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A tuple (Z 1 , ... , Z p) of matrices of size r × r is said to be a commuting extension of a tuple (A 1 , ... , A p) of matrices of size n × n if the Z i pairwise commute and each A i sits in the upper left corner of a block decomposition of Z i (here, r and n are two arbitrary integers with n < r). This notion was discovered and rediscovered in several contexts including algebraic complexity theory (in Strassen's work on tensor rank), in numerical analysis for the construction of cubature formulas and in quantum mechanics for the study of computational methods and the study of the so-called "quantum Zeno dynamics." Commuting extensions have also attracted the attention of the linear algebra community. In this paper we present 3 types of results: (i) Theorems on the uniqueness of commuting extensions for three matrices or more. (ii) Algorithms for the computation of commuting extensions of minimal size. These algorithms work under the same assumptions as our uniqueness theorems. They are applicable up to r = 4 n / 3 , and are apparently the first provably efficient algorithms for this problem applicable beyond r = n + 1. (iii) A genericity theorem showing that our algorithms and uniqueness theorems can be applied to a wide range of input matrices. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the interplay of Dzyaloshinskii–Moriya interaction (DMI) and uniform and staggered fields in x and z directions on entanglement in the spin-1/2 one-dimensional Heisenberg chain. We use the well-known mapping of this model on sine-Gordon theory to calculate the quantum entanglement quantifiers as von Neumann entropy and entanglement negativity, which provides a useful framework for studying the emergence of quantum correlation in this model. How the behavior of the spin velocity implies in a significant impact on energy of elementary excitations, carrying spin S z = ± 1 / 2 , we get that the DMI interaction and external fields generate a large effect on behavior of the spinons energy and quantum correlation. [ABSTRACT FROM AUTHOR]

This research investigates the complex statistical behavior of fermion-antifermion pairs within a (2+1)-dimensional magnetized Bonnor-Melvin background affected by non-zero cosmological conditions. The Bonnor-Melvin magnetic universe model, known for its cylindrical symmetry, preserves the invariance of quantum field dynamics under Lorentz boosts along the z -axis. This framework facilitates the examination of (2+1)-dimensional scenarios, where the corresponding spacetime background is identified as the Bonnor-Melvin magnetic 2+1+0-brane solution within the realm of gravity coupled with nonlinear electrodynamics. Initially, the precise energy spectra of these pairs are summarized using an analytical solution derived from the fully covariant two-body Dirac equation. Subsequently, the statistical properties inherent in these pair formations are investigated. These findings may illuminate the interplay among magnetic fields, spacetime geometry, and the cosmological constant, thereby enhancing our comprehension of the fundamental behaviors of fermions amidst intricate cosmological conditions. It is anticipated that this investigation could offer new insights into the statistical attributes of fermion-antifermion systems. All thermal characteristics, including free energy, total energy, entropy, and specific heat, have been computed. The impact of diverse factors, such as magnetic fields, spacetime geometry, and the cosmological constant, on these characteristics has been scrutinized. [ABSTRACT FROM AUTHOR]

Periodically kicked Floquet systems, such as the kicked rotor, are a paradigmatic and illustrative simple model of chaos. For non-integrable quantum dynamics, there are several diagnostic measures, such as Loschmidt echo, autocorrelation function and out of time order correlator (OTOC) to study the presence of (or the transition to) chaotic behaviour. We analytically compute these measures in terms of the eigensystem of the unitary Floquet operator of the driven quantum systems. We use these expressions to determine the time variation of the measures for the quantum-kicked rotor (QKR) on the torus, for the integrable as well as the chaotic case. For a simpler integrable variant of the kicked rotor, we also give a representation theoretic derivation of its dynamics. [ABSTRACT FROM AUTHOR]

This article sheds new light on the debate between the Discovery and Creation views of entrepreneurial opportunity by drawing on quantum theory. We develop the Quantum view of opportunity, which explains how opportunity is both discovered and created. The Quantum view holds that the ontology and epistemology of opportunity are fundamentally inseparable, which explains why opportunity can never be fully specified. We argue, similar to the Discovery view, that opportunity exists as latent states irrespective of entrepreneurs and that, similar to the Creation view, opportunity is instantiated through entrepreneurial action, which changes opportunity. We use the Quantum view as a thought-provoking metaphor that facilitates the breaking out of the mold of ingrained thinking and moves beyond the Discovery-Creation dichotomy to further our understanding of entrepreneurship. We discuss how the Quantum view relates to established theoretical and empirical research in the entrepreneurship field. Plain English Summary: Rethinking Entrepreneurial Opportunity: A Quantum view! Discover how opportunities are both found and made. #QuantumOpportunity. Entrepreneurial opportunities have long been debated: are they discovered or created? Inspired by quantum mechanics, this article introduces a fresh perspective called the "Quantum view." Instead of seeing opportunities as either discovered or created, the Quantum view suggests that they are both created and discovered. It urges us to rethink conventional wisdom. Instead of just "finding" or "making" opportunities, the Quantum view suggests that opportunities exist in potential states and are realized through entrepreneurial enactment. Entrepreneurs can gather information about opportunities, but they can never fully specify them because every time they interact with an opportunity, they change it. Thus, the Quantum view emphasizes that we can learn about, but never fully specify, opportunities. This helps researchers think differently about opportunities and avoid extreme positions such as that entrepreneurs create something from nothing or that some entrepreneurs can accurately predict the future. [ABSTRACT FROM AUTHOR]

As a prototype adsorption reaction of gas Brønsted acid on oxides, we study the adsorption of formic acid on anatase. We perform infrared spectroscopy measurements of adsorbed HCOOH and HCOOD on TiO2 nanopowders, from 13 K up to room temperature in an ultra‐high vacuum chamber. We assign the IR signals via computed spectra from nuclear quantum dynamics simulations using our divide‐and‐conquer semiclassical ab initio molecular dynamics method. The acid proton forms an extraordinarily short and strong hydrogen bond with the surface oxygen. The strength of this hydrogen bond, that compares to H bonds in ice at high pressures, is at the root of a substantial redshift with respect to the typical free OH stretching frequency, which eludes its straightforward detection. [ABSTRACT FROM AUTHOR]

