Calculation Of Expectation Values Research Articles

Evaluation of Managerial Economics Applications Strategy using the SPSS Method

Managerial Economics is an economy branch is, this economic theory and size using methods solve real-world managerial problems. It helps businesses and organizations make informed decisions by using economic analysis. Here are some common applications of managerial economics: Demand Analysis and Forecasting: Businesses use managerial economics to understand consumer behavior and forecast future demand for their products or services. This involves studying factors that affect demand, such as price, income levels, and consumer preferences. Production and Cost Analysis: Managerial economics helps businesses optimize production processes and minimize costs. It involves analyzing production functions, cost structures, and economies of scale to determine the most efficient way to produce goods or services. Pricing Strategies: A product or the right price for the service It is up to a company to decide Crucial to profitability. Managerial economics helps businesses set prices by considering factors like production costs, competition, and consumer willingness to pay. Market Structure Analysis: Understanding the type of market, a company operates in (e.g., perfect competition, monopoly, oligopoly) is essential for making strategic decisions. Managerial economics helps analyses market structures and determine appropriate strategies for each. Risk and Uncertainty Analysis: Businesses often face uncertainty in various aspects, such as demand fluctuations, production costs, and market conditions. Managerial economics provides tools to assess and manage risks, including techniques like decision tree analysis and expected value calculations. Capital Budgeting and Investment Analysis: Managerial economics assists in evaluating investment opportunities and capital projects. It involves methods Payback period analysis of investments. Regulatory and Government Policy Analysis: Managerial economics helps businesses understand and navigate government regulations and policies that affect their operations. This can include areas like taxation, environmental regulations, and trade policies. Strategic Planning: Using economic analysis, businesses can develop long-term strategies for growth and sustainability. This may involve assessing market trends, competitive dynamics, and potential expansion opportunities. Game Theory and Competitive Strategy: Managerial economics incorporates game theory to analyze strategic interactions between competitors. It helps businesses formulate optimal strategies in competitive environments. Resource Allocation: Efficient allocation of resources, including labor, capital, and technology, is crucial for a company's success. Managerial economics provides tools to distribute funds in a manner that optimisesoverall productivity and profitability. Demand Analysis and Forecasting, Production and Cost Analysis, Pricing Strategies, Market Structure Analysis, Risk and Uncertainty Analysis, Capital Budgeting and Investment Analysis and Regulatory and Government Policy Analysis. The Cranach’s Alpha Reliability result. The overall Cranach’s Alpha value for the model is .744 which indicates 74% reliability. From the literature review, the above 50% Cranach’s Alpha value model can be considered for analysis.

Towards quantum gravity with neural networks: solving the quantum Hamilton constraint of U(1) BF theory

Abstract In the canonical approach of loop quantum gravity, arguably the most important outstanding problem is finding and interpreting solutions to the Hamiltonian constraint. In this work, we demonstrate that methods of machine learning are in principle applicable to this problem. We consider U(1) BF theory in three dimensions, quantised with loop quantum gravity methods. In particular, we formulate a master constraint corresponding to Hamilton and Gauß constraints using loop quantum gravity methods. To make the problem amenable for numerical simulation we fix a graph and introduce a cutoff on the kinematical degrees of freedom, effectively considering U q ( 1 ) BF theory at a root of unity. We show that the neural network quantum state ansatz can be used to numerically solve the constraints efficiently and accurately. We compute expectation values and fluctuations of certain observables and compare them with exact results or exact numerical methods where possible. We also study the dependence on the cutoff.

Capturing non-Markovian polaron dressing with the master equation formalism.

Understanding the dynamics of open quantum systems in strong coupling and non-Markovian regimes remains a formidable theoretical challenge. One popular and well-established method of approximation in these circumstances is provided by the polaron master equation (PME). In this work, we re-evaluate and extend the validity of the PME to capture the impact of non-Markovian polaron dressing, induced by non-equilibrium open system dynamics. By comparing with numerically exact techniques, we confirm that while the standard PME successfully predicts the dynamics of system observables that commute with the polaron transformation (e.g., populations in the Pauli z-basis), it can struggle to fully capture those that do not (e.g., coherences). This limitation stems from the mixing of system and environment degrees of freedom inherent to the polaron transformation, which affects the accuracy of calculated expectation values within the polaron frame. Employing the Nakajima-Zwanzig projection operator formalism, we introduce correction terms that provide an accurate description of observables that do not commute with the transformation. We demonstrate the significance of the correction terms in two cases, the canonical spin-boson model and a dissipative time-dependent Landau-Zener protocol, where they are shown to impact the system dynamics on both short and long timescales.

