Creation And Annihilation Research Articles

Representation of the fermionic boundary operator

The boundary operator is a linear operator that acts on a collection of high-dimensional binary points (simplices) and maps them to their boundaries. This boundary map is one of the key components in numerous applications, including differential equations, machine learning, computational geometry, machine vision and control systems. We consider the problem of representing the full boundary operator on a quantum computer. We first prove that the boundary operator has a special structure in the form of a complete sum of fermionic creation and annihilation operators. We then use the fact that these operators pairwise anticommute to produce an $O(n)$-depth circuit that exactly implements the boundary operator without any Trotterization or Taylor series approximation errors. Having fewer errors reduces the number of shots required to obtain desired accuracies.

Quantum metrology with multimode Gaussian states of multiple point sources

A unified theoretical framework is developed for measuring multimode Gaussian states of multiple point sources. The spatial and temporal mode functions are found analytically by aid of the circular symmetry of the object plane and aperture, as well as by the rectangular spectral density function of the background. They relate the modal operators and statistical moments to the locations of the point sources through the prolate spheroidal functions. An experimentally straightforward implementation is proposed, which consists of a nonabsorptive polarization- and phase-modulating spatial light modulator (SLM), three lenses, and a polarization beam splitter. Interestingly, it is found that the spatial modal annihilation operators are related to the modal field operators in the image plane by a simple complex-valued scale factor. The quantum Fisher information matrix and quantum Cram\'er-Rao bound (QCRB) are also discussed. The numerical calculation of QCRB is completed for the case where the spatially multimode aperture fields are prepared by the spatial propagation from temporally single-mode thermal states, coherent states, or quadrature squeezed states of the point sources in the object plane. The results show that the Rayleigh limit can always be surpassed by means of increasing the mean photon rate or the squeeze parameter.

Optimizing creation operators for charmonium spectroscopy on the lattice

Smearing the bare quantum fields in lattice calculations before applying composite hadron creation operators has a long record of substantially improving overlaps onto low-lying energy eigenstates. A technique called distillation which defines smearing for quark fields as a low-rank linear projection operator into a small vector space of smooth gauge-covariant fields has proven to be both effective and versatile in hadron spectroscopy calculations albeit with significant computational cost . In this paper, more general operators in this space of smooth fields are introduced and optimised, which enhances the performance of the method when tested on systems of heavy quark-anti-quark pairs close to the charmonium energy scale.

A new perspective on quantum field theory revealing possible existence of another kind of fermions forming dark matter

Quantum fields are considered as generators of infinite-dimensional Clifford algebra [Formula: see text], which can be either orthogonal (in the case of fermions) or symplectic (in the case of bosons). A generic quantum state can be expressed as a superposition of the basis elements of [Formula: see text], with the superposition coefficients being multiparticle complex-valued wavefunctions. The basis elements, that are products of the generators of [Formula: see text] in the Witt basis, act as creation and annihilation operators. They create positive and negative energy states that include the bare and the Dirac vacuum as special cases. It is shown that the nonvanishing electric charge arises from an extra dimension or from doubling the number of creation and annihilation operators, which brings an extra imaginary unit [Formula: see text] into the description. A further extension is to consider [Formula: see text] as one of the quaternionic imaginary units and consider a generic state as having values in the quaternionic algebra or, equivalently, in the complexified two-dimensional Clifford algebra, [Formula: see text]. It contains two distinct fundamental representations of [Formula: see text], one associated with the weak isospin doublet [Formula: see text] and the other one with the doublet of new leptons, denoted by [Formula: see text], that together with the new quarks [Formula: see text] can be identified with dark matter.

Existence of a threshold for second-harmonic generation inside high-confinement microresonators as a consequence of the generalized creation and annihilation operators

This work presents a quantum theory of the nonlinear optical process of second-harmonic generation (SHG) in one-dimensional microresonators. More specifically, we show how the manipulation of vacuum field fluctuations in high-confinement systems, leading to a spectrally (and spatially) modulated commutation relation for the photon's generalized formulations of their creation and annihilation operators, deeply affects SHG behavior and gives rise to a threshold level. The two main effects the modulated commutator has on this optical process are an inhibition of the SHG process at low pumping level and a significant (cubic) amplification of the second-harmonic signal production rate once the threshold is overcome (finally reaching the usual quadratic dependence at sufficiently high pumping level). Our predictions, which represent a concrete picture of a fractional quantum system, could be used to probe vacuum field fluctuations present in high-confinement microresonators and emphasize the fundamental importance of vacuum field fluctuations.

