Expected Value Research Articles

On the evolution of the volume in Loop Quantum Cosmology

The dynamics of the expectation value of the volume is one of the key ingredients behind the replacement of the Big Bang singularity by a bounce in Loop Quantum Cosmology. As such, it is of great importance that this quantity is mathematically well-defined in the space of physical states of the theory. A number of caveats have been raised about such a definition entering in conflict with the quantum evolution of states, motivated by the situation found in quantum geometrodynamics. We show that there are ways around these caveats, all of which are related to the existence of quantization prescriptions leading to a nondegenerate curvature operator in Loop Quantum Cosmology. Interestingly, the properties of the curvature operator that may allow for a good behavior of the volume are only possible thanks to the discreteness of the geometry characteristic of the loop quantization procedure.

Detailed Complementary Consistency: Wave Function Tells Particle How to Hop, Particle Tells Wave Function How to Collapse.

In mixed quantum-classical dynamics, the quantum subsystem can have both wave function and particle-like descriptions. However, they may yield inconsistent results for the expectation value of the same physical quantity. We here propose a novel detailed complementary consistency (DCC) method based on the principle of detailed internal consistency. Namely, the wave function along each trajectory tells the particle how to hop, while the particle tells the wave function how to collapse based on active states in the trajectory ensemble. As benchmarked in a diverse array of representative models with localized nonadiabatic couplings, DCC not only achieves fully consistent results (i.e., identical populations calculated based on wave functions and active states) but also closely reproduces the exact quantum results. Due to the high performance, our new DCC method has great potential to give a consistent and accurate mixed quantum-classical description of general nonadiabatic dynamics after further development.

Thermodynamics of spin-1/2 fermions on coarse temporal lattices using automated algebra.

Recent advances in automated algebra for dilute Fermi gases in the virial expansion, where coarse temporal lattices were found advantageous, motivate the study of more general computational schemes that could be applied to arbitrary densities, beyond the dilute limit where the virial expansion is physically reasonable. We propose here such an approach by developing what we call the Quantum Thermodynamics Computational Engine (QTCE). In QTCE, the imaginary-time direction is discretized and the interaction is accounted for via a quantum cumulant expansion, where the coefficients are expressed in terms of non-interacting expectation values. The aim of QTCE is to enable the systematic resolution of interaction effects at fixed temporal discretization, as in lattice Monte Carlo calculations, but here in an algebraic rather than numerical fashion. Using this approach, in combination with numerical integration techniques (both known and alternative ones proposed here), we explore the thermodynamics of spin-1/2 fermions across spatial dimensions, focusing on the unitary limit. We find that, remarkably, extremely coarse temporal lattices, when suitably renormalized using known results from the virial expansion, yield stable partial sums for QTCE's cumulant expansion that are qualitatively and quantitatively correct in wide regions (when compared with known experimental results). This article is part of the theme issue 'The liminal position of Nuclear Physics: from hadrons to neutron stars'.

Алгоритмы построения дискретных приближенно Q-оптимальных планов эксперимента при активной идентификации регрессионных моделей многофакторных систем

In the theory of optimal experiment, there is a group of optimality criteria, for example, such as D-, A-, E-criteria, reflecting the accuracy of estimating model parameters. There is also a group of criteria related to the accuracy of the forecast based on the model, which can be characterized by the variance of estimates of mathematical expectations of responses. For example, using the G-optimality criterion allows you to obtain designs on which the constructed models will minimize the maximum variance of the forecast. Among these is the Q-optimality criterion, which assumes minimizing the average variance of the forecast for the regression model over the planning area. Most of the theoretical and applied research is related to the use of the D-optimality criterion. This is also explained by the fact that the criteria of D- and G-optimality are interconnected. At the same time, it should be noted that minimizing the maximum variance in the general case may not lead to a decrease in the average variance of the forecast area. In this regard, the use of Q-optimal designs in practical regression modeling tasks is relevant. For the widespread introduction into practice of the active identification of regression models of the concept of Q-optimality of experimental designs, an arsenal of effective algorithms for their construction is needed. The paper proposes and describes algorithms for constructing discrete approximate Q-optimal designs. The proposed algorithms are based on the developed approach of consistently increasing the number of points in the designs, as well as procedures for replacing points in the design. The designs obtained by such algorithms are recommended for use in practice when, on average, good prediction accuracy is required for the model over the entire range of input factors.