Harnessing quantum correlations can enable sensing beyond classical precision limits, with the realization of such sensors poised for transformative impacts across science and engineering. Real devices, however, face the accumulated impacts of noise and architecture constraints, making the design and success of practical quantum sensors challenging. Numerical and theoretical frameworks to optimize and analyze sensing protocols in their entirety are thus crucial for translating quantum advantage into widespread practice. Here, we present an end-to-end variational framework for quantum sensing protocols, where parameterized quantum circuits and neural networks form trainable, adaptive models for quantum sensor dynamics and estimation, respectively. The framework is general and can be adapted towards arbitrary qubit architectures, as we demonstrate with experimentally-relevant ansätze for trapped-ion and photonic systems, and enables to directly quantify the impacts that noise and finite data sampling. End-to-end variational approaches can thus underpin powerful design and analysis tools for practical quantum sensing advantage. [ABSTRACT FROM AUTHOR]

Two-dimensional (2D) electron systems are promising for investigating correlated quantum phenomena. In particular, 2D oxides provide a platform that can host various quantum phases such as quantized Hall effect, superconductivity, or magnetism. The realization of such quantum phases in 2D oxides heavily relies on dedicated heterostructure growths. Here we show the integer quantum Hall effect achieved in chemical vapor deposition grown Bi2O2Se - a representative member of a more accessible oxide family. A single or few subband 2D electron system can be prepared in thin films of Bi2O2Se, where the film thickness acts as the key subband design parameter and the occupation is determined by the electric field effect. This oxide platform exhibits characteristic advantages in structural flexibility due to its layered nature, making it suitable for scalable growth. The unique small mass distinguishes Bi2O2Se from other high-mobility oxides, providing a new platform for exploring quantum Hall physics in 2D oxides. The authors demonstrate quantum Hall effect in semiconducting layered oxide Bi2O2Se. Its unique low mass among the oxides of 0.14 me and pronounced layered structure makes Bi2O2Se highly susceptible to the quantum confinement effects. [ABSTRACT FROM AUTHOR]

We provide a justification, via the thermodynamic limit, of the modular formula for entropy production in two-time measurement proposed in [T. Benoist, L. Bruneau, V. Jakšić, A. Panati and C.-A. Pillet, A note on two-times measurement entropy production and modular theory, Lett. Math. Phys. 114:32 (2023), doi:10.1007/s11005-024-01777-0]. We consider the cases of open quantum systems in which all thermal reservoirs are either (discrete) quantum spin systems or free Fermi gases. [ABSTRACT FROM AUTHOR]

In this paper, we explore the relativistic quantum dynamics of spin-0 oscillator fields within the framework of a rotating cosmic string space–time, taking into account the presence of scalar and vector potentials. We solve the Klein–Gordon oscillator equation in this curved space–time, incorporating generalized versions of the Yukawa and Hulthen potentials as vector and scalar potentials, respectively. The analytical solution of the quantum system yields the energy eigenvalue and corresponding eigenfunction, which is expressed in terms of confluent Heun functions. The resulting energy spectrum is shown to depend on various parameters associated with the cosmic string space–time and the confining potentials. We graphically illustrate how the energy spectrum varies with changes in both the potential parameters and the cosmic string parameters. [ABSTRACT FROM AUTHOR]

Non-Hermitian physical systems have attracted considerable attention in recent years for their unique properties around exceptional points (EPs), where the eigenvalues and eigenstates of the system coalesce. Phase transitions near exceptional points can lead to various interesting phenomena, such as unidirectional wave transmission. However, most of those studies are in the classical regime and whether these properties can be maintained in the quantum regime is still a subject of ongoing studies. Using a non-Hermitian on-chip superconducting quantum circuit, here we observe a phase transition and the corresponding exceptional point between the two phases. Furthermore, we demonstrate that unidirectional microwave transmission can be achieved even in the few-photon regime within the broken symmetry phase. This result holds some potential applications, such as on-chip few-photon microwave isolators. Our study reveals the possibility of exploring the fundamental physics and practical quantum devices with non-Hermitian systems based on superconducting quantum circuits. The authors observe an exceptional point and the corresponding phase transition in a superconducting non-Hermitian circuit. They find non-reciprocal microwave transmission can be achieved within the broken symmetry phase in the few-photon regime. [ABSTRACT FROM AUTHOR]

In order to improve efficiency when preventing and controlling spontaneous combustion of coal, a type of compound inhibitor with tea polyphenol and vitamin E as the chemical inhibitor, grafted on a copolymer hydrogel, was prepared. The oxidation resistance of the compound inhibitor to coal was analyzed by thermogravimetric test, Fourier infrared spectroscopy, and quantum chemistry theory. The experiment results showed that: The optimum ratio of tea polyphenols and vitamin E was 1:0.05; tea polyphenols and vitamin E inhibited the oxidation of coal by capturing the decomposition products of hydroperoxides and finally forming stable ether structures, and slowing down the hydrogen supply reaction between aliphatic hydrocarbons and carboxyl groups; the antioxidant properties of vitamin E (VE) and tea polyphenols (EGCG) were mainly due to the presence of active hydroxyl groups in the ring; H22 of VE and H38 of EGCG were able to inhibit the chain reaction of coal effectively. This study provides a new technical method for development of comprehensive fire prevention technology to address spontaneous combustion of coal, and provides a reference for the research into the inhibition mechanism of spontaneous combustion of coal. [ABSTRACT FROM AUTHOR]

The Kirkwood-Dirac quasiprobability distribution, intimately connected with the quantum correlation function of two observables measured at distinct times, is becoming increasingly relevant for fundamental physics and quantum technologies. This quasiprobability distribution can take non-positive values, and its experimental reconstruction becomes challenging when expectation values of incompatible observables are involved. Here, we use an interferometric scheme aided by an auxiliary system to reconstruct the Kirkwood-Dirac quasiprobability distribution. We experimentally demonstrate this scheme in an electron-nuclear spin system associated with a nitrogen-vacancy center in diamond. By measuring the characteristic function, we reconstruct the quasiprobability distribution of work and analyze the behavior of its first and second moments. Our results clarify the physical meaning of the work quasiprobability distribution in the context of quantum thermodynamics. Finally, we study the uncertainty of measuring the Hamiltonian of the system at two times, via the Robertson-Schrödinger uncertainty relation, for different initial states. [ABSTRACT FROM AUTHOR]

Some new types of truncated M-fractional exact soliton solutions of the two important quantum plasma physics models, extended quantum Zakharov–Kuznetsov and extended quantum nonlinear Zakharov–Kuznetsov, are successfully achieved by applying the exp a function technique, the improved ( G ′ / G) -expansion technique, and the Sardar sub-equation technique. These two models have many useful applications when explaining the waves in the quantum electron-positron-ion magnetoplasmas as well as weakly nonlinear ion-acoustic waves in plasma. The obtained results are in the form of dark, bright, periodic, and other soliton solutions. The results are verified and represented by two-dimensional, three-dimensional, and contour graphs. The results are newer than the existing results in the literature due to the use of fractional derivatives. Hence, the solutions will be fruitful in future studies on these models. The solutions obtained are useful in the areas of applied physics, applied mathematics, dynamical systems, and nonlinear waves in plasmas and in dense space plasma. The applied techniques are simple, fruitful, and reliable for solving other models in mathematical physics. [ABSTRACT FROM AUTHOR]