Noncommutative rational Clark measures

Abstract We characterize the noncommutative Aleksandrov–Clark measures and the minimal realization formulas of contractive and, in particular, isometric noncommutative rational multipliers of the Fock space. Here, the full Fock space over $\mathbb {C} ^d$ is defined as the Hilbert space of square-summable power series in several noncommuting (NC) formal variables, and we interpret this space as the noncommutative and multivariable analogue of the Hardy space of square-summable Taylor series in the complex unit disk. We further obtain analogues of several classical results in Aleksandrov–Clark measure theory for noncommutative and contractive rational multipliers. Noncommutative measures are defined as positive linear functionals on a certain self-adjoint subspace of the Cuntz–Toeplitz algebra, the unital $C^*$ -algebra generated by the left creation operators on the full Fock space. Our results demonstrate that there is a fundamental relationship between NC Hardy space theory, representation theory of the Cuntz–Toeplitz and Cuntz algebras, and the emerging field of noncommutative rational functions.

Note on bi-exactness for creation operators on Fock spaces

In this note, we introduce and study a notion of bi-exactness for creation operators acting on full, symmetric and anti-symmetric Fock spaces. This is a generalization of our previous work, in which we studied the case of anti-symmetric Fock spaces. As a result, we obtain new examples of solid actions as well as new proofs for some known solid actions. We also study free wreath product groups in the same context.

Dynamic Collaboration Model of Production Network Based on Cloud Service Bus

The IT system of manufacturing enterprises usually has many problems, such as complex industrial software, different development languages, diverse communication protocols, and complex operation environment. Cloud service bus (CSB) technology based on service model encapsulates various applications existing in enterprises by means of the integration of cloud service bus and micro services, which can realize the rapid cloud migration and deployment of heterogeneous industrial application software. Theoretically, after the production system is connected to CSB, it can be arranged arbitrarily by service choreography technology to produce any possible products. However, in the context of industrial Internet, the production system connected to CSB corresponds to the equipment, materials, personnel, and other resources on the production line one by one. These production nodes need to consider the production capacity and cost of production service nodes and the output value of the whole production network, and cannot be combined arbitrarily. Therefore, when integrating production service nodes, we should not only consider the technical integration, but also consider whether the production conditions support this integration. To solve the problem of production node integration in CSB, a dynamic collaboration model of production network based on cloud service bus is proposed in this paper. The model takes the capacity, cost, and production relationship of production nodes as constraints, and the overall efficiency of production network as the optimization goal. The model can calculate the new creation, modification, deletion, and other scheduling operations of production line services in real time and give the production plan with the highest resource utilization and the greatest value in the current production network. The model can improve the rationality and economy of service choreography and give full play to the value of production network. Taking an enterprise with 11 production nodes and 5 production lines as an example, this paper discusses in detail how to use this model to calculate the optimal production organization scheme and the maximum output value of the enterprise.

Superintegrability on the Dunkl oscillator model in three-dimensional spaces of constant curvature

In this paper, three-dimensional Dunkl oscillator models are studied in a generalized form of superintegrable Euclidean Hamiltonian systems to curved ones. These models are defined based on curved Hamiltonians, which depend on a deformation parameter of underlying space and involve reflection operators. The corresponding symmetries are obtained by the Jordan–Schwinger representations in the family of the Cayley–Klein orthogonal algebras using the creation and annihilation operators of the dynamical sl−1(2) algebra of the one-dimensional Dunkl oscillator. The resulting algebra is a deformation of soκ1κ2(4) with reflections, which is known as the Jordan–Schwinger–Dunkl algebra jsdκ1κ2(4). Hence, it is shown that this model is maximally superintegrable. On the other hand, the superintegrability of the three-dimensional Dunkl oscillator model is studied from the viewpoint of the factorization approach. The spectrum of this system is derived through the separation of variables in geodesic polar coordinates, and the resulting eigenfunctions are algebraically given in terms of Jacobi polynomials.

Quantum algorithm for Gaussian process regression

The Gaussian process is a widely used model for regression problems in supervised machine learning. However, predicting new inputs via a Gaussian process model becomes computationally inefficient when training a large data set. This paper proposes a fast quantum algorithm for prediction based on the Gaussian process regression. The proposed quantum algorithm consists of two subalgorithms: the first one aims to efficiently prepare the squared exponential covariance matrices and covariance functions vector with annihilation and creation operators; the other is to obtain predictive mean values and covariance values for new inputs. Evidence is also shown that the proposed quantum Gaussian process regression algorithm can achieve quadratic speedup over the classical counterpart.