Increasing the Measured Effective Quantum Volume with Zero Noise Extrapolation

Quantum volume is a full-stack benchmark for near-term quantum computers. It quantifies the largest size of a square circuit which can be executed on the target device with reasonable fidelity. Error mitigation is a set of techniques intended to remove the effects of noise present in the computation of noisy quantum computers when computing an expectation value of interest. Effective quantum volume is a proposed metric that applies error mitigation to the quantum volume protocol to evaluate the effectiveness not only of the target device but also of the error mitigation algorithm. Digital zero-noise extrapolation is an error mitigation technique that estimates the noiseless expectation value using circuit folding to amplify errors by known scale factors and then extrapolating computed expectation values to the zero-noise limit. Here we demonstrate that zero-noise extrapolation, with global and local unitary folding with fractional scale factors, in conjunction with dynamical decoupling, can increase the effective quantum volume over the vendor-measured quantum volume. Specifically, we measure the effective quantum volume of four IBM Quantum superconducting processor units, obtaining values that are larger than the vendor-measured quantum volume on each device. This is the first such increase reported.

Hamiltonian dynamics on digital quantum computers without discretization error

We introduce an algorithm to compute expectation values of time-evolved observables on digital quantum computers that requires only bounded average circuit depth to reach arbitrary precision, i.e. produces an unbiased estimator with finite average depth. This finite depth comes with an attenuation of the measured expectation value by a known amplitude, requiring more shots per circuit. The average gate count per circuit for simulation time t is O(t2μ2)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal{O}}({t}^{2}{\\mu }^{2})$$\\end{document} with μ the sum of the Hamiltonian coefficients, without dependence on precision, providing a significant improvement over previous algorithms. With shot noise, the average runtime is O(t2μ2ϵ−2)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal{O}}({t}^{2}{\\mu }^{2}{\\epsilon }^{-2})$$\\end{document} to reach precision ϵ. The only dependence in the sum of the coefficients makes it particularly adapted to non-sparse Hamiltonians. The algorithm generalizes to time-dependent Hamiltonians, appearing for example in adiabatic state preparation. These properties make it particularly suitable for present-day relatively noisy hardware that supports only circuits with moderate depth.

Analytic evolution for complex coupled tight-binding models: Applications to quantum light manipulation

We present analytic solutions to the evolution in generalized tight-binding models, which consider complex first-neighbor couplings with equal amplitude and arbitrary phases. Our findings provide a powerful tool to efficiently calculate expectation values and correlations within the system, which are otherwise difficult to compute numerically. We apply our results to relevant examples in quantum light manipulation using -port linear couplers, describing the evolution of single (multi)-mode squeezing, single-photon added (subtracted) Gaussian states, and second-order site-to-site photon correlations. Significantly, our analytic results outperform standard numerical calculations. Our study paves the way for a comprehensive mathematical framework describing the spatial evolution of quantum states across a wide range of physical systems governed by the tight-binding model. Published by the American Physical Society 2024

Certified algorithms for equilibrium states of local quantum Hamiltonians

Predicting observables in equilibrium states is a central yet notoriously hard question in quantum many-body systems. In the physically relevant thermodynamic limit, certain mathematical formulations of this task have even been shown to result in undecidable problems. Using a finite-size scaling of algorithms devised for finite systems often fails due to the lack of certified convergence bounds for this limit. In this work, we design certified algorithms for computing expectation values of observables in the equilibrium states of local quantum Hamiltonians, both at zero and positive temperature. Importantly, our algorithms output rigorous lower and upper bounds on these values. This allows us to show that expectation values of local observables can be approximated in finite time, contrasting related undecidability results. When the Hamiltonian is commuting on a 2-dimensional lattice, we prove fast convergence of the hierarchy at high temperature and as a result for a desired precision ε, local observables can be approximated by a convex optimization program of quasi-polynomial size in 1/ε.