Dissipation is a ubiquitous phenomenon that affects the fate of chaotic quantum many-body dynamics. Here, we show that chaos can be robust against dissipation but can also assist and anomalously enhance relaxation. We compute exactly the dissipative form factor of a generic Floquet quantum circuit with arbitrary on-site dissipation modeled by quantum channels and find that, for long enough times, the system always relaxes with two distinctive regimes characterized by the presence or absence of gap-closing. While the system can sustain a robust ramp for a long (but finite) time interval in the gap-closing regime, relaxation is "assisted" by quantum chaos in the regime where the gap remains nonzero. In the latter regime, we prove that, if the thermodynamic limit is taken first, the gap does not close even in the dissipationless limit. We complement our analytical findings with numerical results for quantum qubit circuits. Quantum chaos is a useful framework for quantum many-body systems, but it has been mostly applied to isolated systems. Here the authors study the interplay of chaos and dissipation in open quantum circuits, showing that chaos is robust against weak dissipation but can also assist and anomalously enhance relaxation. [ABSTRACT FROM AUTHOR]

Noisy intermediate-scale quantum (NISQ) computers provide a new experimental platform for investigating the behaviour of complex quantum systems. We show that currently available NISQ devices can be used for versatile quantum simulations of chaotic systems. We introduce a classical-quantum hybrid approach for exploring the dynamics of the chaotic quantum kicked top (QKT) on a quantum computer. The programmability of this approach allows us to experimentally explore a broad range of QKT chaoticity parameter regimes inaccessible to previous studies. Furthermore, the number of gates in our simulation does not increase with the number of kicks, thus making it possible to study the QKT evolution for arbitrary number of kicks without fidelity loss. Using a publicly accessible NISQ computer (IBMQ), we observe periodicities in the evolution of the 2-qubit QKT, as well as signatures of chaos in the time-averaged 2-qubit entanglement. We also demonstrate a connection between entanglement and delocalization in the 2-qubit QKT, confirming theoretical predictions. [ABSTRACT FROM AUTHOR]

The aim of the present work is to demonstrate the applicability of machine learning techniques and in particular neural network quantum states in the context of loop quantum gravity, albeit for a simplified theory. We consider 3-dimensional Euclidean gravity in a gauge theoretical formulation in a certain weak coupling limit due to Smolin, and show that the gauge group becomes Abelian, resulting in U (1) 3 BF-theory. The theory is quantised using loop quantum gravity methods. The kinematical degrees of freedom are truncated, on account of computational feasibility, by fixing a graph and deforming the algebra of the holonomies to impose a cutoff on the charge vectors. This leads to a quantum theory related to U q (1) 3 BF-theory. The effect of imposing the cutoff on the charges is examined. We also implement the quantum volume operator of 3d loop quantum gravity. Most importantly we compare two constraints for the quantum model obtained: a master constraint enforcing curvature and Gauß constraint, as well as a combination of a quantum Hamilton constraint constructed using Thiemann's strategy and the Gauß master constraint. The two constraints are solved using the neural network quantum state ansatz, demonstrating its ability to explore models which are out of reach for exact numerical methods. The solutions spaces are quantitatively compared and although the forms of the constraints are radically different, the solutions turn out to have a surprisingly large overlap. We also investigate the behavior of the quantum volume in solutions to the constraints. [ABSTRACT FROM AUTHOR]

Modeling the electrical response of multi-level quantum systems at finite frequency has been typically performed in the context of two incomplete paradigms: (i) input-output theory, which is valid at any frequency but neglects dynamic losses, and (ii) semiclassical theory, which captures dynamic dissipation effects well but is only accurate at low frequencies. Here, we develop a unifying theory, valid for arbitrary frequencies, that captures both the small-signal quantum behavior and the non-unitary effects introduced by relaxation and dephasing. The theory allows a multi-level system to be described by a universal small-signal equivalent-circuit model, a resonant RLC circuit, whose topology only depends on the number of energy levels. We apply our model to a double-quantum-dot charge qubit and a Majorana qubit, showing the capability to continuously describe the systems from adiabatic to resonant and from coherent to incoherent, suggesting new and realistic experiments for improved quantum state readout. Our model will facilitate the design of hybrid quantum–classical circuits and the simulation of qubit control and quantum state readout. [ABSTRACT FROM AUTHOR]

The discovery of the Jones polynomial made an important connection between quantum physics and knot theory. Kauffman and Lomonaco introduced the knot mosaic system to define the quantum knot system for the purpose of representing an actual physical quantum system. This paper is inspired by an open question about the knot mosaic enumeration suggested by them. A knot m × n -mosaic is an m × n array of 11 mosaic tiles representing a knot diagram by adjoining properly. The total number D m × n of knot m × n -mosaics, which indicates the dimension of the Hilbert space of the quantum knot system, is known to grow in a quadratic exponential rate. Recently, Oh et al. developed the state matrix recursion method producing the exact enumeration of knot mosaics, which uses a recursion formula of state matrices. Furthermore, they showed the existence of the knot mosaic constant δ = lim m , n → ∞ (D m × n) 1 m n and found its upper and lower bounds in a series of papers. The latest upper bound was obtained through two new concepts: quasimosaics and cling mosaics. As a sequel to this research program, we adjust the state matrix recursion method to handle cling mosaics inside a quasimosaic, which is called the progressive state matrix recursion method. This method provides recursive matrix-relations producing a sharper bound of the knot mosaic constant: 4 ≤ δ ≤ 4. 1 0 3 5 5 0 7 ⋯. [ABSTRACT FROM AUTHOR]