SU (1,1) the hidden dynamical symmetry group for an exact bound state of the Hulthen potential

In this research work, an exact normalised bound eigenstate and energy eigenvalue of the Hulthen potential, for the zero angular momentum within the framework of the non-relativistic time independent Schrödinger wave equation were obtained using the Nikiforov–Uvarov method. Also, their self-adjoint differential creation and annihilation (ladder) operators were derived, andfrom the commutation relations their Casimir operator was defined. These results showed that the non-compact group is the dynamical group for this exact bound state, described by the representation with a spectrum bounded below.

Higher Order Moments Dynamics for Some Multimode Quantum Master Equations

We derive Heisenberg equations for arbitrary high order moments of creation and annihilation operators in the case of the quantum master equation with a multimode generator which is quadratic in creation and annihilation operators and obtain their solutions. Based on them we also derive similar equations for the case of the quantum master equation, which occur after averaging the dynamics with a quadratic generator with respect to the classical Poisson process. This allows us to show that dynamics of arbitrary finite-order moments of creation and annihilation operators is fully defined by finite number of linear differential equations in this case.

Thermal properties of relativistic Dunkl oscillators

For a better understanding of the physical systems, even at the quantum level, the thermal quantities can be investigated. Recently, we realized that the parity of the system can also be examined simultaneously, by substituting the Dunkl operator with the ordinary differential operator in quantum mechanics. In this manuscript, we consider two relativistic Dunkl-oscillators and investigate their thermal quantities with well-known statistical methods. Besides, we establish a relationship between the Dunkl-Dirac oscillator and the Dunkl-Anti-Jayne-Cummings model by defining the Dunk creation and annihilation operators. Therefore, we conclude that our model can be regarded as an appropriate scenario for the theory of an open quantum system coupled to a thermal bath.

A characterization of rationality in free semicircular operators

For free semicircular elements realized on the full Fock space, we prove an equivalence between rationality of operators obtained from them and finiteness of the rank of their commutators with right annihilation operators. This is an analogue of the result for the reduced C⁎-algebra of the free group by G. Duchamp and C. Reutenauer which was extended by P. A. Linnell to densely defined unbounded operators affiliated with the free group factor. While their result was motivated by quantized calculus in noncommutative geometry, we state our results in terms of free probability theory.

Photon conservation in trans-luminal metamaterials

Structures that appear to move at or near the velocity of light contain singular points. Energy generated by motion accumulates at these points into ever-narrowing peaks. In this paper, we show that energy is generated by a curious process that conserves the number of photons, adding energy by forcing photons already present to climb a ladder of increasing frequency. We present both a classical proof based on conservation of lines of force, and a more formal quantum electrodynamics proof demonstrating the absence of unpaired creation and annihilation operators. Exceptions to this rule are found when negative frequencies make an appearance. Finally, we make a connection to laboratory-based models of black holes and Hawking radiation.

Intelligent Online Selling Point Extraction for E-commerce Recommendation

In the past decade, automatic product description generation for e-commerce have witnessed significant advancement. As the services provided by e-commerce platforms become diverse, it is necessary to dynamically adapt the patterns of descriptions generated. The selling point of products is an important type of product description for which the length should be as short as possible while still conveying key information. In addition, this kind of product description should be eye-catching to the readers. Currently, product selling points are normally written by human experts. Thus, the creation and maintenance of these contents incur high costs. These costs can be significantly reduced if product selling points can be automatically generated by machines. In this paper, we report our experience developing and deploying the Intelligent Online Selling Point Extraction (IOSPE) system to serve the recommendation system in the JD.com e-commerce platform. Since July 2020, IOSPE has become a core service for 62 key categories of products (covering more than 4 million products). So far, it has generated more than 1.1 billion selling points, thereby significantly scaling up the selling point creation operation and saving human labour. These IOSPE generated selling points have increased the click-through rate (CTR) by 1.89% and the average duration the customers spent on the products by more than 2.03% compared to the previous practice, which are significant improvements for such a large-scale e-commerce platform.