Fay Identities of Pfaffian Type for Hyperelliptic Curves

We establish identities of Pfaffian type for the theta function associated with twice or half the period matrix of a hyperelliptic curve. They are implied by the large size asymptotic analysis of exact Pfaffian identities for expectation values of ratios of characteristic polynomials in ensembles of orthogonal or quaternionic self-dual random matrices. We show that they amount to identities for the theta function with the period matrix of a hyperelliptic curve, and in this form we reprove them by direct geometric methods.

Black hole singularity resolution in Wheeler–DeWitt quantum gravity

Ever since Hawking highlighted the puzzle of the existence of a singularity in the classical spacetime of general relativity, implying breakdown of all laws of physics living in the classical spacetime, singularity resolution became a problem of significantly high importance. This undesirable feature, indicating loss of predictability, has intrigued physicists over several decades. It has been hoped that the classical singularity would be resolved in a quantum theory of gravity. However, no appropriate wave function in the vicinity of the black hole singularity has been obtained so far to reach a definite conclusion.In this paper, we focus upon the interior of the Schwarzschild black hole, plagued by a non-removable classical singularity. We consider the interior spacetime of the black hole to be represented by the Kantowski–Sachs metric. Since in a quantum mechanical scenario, existence of spontaneous fluctuations of matter fields should not be ignored, we include a Klein–Gordon field in the system. Quantizing this simple gravity-matter model in the canonical scheme, we obtain the Wheeler–DeWitt equation and find an exact solution in the minisuperspace variables.We find that there exist three classes of solutions belonging to three different subregions of the eigenvalue space. Two of these classes of solutions admit the DeWitt criterion, a necessary condition for singularity resolution, implied by vanishing of the wave function at the singularity. These solutions are well-behaved and finite in the vicinity of the singularity and they indicate the existence of regular black holes in quantum gravity. In these classes of solutions, we further find that the expectation value of the Kretschmann operator is well-behaved and regular near the singularity, confirming a definite resolution to the puzzle of classical black hole singularity. On the other hand, there exists a small subregion in the eigenvalue space where the solution does not satisfy both conditions, the DeWitt criterion and finiteness of the Kretschmann expectation value at the singularity. This last class of solutions does not represent regular quantum black holes.

Deep learning based on randomized quasi-Monte Carlo method for solving linear Kolmogorov partial differential equation

Deep learning algorithms have been widely used to solve linear Kolmogorov partial differential equations (PDEs) in high dimensions, where the loss function is defined as a mathematical expectation. We propose to use the randomized quasi-Monte Carlo (RQMC) method instead of the Monte Carlo (MC) method for computing the loss function. In theory, we decompose the error from empirical risk minimization (ERM) into the generalization error and the approximation error. Notably, the approximation error is independent of the sampling methods. We prove that the convergence order of the mean generalization error for the RQMC method is O(n−1+ϵ) for arbitrarily small ϵ>0, while for the MC method it is O(n−1/2+ϵ) for arbitrarily small ϵ>0. Consequently, we find that the overall error for the RQMC method is asymptotically smaller than that for the MC method as n increases. Our numerical experiments show that the algorithm based on the RQMC method consistently achieves smaller relative L2 error than that based on the MC method.

Path integrals, complex probabilities and the discrete Weyl representation

A discrete formulation of the real-time path integral as the expectation value of a functional of paths with respect to a complex probability on a sample space of discrete valued paths is explored. The formulation in terms of complex probabilities is motivated by a recent reinterpretation of the real-time path integral as the expectation value of a potential functional with respect to a complex probability distribution on cylinder sets of paths. The discrete formulation in this work is based on a discrete version of the Weyl algebra that can be applied to any observable with a finite number of outcomes. The origin of the complex probability in this work is the completeness relation. In the discrete formulation the complex probability exactly factors into products of conditional probabilities and exact unitarity is maintained at each level of approximation. The approximation of infinite dimensional quantum systems by discrete systems is discussed. The method is illustrated by applying it to scattering theory and quantum field theory. The implications of these applications for quantum computing is discussed.