Intraband carrier relaxation in quantum dots (QDs) has been a subject of extensive spectroscopic investigation for several decades, and have been used to optimize the efficiency of opto‐electronic processes. In the past few years, metal halide perovskites‐based QDs have been shown to exhibit slow hot‐carrier cooling characteristics that are desirable for photo‐energy harvesting technologies. While several mechanisms are proposed to rationalize the retardation of the cooling dynamics, including hot‐phonon bottleneck and polaronic effects, the role of inter‐particle connectivity in these dynamics is largely ignored. Here, an in‐depth study of photo‐excitation dynamics and carrier cooling on perovskite QD solids with varying degrees of inter‐dot coupling is presented. It is observed that inter‐particle connectivity has deterministic effects on the many‐body interactions that are relevant for carrier cooling. These include carrier–carrier interactions that result in Auger‐reheating of the carriers, and lattice characteristics that subsequently affect the phonon‐assisted cooling dynamics. This spectroscopic study of ultrafast carrier dynamics in perovskite QD solids establishes inter‐dot separation as a critical material design parameter for the optimization of photo‐generated carrier temperature, which fundamentally determines the luminescence characteristics and thus the opto‐electronic quality of the material. [ABSTRACT FROM AUTHOR]

In this article we investigate no-resonance conditions for quantum many body chaotic systems and random matrix models. No-resonance conditions are properties of the spectrum of a model, usually employed as a theoretical tool in the analysis of late time dynamics. The first order no-resonance condition holds when a spectrum is non-degenerate, while higher order no-resonance conditions imply sums of an equal number of energies are non-degenerate outside of permutations of the indices. This resonance condition is usually assumed to hold for quantum chaotic models. In this work we use several tests from random matrix theory to demonstrate that the statistics of sums of eigenvalues, that are of interest to due to the no-resonance conditions, have Poisson statistics, and lack level repulsion. This result is produced for both a quantum chaotic Hamiltonian as well as the Gaussian Unitary Ensemble and Gaussian Orthogonal Ensemble. This implies some models may have violations of the no-resonance condition or "near" violations. We finish the paper by generalizing important bounds in quantum equilibration theory to cases where the no-resonance conditions are violated, and to the case of random matrix models. [ABSTRACT FROM AUTHOR]

Hands-on experimental experience with quantum systems in the undergraduate physics curriculum provides students with a deeper understanding of quantum physics and equips them for the fast-growing quantum science industry. Here, we present an experimental apparatus for performing quantum experiments with single nitrogen-vacancy (NV) centers in diamond. This apparatus is capable of basic experiments such as single-qubit initialization, rotation, and measurement, as well as more advanced experiments investigating electron–nuclear spin interactions. We describe the basic physics of the NV center and give examples of potential experiments that can be performed with this apparatus. We also discuss the options and inherent trade-offs associated with the choice of diamond samples and hardware. The apparatus described here enables students to write their own experimental control and data analysis software from scratch, all within a single semester of a typical lab course, as well as to inspect the optical components and inner workings of the apparatus. We hope that this work can serve as a standalone resource for any institution that would like to integrate a quantum instructional lab into its undergraduate physics and engineering curriculum. Editor's Note: This paper describes an experimental setup for performing measurements on the nitrogen-vacancy (NV) center in diamond. While three recent AJP papers describe experimental setups for taking measurement on an ensemble of NV centers, this paper takes such studies to the single NV center level. After a review of the basic physics of the NV center, a comprehensive and clear description of a challenging but important set of undergraduate-accessible experiments is presented. These experiments investigate topics including single-qubit initialization, rotation, and measurement as well as advanced studies on electron–nuclear spin interactions. This work will be of interest to those wishing to introduce quantum-related experiments on a forefront research topic in their advanced physics instructional laboratory courses or independent student projects. [ABSTRACT FROM AUTHOR]

Many features of physical systems, both qualitative and quantitative, become sharply defined or tractable only in some limiting situation. Examples are phase transitions in the thermodynamic limit, the emergence of classical mechanics from quantum theory at large action, and continuum quantum field theory arising from renormalization group fixed points. It would seem that few methods can be useful in such diverse applications. However, we here present a flexible modeling tool for the limit of theories, soft inductive limits, constituting a generalization of inductive limits of Banach spaces. In this context, general criteria for the convergence of dynamics will be formulated, and these criteria will be shown to apply in the situations mentioned and more. [ABSTRACT FROM AUTHOR]

The purpose of this study is to address the problem of reconstructing damaged styrene–butadiene–styrene (SBS) molecular structures in order to facilitate the effective recycling of aged SBS-modified asphalt (SBSMA). Traditional experimental methods face challenges when attempting to investigate the reconstruction process and reaction mechanism of aged SBS molecules. To explore the reaction mechanism of aged SBSMA with active rejuvenators and to promote the recycling of aged SBSMA, this study employs molecular dynamics and quantum chemistry to investigate the reconstruction process of the damaged SBS molecular structure using two reactive compounds, namely, methylene diphenyl diisocyanate (MDI) and toluene diisocyanate (TDI), from a molecular perspective. The results showed that the carbon–carbon double bonds in the SBS molecules are susceptible to oxidation, leading to the formation of hydroxyl and carboxyl groups. The reaction between the hydroxyl groups in aged SBS and TDI can spontaneously proceed, while the reaction between the carboxyl groups and MDI can also spontaneously proceed. When the proportion of hydroxyl groups in aged SBS molecules is higher, TDI can be the preferred choice for reconstructing aged SBS molecules. Conversely, when the aged SBS molecules contain more carboxyl groups, MDI can be selected as the better reactive compound. By reconnecting the aged SBS molecules, the need for new SBSMA can be reduced, leading to lower demand for original resources, extended material service life, reduced waste generation, and effective resource recycling. This study provides a new method to explore the problem of SBS molecular structure damage reconstruction and offers a possible mechanism explanation of reaction between aged SBS molecules and reactive compounds. These findings are expected to promote the sustainable development and environmental applications of SBSMA. [ABSTRACT FROM AUTHOR]

By employing a weighted Frobenius norm with a positive definite matrix ω , we introduce natural generalizations of the famous Böttcher-Wenzel (BW) inequality. Based on the combination of the weighted Frobenius norm ▪ and the standard Frobenius norm ▪, there are exactly five possible generalizations, labeled (i) through (v), for the bounds on the norms of the commutator [ A , B ] : = A B − B A. In this paper, we establish the tight bounds for cases (iii) and (v), and propose conjectures regarding the tight bounds for cases (i) and (ii). Additionally, the tight bound for case (iv) is derived as a corollary of case (i). All these bounds (i)-(v) serve as generalizations of the BW inequality. The conjectured bounds for cases (i) and (ii) (and thus also (iv)) are numerically supported for matrices up to size n = 15. Proofs are provided for n = 2 and certain special cases. Interestingly, we find applications of these bounds in quantum physics, particularly in the contexts of the uncertainty relation and open quantum dynamics. [ABSTRACT FROM AUTHOR]

