods. These communication savings come at the cost of increasing computation at the learning agent, and thus our approach is beneficial in scenarios where communication load is the main problem.

Deformation quantization of moduli spaces of Higgs bundles on a Riemann surface with translation structure

Let X be a compact connected Riemann surface of genus g ≥ 1 equipped with a nonzero holomorphic 1-form. Let MX(r) denote the moduli space of semistable Higgs bundles on X of rank r and degree r(g − 1) + 1; it is a complex symplectic manifold. Using the translation structure on the open subset of X where the 1-form does not vanish, we construct a natural deformation quantization of a certain nonempty Zariski open subset of MX(r).

A cryogenic memory array based on superconducting memristors

A scalable cryogenic memory system is one of the prime requirements for the implementation of practical quantum computers, large-scale single flux quantum circuits, and space electronics. Here, we leverage the memristive behavior of a conductance-asymmetric superconducting quantum interference device (CA SQUID) to design an ultra-fast and low-power memory system. We develop a physics-based circuit-compatible model for CA-SQUID-based superconducting memristors (ScMs). Using this compact model, we design and test an ScM-based nonvolatile cryogenic memory system and explore the design space. Via analyzing the sensitivity and tunability of the device hysteresis up to the array level, we provide a comprehensive guideline for its experimental realization. The ScM-based memory system has the potential to solve the scalability issue of the state-of-the-art superconducting data storage systems and may trigger rapid advancement in quantum computing, space electronics, and cryogenic neuromorphic systems.

The existence and propagation of dust acoustic waves in quantum four-component plasma

The existence and propagation of dust acoustic waves in quantum four-component plasma are investigated by employing Sagdeev pseudo-potential. The plasma under consideration consists of both quantum electrons and ions beside negative and positive dust particulates. The general determining equation of the Sagdeev pseudo-potential is obtained, and it is found that the equation is very difficult to integrate. Due to the complexity involved in the structure of Sagdeev potential, this equation can only be solved in some limiting cases, such as semi-classical limit and small amplitude approximation. Our findings support the existence of compressive, rarefactive solitary waves and double layers in our plasma system. The influence of the relevant plasma parameters on the existence and profile of the obtained quantum nonlinear waves has been studied. The implications of the obtained results have wide relevance in the study of space and laboratory quantum dusty plasmas situations such as Jupiter’s magnetosphere, upper and lower mesosphere, and comet tails, as well as in condensed matter systems.

Evolutionary Multi-Objective Model Compression for Deep Neural Networks

While deep neural networks (DNNs) deliver state-of-the-art accuracy on various applications from face recognition to language translation, it comes at the cost of high computational and space complexity, hindering their deployment on edge devices. To enable efficient processing of DNNs in inference, a novel approach, called Evolutionary Multi-Objective Model Compression (EMOMC), is proposed to optimize energy efficiency (or model size) and accuracy simultaneously. Specifically, the network pruning and quantization space are explored and exploited by using architecture population evolution. Furthermore, by taking advantage of the orthogonality between pruning and quantization, a two-stage pruning and quantization co-optimization strategy is developed, which considerably reduces time cost of the architecture search. Lastly, different dataflow designs and parameter coding schemes are considered in the optimization process since they have a significant impact on energy consumption and the model size. Owing to the cooperation of the evolution between different architectures in the population, a set of compact DNNs that offer trade-offs on different objectives (e.g., accuracy, energy efficiency and model size) can be obtained in a single run. Unlike most existing approaches designed to reduce the size of weight parameters with no significant loss of accuracy, the proposed method aims to achieve a trade-off between desirable objectives, for meeting different requirements of various edge devices. Experimental results demonstrate that the proposed approach can obtain a diverse population of compact DNNs that are suitable for a broad range of different memory usage and energy consumption requirements. Under negligible accuracy loss, EMOMC improves the energy efficiency and model compression rate of VGG-16 on CIFAR-10 by a factor of more than 8 9. X and 2.4 X, respectively.