Vector dark matter with Higgs portal in type II seesaw framework

We study the phenomenology of a vector dark matter (VDM) in a U(1)X gauged extension of the Standard Model (SM), which is set in a type II seesaw framework. When this U(1)X symmetry is spontaneously broken by the vacuum expectation value (VEV) of a newly introduced complex scalar singlet, the gauge boson Z′ becomes massive. The stability of the dark matter (DM) is ensured by the presence of an exact charge conjugation symmetry resulting from the structure of the Lagrangian. On the other hand, the SU(2)L triplet scalar facilitates light neutrino masses via the type II seesaw mechanism. We have studied the phenomenology of the usual WIMP DM, considering all possible theoretical and experimental constraints that are applicable. Due to the presence of a triplet scalar, the present framework can also accommodate the observed 2σ deviation in h→Zγ decay rate, recently measured at the LHC. The possibility of nonthermal production of DM from the decay of the singlet scalar has also been briefly discussed. Published by the American Physical Society 2024

Evaluasi Kesesuaian Lahan Pasang Surut untuk Tanaman Lada (Piper nigrum Linn.) di Desa Galing Kecamatan Galing Kabupaten Sambas

Land evaluation is an approach for assessing the potential of land resources. Results of the evaluation will give information about land anduse necessary direction, and finally the value of production expectations that can be obtained. This study aims to identify the limiting factors for pepper plants in the Galing village, Galing sub-district, Sambas district. To create a class of actual and potential land suitability. This research was conducted in the village of the District Galing Galing Sambas district, then followed by analysis of soil samples in the Laboratory of Chemistry and Soil Fertility Faculty of Agriculture Universitas Tanjungpura. The research started from December 2014 until Fabruari 2015. The results showed that there are two units of Soil Map is Sulfic Endoaquents and Typic Sulfaquents. Actual land suitability on soil type Sulfic Endoaquents (SPT 1) is the appropriate marginal (S2) with inhibitors to Factor pepper plant is a low pH, nutrient availability, and the depth of the actual land sulfidik. Suitability for pepper plants are S3 nfx. While the actual land suitability on the type of Typic Sulfaquents (SPT 2) inhibiting factor is the low pH, nutrient availability, and the depth of the actual land sulfidik. Suitability for pepper plants are N-x. Recommendations for improvements in SPT 1 and SPT 2 is water regulation, liming and fertilizing N, P, and K with the processing level is medium to high, then the suitability of potential land for pepper plants in SPT 1 to be fit while on SPT 2 appropriate to marginal

Exploring the recycled water acceptance based on the technological perspective of UTAUT2: a hybrid analytical approach.

The development of advanced sewage technologies empowers the industry to produce high-quality recycled water, which greatly influences human's life and health. Thus, this study investigates the mechanism of individuals' adoption of recycled water from the technology adoption perspective. Employing the mixed method of structural equation modeling and artificial neural network analysis, we examined a research model developed from the extended Unified Theory of Acceptance and Use of Technology (UTAUT2) framework. To examine the research model, this study employs a leading web-survey company (Sojump) to collect 308 valid samples from the residents in mainland China. The structural equation modeling results verified the associations between the six predictors (performance expectancy, effort expectancy, social influence, facilitating conditions, environmental motivation, and price value), individuals' cognitive and emotional attitudes, and acceptance intention. The artificial neural network analysis validates and complements the structural equation modeling results by unveiling the importance rank of the significant determinants of the acceptance decisions. The study provides theoretical implications for recycled water research and useful insights for practitioners and policymakers to reduce the environmental hazards of water scarcity.