Developing emerging technologies in Internet of Things and artificial intelligence requires high-speed, low-power, high-sensitivity, and switchable-functionality strain sensors capable of sensing subtle mechanical stimuli in complex ambience. Resonant tunneling diodes (RTDs) are the good candidate for such sensing applications due to the ultrafast transport process, lower tunneling current, and negative differential resistance. However, notably enhancing sensing sensitivity remains one of the greatest challenges for RTD-related strain sensors. Here, we use piezotronic effect to improve sensing performance of strain sensors in double-barrier ZnO nanowire RTDs. This strain sensor not only possesses an ultrahigh gauge factor (GF) 390 GPa−1, two orders of magnitude higher than these reported RTD-based strain sensors, but also can switch the sensitivity with a GF ratio of 160 by adjusting bias voltage in a small range of 0.2 V. By employing Landauer–Büttiker quantum transport theory, we uncover two primary factors governing piezotronic modulation of resonant tunneling transport, i.e., the strain-mediated polarization field for manipulation of quantized subband levels, and the interfacial polarization charges for adjustment of space charge region. These two mechanisms enable strain to induce the negative differential resistance, amplify the peak-valley current ratio, and diminish the resonant bias voltage. These performances can be engineered by the regulation of bias voltage, temperature, and device architectures. Moreover, a strain sensor capable of electrically switching sensing performance within sensitive and insensitive regimes is proposed. This study not only offers a deep insight into piezotronic modulation of resonant tunneling physics, but also advances the RTD towards highly sensitive and multifunctional sensor applications. [ABSTRACT FROM AUTHOR]

Ionic liquids (ILs) are promising solvents for separating aromatics from fuel oils. However, studies for separate polycyclic aromatics with ILs are rare and insufficient, and the impact of solute structure on extraction performance still needs to be determined. In this work, we use 1‐ethyl‐3‐methylimidazolium bis([trifluoromethyl]sulfonyl)imide ([EMIM][NTF2]) as an extractant to separate 1‐methylnaphthalene, quinoline, and benzothiophene from dodecane mixtures. Liquid–liquid equilibrium experiments identified the optimal operating conditions. Nine solute molecules, including five alkanes and four aromatic hydrocarbons, were used to study the relationship between extraction performance and solute structure. Molecular dynamics simulation and quantum chemistry calculations gave a deep insight and reasonable interpretation of the structure‐performance relationship at the molecular level. An industrial‐scale extraction process was proposed. The IL can be easily regenerated using heptane as a back‐extractive solvent. A high‐purity fuel oil with aromatic content below 0.5 wt% is obtained after 8‐stage extraction. [ABSTRACT FROM AUTHOR]

In this work, we discuss the use of a recently introduced machine learning (ML) technique known as Fourier neural operators (FNO) as an efficient alternative to the traditional solution of the time‐dependent Schrödinger equation (TDSE). FNOs are ML models which are employed in the approximated solution of partial differential equations. For a wavepacket propagating in an anharmonic potential and for a tunneling system, we show that the FNO approach can accurately and faithfully model wavepacket propagation via the density. Additionally, we demonstrate that FNOs can be a suitable replacement for traditional TDSE solvers in cases where the results of the quantum dynamical simulation are required repeatedly such as in the case of parameter optimization problems (e.g., control). The speed‐up from the FNO method allows for its combination with the Markov‐chain Monte Carlo approach in applications that involve solving inverse problems such as optimal and coherent laser control of the outcome of dynamical processes. [ABSTRACT FROM AUTHOR]

Understanding the training dynamics of quantum neural networks is a fundamental task in quantum information science with wide impact in physics, chemistry and machine learning. In this work, we show that the late-time training dynamics of quantum neural networks with a quadratic loss function can be described by the generalized Lotka-Volterra equations, leading to a transcritical bifurcation transition in the dynamics. When the targeted value of loss function crosses the minimum achievable value from above to below, the dynamics evolve from a frozen-kernel dynamics to a frozen-error dynamics, showing a duality between the quantum neural tangent kernel and the total error. In both regions, the convergence towards the fixed point is exponential, while at the critical point becomes polynomial. We provide a non-perturbative analytical theory to explain the transition via a restricted Haar ensemble at late time, when the output state approaches the steady state. Via mapping the Hessian to an effective Hamiltonian, we also identify a linearly vanishing gap at the transition point. Compared with the linear loss function, we show that a quadratic loss function within the frozen-error dynamics enables a speedup in the training convergence. The theory findings are verified experimentally on IBM quantum devices. Understanding the training dynamics of quantum neural networks is a fundamental task in quantum information science. Here, the authors show how these follow generalized Lotka-Volterra equations, revealing a transition between frozen-kernel, critical point and frozen-error dynamics. Theoretical findings, validated on IBM devices, provide insight to cost function design. [ABSTRACT FROM AUTHOR]

Synchronization of Bloch oscillations in small Josephson junctions (JJs) under microwave radiation, which leads to current quantization, has been proposed as an effect that is dual to the appearance of Shapiro steps. This current quantization was recently demonstrated in superconducting nanowires in a compact high-impedance environment. Direct observation of current quantization in JJs would confirm the synchronization of Bloch oscillations with microwaves and help with the realisation of the metrological current standard. Here, we place JJs in a high-impedance environment and demonstrate dual Shapiro steps for frequencies up to 24 GHz (I = 7.7 nA). Current quantization exists, however, only in a narrow range of JJ parameters. We carry out a systematic study to explain this by invoking the model of a JJ in the presence of thermal noise. The findings are important for fundamental physics and application in quantum metrology. Josephson junctions are used for SQUIDs, voltage standards, and superconducting qubits. These applications are located at one corner of the device parameter space. Here, the authors shed light on the other corner and show the quantized current of Josephson junctions — dual to the quantized voltage. [ABSTRACT FROM AUTHOR]

In this paper, a (t, n) threshold quantum image secret sharing scheme based on combination theory is proposed. Here, the threshold t is a constant number that should satisfy the condition t ≤ n . In sharing process, the secret image is divided into n shadow images according to n sample matrices constructed by the combination theory and sent to n participants individually. During the recovery process, the original secret image can be fully restored if q (q ≥ t) participants are chosen. However, if the number of chosen participants is less than t, no information about the original secret image can be obtained. The quantum matrix multiplier is first introduced for encryption of the secret images. Then the quantum ⋂ gate is chosen for producing sample matrices. In the recovering steps, we use quantum ⋃ gates to collect shadow images. After that, the quantum circuits of the proposed scheme are given and the complexity of the circuits is discussed. We then conduct numerical simulations of our scheme on grayscale images and RGB images. The results shows that our scheme has a good effect on threshold quantum image secret sharing. [ABSTRACT FROM AUTHOR]