Probing Kinetic Inductance Pulses Below the Hotspot Activation Threshold of a Superconducting Nanowire

Superconducting Nanowire Single Photon Detectors (SNSPDs) have demonstrated timing and efficiency properties that have placed them at the frontier in single photon sensing applications (e.g. photon counting, deep space optical communications, quantum communication, and quantum encryption). Properties such as timing jitter as low as 3 ps, dark counts under 90 counts per day, high detection efficiency (>90%), short dead time and sensitivity over a wide range of photon energies (UV to IR). SNSPDs have a cutoff energy where the photon does not have enough energy to trigger the detection mechanism. In this paper, we lay out the framework and experimental setup to explore a modified approach in detecting photons below the cut off energy typical in an SNSPD. Leveraging the nanowire's change in kinetic inductance from photon absorption, the resulting voltage pulse is measured through a coupled quantum-noise-limited parametric amplifier. We consider nanowires with widths less than the vortex entry limit of w <; 4.4ξ, where ξ is the coherence length, limiting the sources of noise.

Experimental force reconstruction on plates of arbitrary shape using neural networks

Measuring the forces that excite a structure into vibration is an important tool in modeling the system and investigating ways to reduce the vibration. However, determining the forces that have been applied to a vibrating structure can be a challenging inverse problem, even when the structure is instrumented with a large number of sensors. Previously, an artificial neural network was developed to identify the location of an impulsive force on a rectangular plate. In this research, the techniques were extended to plates of arbitrary shape. The principal challenge of arbitrary shapes is that some combinations of network outputs (x- and y-coordinates) are invalid. For example, for a plate with a hole in the middle, the network should not output that the force was applied in the center of the hole. Different methods of accommodating arbitrary shapes were investigated, including output space quantization and selecting the closest valid region.

Particle physics processes in cosmology through an effective Minkowski space formulation and the limitations of the method

We introduce a method where particle physics processes in cosmology may be calculated by the usual perturbative flat space quantum field theory through an effective Minkowski space description at small time intervals provided that the running of the effective particle masses are sufficiently slow. We discuss the necessary conditions for the applicability of this method and illustrate the method through a simple example. This method has the advantage of avoiding the effects of gravitational particle creation in the calculation of rates and cross sections i.e. giving directly the rates and the cross sections due to the scatterings or the decay processes.

Significant inverse magnetocaloric effect induced by quantum criticality

The criticality-enhanced magnetocaloric effect (MCE) near a field-induced quantum critical point (QCP) in the spin systems constitutes a very promising and highly tunable alternative to conventional adiabatic demagnetization refrigeration. Strong fluctuations in the low-$T$ quantum critical regime can give rise to a large thermal entropy change and thus significant cooling effect when approaching the QCP. In this work, through efficient and accurate many-body calculations, we show there exists a significant inverse MCE (iMCE) in the spin-1 quantum chain materials (${\mathrm{CH}}_{3}{)}_{4}\mathrm{NNi}{({\mathrm{NO}}_{2})}_{3}$ (TMNIN) and ${\mathrm{NiCl}}_{2}\text{\ensuremath{-}}4\mathrm{SC}{({\mathrm{NH}}_{2})}_{2}$ (DTN), where DTN has substantial low-$T$ refrigeration capacity while requiring only moderate magnetic fields. The iMCE characteristics, including the adiabatic temperature change $\mathrm{\ensuremath{\Delta}}{T}_{\mathrm{ad}}$, isothermal entropy change $\mathrm{\ensuremath{\Delta}}S$, differential Gr\"uneisen parameter, and the entropy change rate, are obtained with quantum many-body calculations at finite temperature. The cooling performance, i.e., the efficiency factor and hold time, of the two compounds is also discussed. Based on the many-body calculations on realistic models for the spin-chain materials, we conclude that the compound DTN constitutes a very promising and highly efficient quantum magnetic coolant with pronounced iMCE properties. We advocate that such quantum magnets can be used in cryofree refrigeration for space applications and quantum computing environments.

The quantum disk is not a quantum group

In this paper, we show that the quantum disk, i.e. the quantum space corresponding to the Toeplitz [Formula: see text]-algebra does not admit any compact quantum group structure. We prove that if such a structure existed the resulting compact quantum group would simultaneously be of Kac type and not of Kac type. The main tools used in the solution come from the theory of operators on Hilbert spaces.