ВДОСКОНАЛЕННЯ МЕХАНІЗМІВ УПРАВЛІННЯ ОПЕРАЦІЙНИМИ РИЗИКАМИ БАНКУ

The article examines the mechanisms and methods of operational risk management in Ukrainian banks. It is determined that operational risk is a complex type of banking risk, and the peculiarity of its implementation is that it is inherent in all banking processes, products, business lines and activities and has an unpredictable nature. It is proved that the improvement of operational risk management contributes to the sustainable functioning of banks and the stability of the entire banking system. The main principles of the bank's operational risk management system formation and functioning are determined, which include: objectivity and regularity of risk identification and assessment; timeliness of their detection and evaluation; complexity; structured management; proportionality; delimitation of control functions and operational activities; independence of individual governing bodies; confidentiality; transparency and efficiency. Given the complex and dynamic nature of operational risks, as well as the active digitalization of the banking business, it is recommended that operational risks include reputational risks, information risks and cyber risks. Based on the calculations, it is established that the impact of operational risks on the performance of domestic banks tends to increase, the leveling of which requires the development of new management mechanisms through the creation and effective operation of operational risk management. A system of measures to improve operational risk management based on the use of the «three lines of protection», which includes classification, identification, measurement, monitoring, control and reporting of operational risks, as well as assessment of economic and social consequences of risk events. The main methods of operational risk management are identified and it is proved that the key direction of their use should be preventive measures to avoid or minimize the economic consequences of risks, and coverage of losses arising from their implementation should be provided by specially formed reserves of internal capital. An indicative list of key indicators has been developed and approaches to characterizing operational risk events that can be used by domestic banks in practice to minimize the consequences of operational risks have been improved.

Taxation of Fiat Money Using Dynamic Control

The treasury analogy is widely used in most countries in the execution of fiscal policies striving to match taxation with public expenditure while, at the same time, the central banks tinker with interest rates and reserve requirements and conduct open market operations for regulating money supply. This paper investigates the relevance of those policy actions to the ubiquitous use of fiat money tokens which in addition to meeting public expenditure and paying taxes also facilitate transactions in the economy. A parsimonious model of the macroeconomic system subsuming the prevalent fiscal and monetary interventions is developed and experimented with to explore alternative policy levers for funding public expenditure and controlling money supply. A novel dynamic control regimen to regulate taxation and open market operations for controlling inflation is proposed. It is shown that while the public spending can be entirely met through new money creation, taxation and open market operations must be used as inflation control instruments, whereas expenditure instruments can be used to alleviate the regressivity of taxation regimen.

Introduction to coherent quantization

This paper studies coherent quantization, the way operators in the quantum space of a coherent space—defined in the recent book ’Coherent Quantum Mechanics’ by the first author—can be studied in terms of objects defined directly on the coherent space. The results may be viewed as a generalization of geometric quantization, including the non-unitary case. Care has been taken to work with the weakest meaningful topology and to assume as little as possible about the spaces and groups involved. Unlike in geometric quantization, the groups are not assumed to be compact, locally compact, or finite-dimensional. This implies that the setting can be successfully applied to quantum field theory, where the groups involved satisfy none of these properties. The paper characterizes linear operators acting on the quantum space of a coherent space in terms of their coherent matrix elements. Coherent maps and associated symmetry groups for coherent spaces are introduced, and formulas are derived for the quantization of coherent maps. The importance of coherent maps for quantum mechanics is due to the fact that there is a quantization map that associates homomorphically with every coherent map a linear operator from the quantum space into itself. The quantization map generalizes the second quantization procedure for free classical fields to symmetry groups of general coherent spaces. Field quantization is obtained by specialization to Klauder spaces, whose quantum spaces are the bosonic Fock spaces. Implied by the new approach is a short, coordinate-free derivation of all basic properties of creation and annihilation operators in Fock spaces.

Unstable vacuum and fermion total reflection by the Klein step

Abstract The so-called Klein tunneling is re-examined within the framework of quantum field theory, but from a different point of view on the asymptotic states. We treat it as a one-dimensional scattering process of a fermion incident to a step potential and introduce asymptotic operators as appropriate t = ±∞ limits of the field operator responsible for the process. For the so-called Klein energy range, two asymptotic vacua naturally emerge which are defined as states annihilated by the asymptotic annihilation operators. They are related by a similarity transformation, which entails an unstable vacuum. When a fermion with incident energy in the Klein region is injected to the step, it is shown to be reflected with probability one, accompanied by fermion–anti-fermion pairs that are vacuum decay products.