Topological defects are discontinuities of a system protected by global properties, with wide applications in mathematics and physics. While previous experimental studies mostly focused on their classical properties, it has been predicted that topological defects can exhibit quantum superposition. Despite the fundamental interest and potential applications in understanding symmetry-breaking dynamics of quantum phase transitions, its experimental realization still remains a challenge. Here, we report the observation of quantum superposition of topological defects in a trapped-ion quantum simulator. By engineering long-range spin-spin interactions, we observe a spin kink splitting into a superposition of kinks at different positions, creating a "Schrodinger kink" that manifests nonlocality and quantum interference. Furthermore, by preparing superposition states of neighboring kinks with different phases, we observe the propagation of the wave packet in different directions, thus unambiguously verifying the quantum coherence in the superposition states. Our work provides useful tools for nonequilibrium dynamics in quantum Kibble-Zurek physics. [ABSTRACT FROM AUTHOR]

We study the representation theory of a hybrid quantum group at root of unity \zeta introduced by Gaitsgory. After discussing some basic properties of its category \mathcal {O}, we study deformations of the category \mathcal {O}. For subgeneric deformations, we construct the endomorphism algebra of big projective object and compute it explicitly. Our main result is an algebra isomorphism between the center of deformed category \mathcal {O} and the equivariant cohomology of \zeta-fixed locus on the affine Grassmannian attached to the Langlands dual group. [ABSTRACT FROM AUTHOR]

In this paper, we briefly survey some developments in gauged linear sigma models (GLSMs). Specifically, we give an overview of progress on constructions of GLSMs for various geometries, GLSM-based computations of quantum cohomology, quantum sheaf cohomology, and quantum K theory rings, as well as two-dimensional abelian and nonabelian mirror constructions. [ABSTRACT FROM AUTHOR]

Several approaches to quantum gravity lead to nonlocal modifications of fields' dynamics. This, in turn, can give rise to nonlocal modifications of quantum mechanics at non-relativistic energies. Here, we analyze the nonlocal Schrödinger evolution of a quantum harmonic oscillator in one such scenario, where the problem can be addressed without the use of perturbation theory. We demonstrate that although deviations from standard quantum predictions occur at low occupation numbers, where they could potentially be detected or constrained by high-precision experiments, the classical limits of quantum probability densities and free energy remain unaffected up to energies comparable with the nonlocality scale. These results provide an example of nonlocal quantum dynamics compatible with classical predictions, suggesting massive quantum objects as a promising avenue for testing some phenomenological aspects of quantum gravity. [ABSTRACT FROM AUTHOR]

Measurement-induced state disturbance is a major challenge in obtaining quantum statistics at multiple time points. We propose a method to extract dynamic information from a quantum system at intermediate time points, namely snapshotting quantum dynamics. To this end, we apply classical post-processing after performing the ancilla-assisted measurements to cancel out the impact of the measurements at each time point. Based on this, we reconstruct a multi-time quasi-probability distribution (QPD) that correctly recovers the probability distributions at the respective time points. Our approach can also be applied to simultaneously extract exponentially many correlation functions with various time-orderings. We provide a proof-of-principle experimental demonstration of the proposed protocol using a dual-species trapped-ion system by employing 171Yb+ and 138Ba+ ions as the system and the ancilla, respectively. Multi-time measurements are performed by repeated initialization and detection of the ancilla state without directly measuring the system state. The two- and three-time QPDs and correlation functions are reconstructed reliably from the experiment, negativity and complex values in the QPDs clearly indicate a contribution of the quantum coherence throughout dynamics. Sequential incompatible measurements on a quantum state would need a full multi-time generalisation of quasiprobability in order to be adequately described. Here, the authors propose such a framework, and test it on a trapped-ion system measuring up to three-time correlation functions. [ABSTRACT FROM AUTHOR]

Quantum Key Distribution (QKD) is a cryptography protocol based on the fundamental principles of quantum physics (QP). Teaching this subject does not require extensive knowledge beyond these principles, making it suitable for inclusion in high school (HS) curricula. Despite its relevance, teaching QKD in HS is yet understudied. In this study, we collected responses from 12th-grade students from various schools that adopted and applied the Discipline-Culture vision of the physics curriculum. We assessed their understanding through conceptual and quantitative problems and examined their attitudes regarding the motivation to study this subject. We analyzed the responses using content analysis, identifying the challenges and affordances of teaching QKD. The challenges faced by students have been categorized into three themes: difficulties with QP, difficulties with the QKD protocol, and difficulties with the mathematics involved in this context. Despite these challenges, we found that teaching QKD reinforces students' conceptual understanding of QP concepts and problem-solving skills. This work enhances educators' ability to address the challenges of teaching QP and suggests that teaching QKD in HS strengthens students' motivation to study QP. [ABSTRACT FROM AUTHOR]

The collisions between Na atoms and H2 molecules are of great significance in the field of chemical reaction dynamics, but the corresponding dynamics results of ground-state reactions have not been reported experimentally or theoretically. Herein, a global and high-precision potential energy surface (PES) of NaH2 (12A′) is constructed by the neural network model based on 21,873 high-level ab initio points. On the newly constructed PES, the quantum dynamics calculations on the Na(2S) + H2(v0 = 0, j0 = 0) → NaH + H reaction are carried out using the time-dependent wave packet method to study the microscopic reaction mechanism at the state-to-state level. The calculated results show that the low-vibrational products are mainly formed by the dissociation of the triatomic complex; whereas, the direct reaction process dominates the generation of the products with high-vibrational states. The reaction generally follows the direct H-abstraction process, and there is also the short-lived complex-forming mechanism that occurs when the collision energy exceeds the reaction threshold slightly. The PES could be used to further study the stereodynamics effects of isotope substitution and rovibrational excitations on the title reaction, and the presented dynamics data would provide an important reference on the corresponding experimental research at a higher level. [ABSTRACT FROM AUTHOR]

In this proof‐of‐concept paper, we show how exchange‐correlation effects can be simply recovered for interatomic energies within the interacting quantum atoms decomposition when local, gradient generalized, or meta‐gradient generalized approximations are used in density functional theory (DFT) calculations. We also demonstrate how inhomogeneity and non‐local effects can be introduced even from a pure local scheme, without resorting to any orbital information. Finally, we provide numerical evidence on a database of selected energetic molecules that this decomposition scheme can be efficiently used to build accurate models for the prediction of molecular energies from an initial "cheap" DFT calculation. [ABSTRACT FROM AUTHOR]