Doubly-charged Tcc++ states in the dynamical diquark model

One of the celebrated tools in explaining the hydrogen atom is Born-Oppenheimer approximation. The resemblance of QQq¯q¯ tetraquarks to hydrogen atom within quantum chromodynamics implies usage of Born-Oppenheimer approximation for these multiquark states. In this work, we use dynamical diquark model to calculate mass spectra and sizes of doubly charmed and charged tetraquark states denoted as Tcc++. Our results for mass spectra indicate some bound-state candidates with respect to corresponding two-meson thresholds. Calculation of expectation values of ⟨r2⟩ reflects that doubly charmed and charged tetraquark states are compact. Published by the American Physical Society 2024

Quantum Equation of Motion with Orbital Optimization for Computing Molecular Properties in Near-Term Quantum Computing.

Determining the properties of molecules and materials is one of the premier applications of quantum computing. A major question in the field is how to use imperfect near-term quantum computers to solve problems of practical value. Inspired by the recently developed variants of the quantum counterpart of the equation-of-motion (qEOM) approach and the orbital-optimized variational quantum eigensolver (oo-VQE), we present a quantum algorithm (oo-VQE-qEOM) for the calculation of molecular properties by computing expectation values on a quantum computer. We perform noise-free quantum simulations of BeH2 in the series of STO-3G/6-31G/6-31G* basis sets and of H4 and H2O in 6-31G using an active space of four electrons and four spatial orbitals (8 qubits) to evaluate excitation energies, electronic absorption, and, for twisted H4, circular dichroism spectra. We demonstrate that the proposed algorithm can reproduce the results of conventional classical CASSCF calculations for these molecular systems.

Coordinated risk-averse distributionally robust optimization for maintenance and generation schedules of offshore wind farm cluster

The coordinated optimization of maintenance and generation schedules of multiple offshore wind farms (OWFs) bring great benefits in reducing the maintenance and operation cost of OWF cluster. Firstly, a two-stage coordinated risk-averse distributionally robust optimization (CRDRO) model for maintenance and generation schedules of wind turbines (WTs) in OWF cluster is proposed. This model takes into account uncertainties related to the prediction errors in WTs’ maximum available active power outputs, the travel time of maintenance vessels, and the high operational cost risks associated with these uncertainties. A feasible route generating algorithm is designed to obtain all feasible maintenance combinations for WTs and the corresponding routes of maintenance vessels for the CRDRO model. The risk-averse term, which is a weighted sum of expected operation costs and GlueVaR value, is used to measure the tail risk of the worst probability distribution. To solve the two-stage CRDRO model, the risk-averse term is simplified into the form of expected value calculation, which can be further transformed into the tractable form by using the strong duality theorem. Finally, the two-stage CRDRO model is solved by the column-and-constraint generation algorithm, with the nonconvex sub-problem being addressed by the outer approximation algorithm. Case studies on an real-world cluster comprising three OWFs verify the correctness and efficiency of the proposed method, and demonstrate that the CRDRO model enhances the overall economic efficiency and reduces the high operational cost risk under extreme scenarios.

On the normalization and density of 1D scattering states

The normalization of scattering states is more than a rote step necessary to calculate expectation values. This normalization actually contains important information regarding the density of the scattering spectrum (along with useful details on the bound states). For many applications, this information is more useful than the wavefunctions themselves. In this paper, we show that this correspondence between scattering state normalization and the density of states is a consequence of the completeness relation, and we present formulas for calculating the density of states, which are applicable to certain potentials. We then apply these formulas to the delta function potential and the square well. We then illustrate how the density of states can be used to calculate the partition function for a system of two particles with a point-like (delta potential) interaction.

First simultaneous global QCD analysis of dihadron fragmentation functions and transversity parton distribution functions

We perform a comprehensive study within quantum chromodynamics (QCD) of dihadron observables in electron-positron annihilation, semi-inclusive deep-inelastic scattering, and proton-proton collisions, including recent cross section data from Belle and azimuthal asymmetries from STAR. We extract simultaneously for the first time π+π− dihadron fragmentation functions (DiFFs) and the nucleon transversity distributions for up and down quarks as well as antiquarks. For the transversity distributions we impose their small-x asymptotic behavior and the Soffer bound. In addition, we utilize a new definition of DiFFs that has a number density interpretation to then calculate expectation values for the dihadron invariant mass and momentum fraction. Furthermore, we investigate the compatibility of our transversity results with those from single-hadron fragmentation (from a transverse momentum dependent/collinear twist-3 framework) and the nucleon tensor charges computed in lattice QCD. We find a universal nature to all of this available information. Future measurements of dihadron production can significantly further this research, especially, as we show, those that are sensitive to the region of large parton momentum fractions. Published by the American Physical Society 2024

Fast and converged classical simulations of evidence for the utility of quantum computing before fault tolerance.