Quantum Fisher kernel for mitigating the vanishing similarity issue

Quantum kernel (QK) methods exploit quantum computers to calculate QKs for the use of kernel-based learning models. Despite a potential quantum advantage of the method, the commonly used fidelity-based QK suffers from a detrimental issue, which we call the vanishing similarity issue; the exponential decay of the expectation value and the variance of the QK deteriorates implementation feasibility and trainability of the model with the increase of the number of qubits. This implies the need to design QKs alternative to the fidelity-based one. In this work, we propose a new class of QKs called the quantum Fisher kernels (QFKs) that take into account the geometric structure of the data source. We analytically and numerically demonstrate that the QFK can avoid the issue when shallow alternating layered ansatzes are used. In addition, the Fourier analysis numerically elucidates that the QFK can have the expressivity comparable to the fidelity-based QK. Moreover, we demonstrate synthetic classification tasks where QFK outperforms the fidelity-based QK in performance due to the absence of vanishing similarity. These results indicate that QFK paves the way for practical applications of quantum machine learning toward possible quantum advantages.

Sample-optimal classical shadows for pure states

We consider the classical shadows task for pure states in the setting of both joint and independent measurements. The task is to measure few copies of an unknown pure state ρ in order to learn a classical description which suffices to later estimate expectation values of observables. Specifically, the goal is to approximate Tr(Oρ) for any Hermitian observable O to within additive error ϵ provided Tr(O2)≤B and ‖O‖=1. Our main result applies to the joint measurement setting, where we show Θ~(Bϵ−1+ϵ−2) samples of ρ are necessary and sufficient to succeed with high probability. The upper bound is a quadratic improvement on the previous best sample complexity known for this problem. For the lower bound, we see that the bottleneck is not how fast we can learn the state but rather how much any classical description of ρ can be compressed for observable estimation. In the independent measurement setting, we show that O(Bdϵ−1+ϵ−2) samples suffice. Notably, this implies that the random Clifford measurements algorithm of Huang, Kueng, and Preskill, which is sample-optimal for mixed states, is not optimal for pure states. Interestingly, our result also uses the same random Clifford measurements but employs a different estimator.

Learning Quantum Processes and Hamiltonians via the Pauli Transfer Matrix

Learning about physical systems from quantum-enhanced experiments can outperform learning from experiments in which only classical memory and processing are available. Whereas quantum advantages have been established for state learning, quantum process learning is less understood. We establish an exponential quantum advantage for learning an unknown n -qubit quantum process \(\mathcal {N}\) . We show that a quantum memory allows to efficiently solve the following tasks: (a) learning the Pauli transfer matrix (PTM) of an arbitrary \(\mathcal {N}\) , (b) predicting expectation values of Pauli-sparse observables measured on the output of an arbitrary \(\mathcal {N}\) upon input of a Pauli-sparse state, and (c) predicting expectation values of arbitrary observables measured on the output of an unknown \(\mathcal {N}\) with sparse PTM upon input of an arbitrary state. With quantum memory, these tasks can be solved using linearly-in- n many copies of the Choi state of \(\mathcal {N}\) . In contrast, any learner without quantum memory requires exponentially-in- n many queries, even when using adaptively designed experiments. In proving this separation, we extend existing shadow tomography bounds from states to channels. Moreover, we combine PTM learning with polynomial interpolation to learn arbitrary Hamiltonians from short-time dynamics. Our results highlight the power of quantum-enhanced experiments for learning highly complex quantum dynamics.

Quantum Circuit Cutting for Classical Shadows

Classical shadow tomography is a sample-efficient technique for characterizing quantum systems and predicting many of their properties. Circuit cutting is a technique for dividing large quantum circuits into smaller fragments that can be executed more robustly using fewer quantum resources. We introduce a divide-and-conquer circuit cutting method for estimating the expectation values of observables using classical shadows. We derive a general formula for making predictions using the classical shadows of circuit fragments from arbitrarily cut circuits and provide the sample complexity analysis for the case when observables factorize across fragments. Then, we numerically show that our divide-and-conquer method outperforms traditional uncut shadow tomography when estimating high-weight observables that act non-trivially on many qubits and discuss the mechanisms for this advantage.