Maintaining quantum coherence and entanglement in the presence of environmental noise, particularly within non-Markovian contexts, represents a significant challenge for the progression of quantum information science and technology. This study offers a substantial advancement by investigating the dynamics of a two-qubit system subjected to diverse noise conditions, encompassing relaxation, dephasing, and their cumulative effects. By employing quantum-state-diffusion equations specifically crafted for non-Markovian environments, we introduce an innovative strategy to counteract the detrimental influences of environmental noise on quantum teleportation fidelity and entanglement concurrence. Our results underscore the potential for external interventions to markedly improve the resilience of quantum information processing tasks over prolonged durations, especially in settings where dephasing noise prevails. A key revelation is the intricate relationship between dephasing noise and the initial state of entanglement, which profoundly impacts the occurrence of entanglement sudden death. This research not only deepens our comprehension of quantum system dynamics under noisy circumstances but also furnishes practical directives for engineering robust quantum systems, a necessity for the development of scalable quantum technologies. [ABSTRACT FROM AUTHOR]

Open-domain question-answering systems need models capable of referencing multiple passages simultaneously to generate accurate answers. The Rational Fusion-in-Decoder (RFiD) model focuses on differentiating between causal relationships and spurious features by utilizing the encoders of the Fusion-in-Decoder model. However, RFiD reliance on partial token information limits its ability to determine whether the corresponding passage is a rationale for the question, potentially leading to inappropriate answers. To address this issue, we propose a Quantum-Inspired Fusion-in-Decoder (QFiD) model. Our approach introduces a Quantum Fusion Module (QFM) that maps single-dimensional into multi-dimensional hidden states, enabling the model to capture more comprehensive token information. Then, the classical mixture method from quantum information theory is used to fuse all information. Based on the fused information, the model can accurately predict the relationship between the question and passage. Experimental results on two prominent ODQA datasets, Natural Questions and TriviaQA, demonstrate that QFiD outperforms the strong baselines in automatic evaluations. [ABSTRACT FROM AUTHOR]

Greenberger-Horne-Zeilinger (GHZ) states, also known as two-component Schrödinger cats, play vital roles in the foundation of quantum physics and the potential quantum applications. Enlargement in size and coherent control of GHZ states are both crucial for harnessing entanglement in advanced computational tasks with practical advantages, which unfortunately pose tremendous challenges as GHZ states are vulnerable to noise. Here we propose a general strategy for creating, preserving, and manipulating large-scale GHZ entanglement, and demonstrate a series of experiments underlined by high-fidelity digital quantum circuits. For initialization, we employ a scalable protocol to create genuinely entangled GHZ states with up to 60 qubits, almost doubling the previous size record. For protection, we take a different perspective on discrete time crystals (DTCs), originally for exploring exotic nonequilibrium quantum matters, and embed a GHZ state into the eigenstates of a tailor-made cat scar DTC to extend its lifetime. For manipulation, we switch the DTC eigenstates with in-situ quantum gates to modify the effectiveness of the GHZ protection. Our findings establish a viable path towards coherent operations on large-scale entanglement, and further highlight superconducting processors as a promising platform to explore nonequilibrium quantum matters and emerging applications. The Greenberger-Horne-Zeilinger states are multipartite entangled quantum states with strong non-local entanglement. Here the authors generate large-scale states of this type with up to 60 qubits and show that discrete time crystals can effectively protect such fragile states. [ABSTRACT FROM AUTHOR]

This work presents a new method called Dimensionless Fluctuation Balance (DFB), which makes it possible to obtain distributions as solutions of Partial Differential Equations (PDEs). In the first case study, DFB was applied to obtain the Boltzmann PDE, whose solution is a distribution for Boltzmann gas. Following, the Planck photon gas in the Radiation Law, Fermi–Dirac, and Bose–Einstein distributions were also verified as solutions to the Boltzmann PDE. The first case study demonstrates the importance of the Boltzmann PDE and the DFB method, both introduced in this paper. In the second case study, DFB is applied to thermal and entropy energies, naturally resulting in a PDE of Boltzmann's entropy law. Finally, in the third case study, quantum effects were considered. So, when applying DFB with Heisenberg uncertainty relations, a Schrödinger case PDE for free particles and its solution were obtained. This allows for the determination of operators linked to Hamiltonian formalism, which is one way to obtain the Schrödinger equation. These results suggest a wide range of applications for this methodology, including Statistical Physics, Schrödinger's Quantum Mechanics, Thin Films, New Materials Modeling, and Theoretical Physics. [ABSTRACT FROM AUTHOR]

The Heisenberg uncertainty relation, together with Robertson's generalisation, serves as a fundamental concept in quantum mechanics, showing that noncommutative pairs of observables cannot be measured precisely. In this study, we explore the Robertson-type uncertainty relations to demonstrate their effectiveness in establishing a series of thermodynamic uncertainty relations and quantum speed limits in open quantum dynamics. The derivation utilises a scaled continuous matrix product state representation that maps the time evolution of the quantum continuous measurement to the time evolution of the system and field. Specifically, we consider the Maccone–Pati uncertainty relation, a refinement of the Robertson uncertainty relation, to derive thermodynamic uncertainty relations and quantum speed limits. These newly derived relations, which use a state orthogonal to the initial state, yield bounds that are tighter than previously known bounds. Moreover, we consider the Robertson–Schrödinger uncertainty, which extends the Robertson uncertainty relation. Our findings not only reinforce the significance of the Robertson-type uncertainty relations, but also expand its applicability in identifying uncertainty relations in open quantum dynamics. [ABSTRACT FROM AUTHOR]

Engines are systems and devices that convert one form of energy into another, typically into a more useful form that can perform work. In the classical setup, physical, chemical, and biological engines largely involve the conversion of heat into work. This energy conversion is at the core of thermodynamic laws and principles and is codified in textbook material. In the quantum regime, however, the principles of energy conversion become ambiguous, since quantum phenomena come into play. As with classical thermodynamics, fundamental principles can be explored through engines and refrigerators, but, in the quantum case, these devices are miniaturized and their operations involve uniquely quantum effects. Our work provides a broad overview of this active field of quantum engines and refrigerators, reviewing the latest theoretical proposals and experimental realizations. We cover myriad aspects of these devices, starting with the basic concepts of quantum analogs to the classical thermodynamic cycle and continuing with different quantum features of energy conversion that span many branches of quantum mechanics. These features include quantum fluctuations that become dominant in the microscale, non-thermal resources that fuel the engines, and the possibility of scaling up the working medium's size, to account for collective phenomena in many-body heat engines. Furthermore, we review studies of quantum engines operating in the strong system–bath coupling regime and those that include non-Markovian phenomena. Recent advances in thermoelectric devices and quantum information perspectives, including quantum measurement and feedback in quantum engines, are also presented. • Quantum Engines link quantum phenomena with nonequilibrium thermodynamics. • The role of quantum fluctuations, non-Markovianity, and strong coupling in energy conversion. • Many-body systems and non-thermal baths are building blocks of Quantum Engines. • Recent developments in thermoelectric devices open new experimental possibilities. • Quantum correlation measurements and feedback can serve as resources for work extraction and cooling. [Display omitted] [ABSTRACT FROM AUTHOR]