A recent quantum simulation of observables of the kicked Ising model on 127 qubits implemented circuits that exceed the capabilities of exact classical simulation. We show that several approximate classical methods, based on sparse Pauli dynamics and tensor network algorithms, can simulate these observables orders of magnitude faster than the quantum experiment and can also be systematically converged beyond the experimental accuracy. Our most accurate technique combines a mixed Schrödinger and Heisenberg tensor network representation with the Bethe free entropy relation of belief propagation to compute expectation values with an effective wave function-operator sandwich bond dimension >16,000,000, achieving an absolute accuracy, without extrapolation, in the observables of <0.01, which is converged for many practical purposes. We thereby identify inaccuracies in the experimental extrapolations and suggest how future experiments can be implemented to increase the classical hardness.

Discrete Event Probabilistic Simulation (DEPS) integrated into a Reinforcement Learning Framework for Optimal Production

This paper introduces an innovative simulation method that significantly accelerates the training of reinforcement learning agents in manufacturing, surpassing the constraints of traditional simulations. While prior Discrete Event Simulations (DES) of production lines have a runtime complexity of O(NMS) for N (batched) products, M machines, and S samples, our Discrete Event Probabilistic Simulation (DEPS) can reduce an expected value computation complexity of O(KM) for K time windows and M machines. Furthermore, unlike traditional DES, our developed DEPS is probabilistic enabling trustworthy decision-making by providing creditable uncertainty and risk bounds. By conditioning the product quality on machine parameters, DEPS enables rapid, risk-free AI agent training, paving the way for their integration into production lines. We (1) demonstrate that our simulation offers a state-of-the-art simulation speed, (2) provide an adaptable open-source framework for probabilistic production-line-level simulation and modelling, and (3) share a physically plausible benchmark environment. Our contribution seeks to provide a new standard for industrial Artificial Intelligence (AI) applications, allowing manufacturers and researchers to leverage Reinforcement Learning (RL) agents’ potential for optimising production-line-level efficiency, process optimisation, and resource allocation.

Exact entanglement in the driven quantum symmetric simple exclusion process

Entanglement properties of driven quantum systems can potentially differ from the equilibrium situation due to long range coherences. We confirm this observation by studying a suitable toy model for mesoscopic transport: the open quantum symmetric simple exclusion process (QSSEP). We derive exact formulae for its mutual information between different subsystems in the steady state and show that it satisfies a volume law. Surprisingly, the QSSEP entanglement properties only depend on data related to its transport properties and we suspect that such a relation might hold for more general mesoscopic systems. Exploiting the free probability structure of QSSEP, we obtain these results by developing a new method to determine the eigenvalue spectrum of sub-blocks of random matrices from their so-called local free cumulants – a mathematical result on its own with potential applications in the theory of random matrices. As an illustration of this method, we show how to compute expectation values of observables in systems satisfying the Eigenstate Thermalization Hypothesis (ETH) from the local free cumulants.

Non-directed (altruistic) kidney donation: Altruism or insurance policy?

Since non-directed (altruistic) kidney donors do not stand to benefit from the lengthening and strengthening of a relationship that they intrinsically value, their donations are considered to constitute the most altruistic variety of living kidney donation. This paper uses publicly-available data to assess the expected value that accrues to the donor of altruistic kidney donation. Compared to healthy non-donors, living kidney donors experience only marginally increased absolute risks of poor physical health outcomes, and no difference in important psychosocial health outcomes. Crucially, the chance of requiring a kidney donation is only marginally increased by becoming a living kidney donor. In the United Kingdom, previous living kidney donors that subsequently become in need of any organ donation (not only kidneys) themselves are considered priority patients for these donations. They consequently experience shorter waiting times for these organs and reduced exposure to the inherently harmful effects of dialysis therapy (if a kidney donation is required) compared to non-donors in need of organ donation. As such, while key data points required to compute an accurate and complete expected value calculation are unavailable, it is likely that the additional risk incurred by becoming a living kidney donor is outweighed by the benefit of being considered a priority patient for the donation of any type of organ in the event that this is needed. Accordingly, the expected value of becoming a living kidney donor is likely to be positive, meaning the act of doing so may be considered akin to the taking out of an insurance policy. In the context of non-directed (altruistic) kidney donation, this may diminish the extent to which such a donation is considered altruistic.