Exponential gravity with logarithmic corrections in the presence of axion dark matter

An exponential modified gravity with additional logarithmic corrections is considered with the presence of an axion-like scalar field in the role of dark matter. Axion fields are thought to become important at late-times when the axion-like scalar field oscillates around its vacuum expectation value, mimicking dark matter behaviour. The model is compared with the usual pressureless fluid description of dark matter. Both models are tested with observational data including some of the latest sources, providing similar fits in comparison with the ΛCDM model. Despite results are not statistically relevant to rule out any model, the number of free parameters still favours ΛCDM model, as shown by computing the goodness of the fits.

Improved constraints on the variation of the weak scale from Big Bang nucleosynthesis

We present an improved calculation of the light element abundances in the framework of Big Bang nucleosynthesis as a function of the Higgs vacuum expectation value v. We compare the methods of our calculation to previous literature including the recently published work of Burns et al. [1]. The PDG result for the 4He abundance can be explained within 2σ by −0.014 ≤ δv/v ≤ 0.026, for deuterium we find the constraint −0.005 ≤ δv/v ≤ −0.001. These bounds are more stringent than what was found earlier.

Mitigating Errors on Superconducting Quantum Processors Through Fuzzy Clustering

AbstractQuantum utility is severely limited in superconducting quantum hardware until now by the modest number of qubits and the relatively high level of control and readout errors, due to the intentional coupling with the external environment required for manipulation and readout of the qubit states. Practical applications in the Noisy Intermediate Scale Quantum (NISQ) era rely on Quantum Error Mitigation (QEM) techniques, which are able to improve the accuracy of the expectation values of quantum observables by implementing classical post‐processing analysis from an ensemble of repeated noisy quantum circuit runs. In this work, a recent QEM technique that uses Fuzzy C‐Means (FCM) clustering to specifically identify measurement error patterns is focused. For the first time, a proof‐of‐principle validation of the technique on a two‐qubit register, obtained as a subset of a real NISQ five‐qubit superconducting quantum processor based on transmon qubits is reported. It is demonstrated that the FCM‐based QEM technique allows for reasonable improvement of the expectation values of single‐ and two‐qubit gates‐based quantum circuits, without necessarily invoking state‐of‐the‐art coherence, gate, and readout fidelities.

Gravitational waves effects in a Lorentz–violating scenario

This paper focuses on how the production and polarization of gravitational waves are affected by spontaneous Lorentz symmetry breaking, which is driven by a self–interacting vector field. Specifically, we examine the impact of a smooth quadratic potential and a non–minimal coupling, discussing the constraints and causality features of the linearized Einstein equation. To analyze the polarization states of a plane wave, we consider a fixed vacuum expectation value (VEV) of the vector field. Remarkably, we verify that a space–like background vector field modifies the polarization plane and introduces a longitudinal degree of freedom. In order to investigate the Lorentz violation effect on the quadrupole formula, we use the modified Green function. Finally, we show that the space–like component of the background field leads to a third–order time derivative of the quadrupole moment, and the bounds for the Lorentz–breaking coefficients are estimated as well.

Using the Extended Unified Theory of Acceptance and Use of Technology to explore how to increase users’ intention to take a robotaxi

In recent years, many governments and companies have gradually launched robotaxi projects to help make transportation systems smarter, improve travel efficiency, and reduce travel costs. Robotaxi is a new mode of travel that replaces human driving with machines, freeing up social labour and enriching people’s travel choices. This study employs the Extended Unified Theory of Acceptance and Use of Technology (UTAUT2) to understand the influencing factors of users’ adoption and usage of robotaxis in China to facilitate the broader integration of robotaxis into urban transportation systems. This study surveyed the preferences of 2048 respondents and analysed the data through structural equation modelling. The results indicate that performance expectancy, hedonic motivation, and price value are the factors influencing users’ behavioural intentions, while effort expectancy and social influence affect use behaviour. In contrast, habit is an important factor that affect both behavioural intention and actual use behaviour. Based on the findings, we have proposed practical strategies to improve robotaxi services and updated the UTAUT2 model in the context of robotaxi. We suggest that robotaxi operators can promote user acceptance and use by reducing the difficulty of use, improving the cost performance and the ride experience, and making appropriate publicity and guidance.