In quantum systems, a counterintuitive phenomenon known as quantum Zeno dynamics is usually exploited to tailor and protect the coherent evolution of quantum states by the back action of quantum measurements and strong couplings. Here, with the quantum-classical analogy, we report that the acoustic Zeno dynamics can be reproduced in acoustic waveguide arrays by setting segmented waveguides. We experimentally demonstrate that the segmented waveguide acts as an acoustic barrier to tailor the whole Hilbert space into different subspaces by separating the communication between waveguides. By arranging the acoustic Zeno barriers, we can control the sound transport in waveguide arrays into the target output ports, such as the Zeno dynamics, analog-quantum walk, and analog-quantum logic gates. In this context, we highlight that the Zeno barrier can be a versatile tool to arbitrarily control and guide the sound transport in waveguide arrays, which can provide an alternative choice for acoustic metamaterials and metasurfaces without cumbersome and complicated structure design. The acoustic Zeno barrier may provide a versatile approach to manipulate acoustic wave propagation for designing advanced on-chip integrated sound devices. [ABSTRACT FROM AUTHOR]

Noisy Intermediate-Scale Quantum (NISQ) devices lack error correction, limiting scalability for quantum algorithms. In this context, digital-analog quantum computing (DAQC) offers a more resilient alternative quantum computing paradigm that outperforms digital quantum computation by combining the flexibility of single-qubit gates with the robustness of analog simulations. This work explores the impact of noise on both digital and DAQC paradigms and demonstrates DAQC's effectiveness in error mitigation. We compare the quantum Fourier transform and quantum phase estimation algorithms under a wide range of single and two-qubit noise sources in superconducting processors. DAQC consistently surpasses digital approaches in fidelity, particularly as processor size increases. Moreover, zero-noise extrapolation further enhances DAQC by mitigating decoherence and intrinsic errors, achieving fidelities above 0.95 for 8 qubits, and reducing computation errors to the order of 10−3. These results establish DAQC as a viable alternative for quantum computing in the NISQ era. The authors explore the digital-analog quantum computing paradigm, which combines fast single-qubit gates with the natural dynamics of quantum devices. They find the digital-analog paradigm more robust against certain experimental imperfections than the standard fully-digital one and successfully apply error mitigation techniques to this approach. [ABSTRACT FROM AUTHOR]

In this paper, we propose an effective scheme for rapidly implementing π phase gate in a two-distant-atom–cavity system by combining superadiabatic scheme and quantum Zeno dynamics to construct shortcuts to adiabatic passage. As a typical application of the fast phase gates, a creation of N-atom cluster states is put forward. The influence of various decoherence processes such as atomic spontaneous emission and cavity decay on the fidelity is discussed. Numerical simulations show that the scheme is robust against decoherence caused by atomic spontaneous emission and cavity decay. In this work, superadiabatic shortcuts are used to prepare cluster states for the first time, which is faster than the traditional adiabatic passage technique. [ABSTRACT FROM AUTHOR]

Classical General Relativity is a dynamical theory of spacetime metrics of Lorentzian signature. In particular the classical metric field is nowhere degenerate in spacetime. In its initial value formulation with respect to a Cauchy surface the induced metric is of Euclidian signature and nowhere degenerate on it. It is only under this assumption of non-degeneracy of the induced metric that one can derive the hypersurface deformation algebra between the initial value constraints which is absolutely transparent from the fact that the inverse of the induced metric is needed to close the algebra. This statement is independent of the density weight that one may want to equip the spatial metric with. Accordingly, the very definition of a non-anomalous representation of the hypersurface deformation algebra in quantum gravity has to address the issue of non-degeneracy of the induced metric that is needed in the classical theory. In the Hilbert space representation employed in Loop Quantum Gravity (LQG) most emphasis has been laid to define an inverse metric operator on the dense domain of spin network states although they represent induced quantum geometries which are degenerate almost everywhere. It is no surprise that demonstration of closure of the constraint algebra on this domain meets difficulties because it is a sector of the quantum theory which is classically forbidden and which lies outside the domain of definition of the classical hypersurface deformation algebra. Various suggestions for addressing the issue such as non-standard operator topologies, dual spaces (habitats) and density weights have been proposed to address this issue with respect to the quantum dynamics of LQG. In this article we summarise these developments and argue that insisting on a dense domain of non-degenerate states within the LQG representation may provide a natural resolution of the issue thereby possibly avoiding the above mentioned non-standard constructions. [ABSTRACT FROM AUTHOR]

In the present work, we study the initial moments of a homogeneous and isotropic Friedmann-Lemaître-Robertson-Walker (FLRW) cosmological model, considering Hořava-Lifshitz (HL) as the gravitational theory. The matter content of the model is a radiation perfect fluid. In order to study the initial moments of the universe in the present model, we consider quantum cosmology. More precisely the quantum mechanical tunneling mechanism. In that mechanism, the universe appears after the wavefunction associated to that universe tunnels through a potential barrier. We started studying the classical model. We draw the phase portrait of the model and identify qualitatively all types of dynamical behaviors associated to it. Then, we write the Hamiltonian of the model and apply the Dirac quantization procedure to quantize a constrained theory. We find the appropriate Wheeler-DeWitt equation and solve it using the Wentzel-Kramers-Brillouin (WKB) approximation. Using the WKB solution, to the Wheeler-DeWitt equation, we compute the tunneling probabilities for the birth of that universe ( T P WKB ). Since the WKB wavefunction depends on the radiation energy (E) and the free parameters coming from the HL theory ( g c , g r , g s , g Λ ), we compute the behavior of T P WKB as a function of E and all the HL's parameters g c , g r , g s , g Λ . As a new result, due to the HL theory, we notice that, in the present model, the universe cannot tunnel through the barrier close to the origin. It happens because that tunneling probability is nil. Therefore, here, the universe cannot starts from a zero size and is free from the big bang singularity. [ABSTRACT FROM AUTHOR]