Smoothing Codes and Lattices: Systematic Study and New Bounds

In this article we revisit smoothing bounds in parallel between lattices <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">and</i> codes. Initially introduced by Micciancio and Regev, these bounds were instantiated with Gaussian distributions and were crucial for arguing the security of many lattice-based cryptosystems. Unencumbered by direct application concerns, we provide a systematic study of how these bounds are obtained for both lattices <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">and</i> codes, transferring techniques between both areas. We also consider multiple choices of spherically symmetric noise distributions. We found that the best strategy for a worst-case bound combines Parseval’s Identity, the Cauchy-Schwarz inequality, and the second linear programming bound, and this holds for both codes and lattices and all noise distributions at hand. For an average-case analysis, the linear programming bound can be replaced by an expected value computation. This alone gives optimal results for spherically uniform noise over random codes and random lattices. This also improves prior Gaussian smoothing bounds for worst-case lattices, but surprisingly this provides even better results with uniform ball noise than for Gaussian (or Bernoulli noise for codes). This counterintuitive situation can be resolved by adequate decomposition and truncation of Gaussian and Bernoulli distributions into a superposition of uniform noise, giving further improvement for those cases, and putting them on par with the uniform cases.

Remarks on the quasi-position representation in models of generalized uncertainty principle

This note aims to elucidate certain aspects of the quasi-position representation frequently used in the investigation of one-dimensional models based on the generalized uncertainty principle (GUP). We specifically focus on two key points: (i) contrary to recent claims, the quasi-position operator can possess physical significance even though it is non-Hermitian, and (ii) in the quasi-position representation, operators associated with the position, such as the potential energy, also behave as a derivative operator on the quasi-position coordinate, unless the method of computing expectation values is modified. The development of both points revolves around the observation that the position and quasi-position operators share the same set of eigenvalues and are connected through a non-unitary canonical transformation. This outcome may have implications for widely referenced constraints on GUP parameters.

Backward induction and expected value calculations in an anonymous XVth century Italian manuscript

Blaise Pascal famously calculated the expected value of a risky lottery in the 1654 correspondence with Pierre de Fermat in the context of the so-called points problem. Pascal solved this problem by backward induction, whereas Fermat—by counting combinations. This paper analyzes a more complex version of the points problem from an anonymous XVth century Italian manuscript stored in the Vatican Apostolic Library. In this manuscript, the problem of points is solved by backward induction in a similar way to Pascal’s train of thought. In this light, Pascal’s pioneering contribution may be not as novel as it is traditionally believed.

An Algorithm Design about Psychological Counseling Platform Using the Derivative Works

The psychological counseling platform using the derivative works in this study includes four main modules and two sub modules. The first main one is a content database that stores a plurality of derivative works in which keywords are set. The second is a message input module including a request message providing unit that displays a request message input from the client terminal on the counselor's terminal, and a counseling message input unit that receives a counseling message written based on the request message from the counselor's terminal. The third main module is a keyword extraction module that extracts keywords by analyzing the counseling message. Final one is an answer providing module that provides derivative works corresponding to the extracted keyword and the consultation message to the client terminal. As the sub modules, this system consists of a region division module and a chart generation module. The region division module allows the screen of the client terminal to correspond to the central region where the counseling message is placed and the vertices of an equilateral triangle having the central point of the central region as the outer center. The chart generation module consists of a chart display unit, an expected value calculation unit, and a variable value setting unit. Based on the proposed algorithm, this system has the effect of increasing the effectiveness of psychological counseling and improving the concentration of counseling by providing recreated secondary copyrighted content using copyright-protected videos, images, music, and photos together with psychological counseling at the same time.