Recently proposed correlation-matrix based sufficient conditions for bipartite steerability from Alice to Bob are applied to local informationally complete positive operator valued measures (POVMs) of the $(N,M)$-type. These POVMs allow for a unified description of a large class of local generalized measurements of current interest. It is shown that this sufficient condition exhibits a peculiar scaling property. It implies that all types of informationally complete $(N,M)$-POVMs are equally powerful in detecting bipartite steerability from Alice to Bob and, in addition, they are as powerful as local orthonormal hermitian operator bases (LOOs). In order to explore the typicality of steering numerical calculations of lower bounds on Euclidean volume ratios between steerable bipartite quantum states from Alice to Bob and all quantum states are determined with the help of a hit-and-run Monte-Carlo algorithm. These results demonstrate that with the single exception of two qubits this correlation-matrix based sufficient condition significantly underestimates these volume ratios. These results are also compared with a recently proposed method which reduces the determination of bipartite steerability from Alice's qubit to Bob's arbitrary dimensional quantum system to the determination of bipartite entanglement. It is demonstrated that in general this method is significantly more effective in detecting typical steerability provided entanglement detection methods are used which transcend local measurements.

Building on the development of momentum state lattices (MSLs) over the past decade, we introduce a simple extension of this technique to higher dimensions. Based on the selective addressing of unique Bragg resonances in matter-wave systems, MSLs have enabled the realization of tight-binding models with tunable disorder, gauge fields, non-Hermiticity, and other features. Here, we examine and outline an experimental approach to building scalable and tunable tight-binding models in two dimensions describing the laser-driven dynamics of atoms in momentum space. Using numerical simulations, we highlight some of the simplest models and types of phenomena this system is well-suited to address, including flat-band models with kinetic frustration and flux lattices supporting topological boundary states. Finally, we discuss many of the direct extensions to this model, including the introduction of disorder and non-Hermiticity, which will enable the exploration of new transport and localization phenomena in higher dimensions.

Entropic uncertainty relations are interesting in their own rights as well as for a lot of applications. Keeping this in mind, we try to make the corresponding inequalities as tight as possible. The use of parametrized entropies also allows one to improve relations between various information measures. Measurements of special types are widely used in quantum information science. For many of them we can estimate the index of coincidence defined as the total sum of squared probabilities. Inequalities between entropies and the index of coincidence form a long-standing direction of researches in classical information theory. The so-called information diagrams provide a powerful tool to obtain inequalities of interest. In the literature, results of such a kind mainly deal with standard information functions linked to the Shannon entropy. At the same time, generalized information functions have found use in questions of quantum information theory. In effect, R\'{e}nyi and Tsallis entropies and related functions are of a separate interest. This paper is devoted to entropic uncertainty relations derived from information diagrams. The obtained inequalities are then applied to mutually unbiased bases, symmetric informationally complete measurements and their generalizations. We also improve entropic uncertainty relations for quantum measurement assigned to an equiangular tight frame.

We study the heat transfer between N coupled quantum resonators with applied synthetic electric and magnetic fields realized by changing the resonators parameters by external drivings. To this end we develop two general methods, based on the quantum optical master equation and on the Langevin equation for $N$ coupled oscillators where all quantum oscillators can have their own heat baths. The synthetic electric and magnetic fields are generated by a dynamical modulation of the oscillator resonance with a given phase. Using Floquet theory we solve the dynamical equations with both methods which allow us to determine the heat flux spectra and the transferred power. With apply these methods to study the specific case of a linear tight-binding chain of four quantum coupled resonators. We find that in that case, in addition to a non-reciprocal heat flux spectrum already predicted in previous investigations, the synthetic fields induce here non-reciprocity in the total heat flux hence realizing a net heat flux rectification.

Within a strongly interacting Fermi liquid framework, we calculate the effects of the Zeeman energy $\omega_H$ for a finite magnetic field, in a metallic system with a van Hove peak in the density of states, located close to and below the Fermi surface. We find that the chemical potential increases with the square of $\omega_H$. We obtain a characteristic quasiparticle scattering rate linear in the maximum of $\omega_H$ and temperature, both in the normal and the d-wave superconducting state. We predict that ARPES experiments should be able to elucidate this behavior of the scattering rate, and in particular, the difference between spin up and down electrons.

Quantum learning paradigms address the question of how best to harness conceptual elements of quantum mechanics and information processing to improve operability and functionality of a computing system for specific tasks through experience. It is one of the fastest evolving framework, which lies at the intersection of physics, statistics and information processing, and is the next frontier for data sciences, machine learning and artificial intelligence. Progress in quantum learning paradigms is driven by multiple factors: need for more efficient data storage and computational speed, development of novel algorithms as well as structural resonances between specific physical systems and learning architectures. Given the demand for better computation methods for data-intensive processes in areas such as advanced scientific analysis and commerce as well as for facilitating more data-driven decision-making in education, energy, marketing, pharmaceuticals and health-care, finance and industry.

State preparation for quantum algorithms is crucial for achieving high accuracy in quantum chemistry and competing with classical algorithms. The localized active space unitary coupled cluster (LAS-UCC) algorithm iteratively loads a fragment-based multireference wave function onto a quantum computer. In this study, we compare two state preparation methods, quantum phase estimation (QPE) and direct initialization (DI), for each fragment. We analyze the impact of QPE parameters, such as the number of ancilla qubits and Trotter steps, on the prepared state. We find a trade-off between the methods, where DI requires fewer resources for smaller fragments, while QPE is more efficient for larger fragments. Our resource estimates highlight the benefits of system fragmentation in state preparation for subsequent quantum chemical calculations. These findings have broad applications for preparing multireference quantum chemical wave functions on quantum circuits, particularly via QPE circuits.

In quantum mechanics, bosonic operators are mathematical objects that are used to represent the creation ($a^\dagger$) and annihilation ($a$) of bosonic particles. The natural power of a linear combination of bosonic operators represents an operator $(a^\dagger x+ay)^n$ with $n$ as the exponent and $x,\,y$ are the variables free from bosonic operators. The normal ordering of these operators is a mathematical technique that arranges the operators so that all the creation operators are to the left of the annihilation operators, reducing the number of terms in the expression. In this paper, we present a general expansion of the natural power of a linear combination of bosonic operators in normal order. We show that the expansion can be expressed in terms of binomial coefficients and the product of the normal-ordered operators using the direct method and than prove it using the fundamental principle of mathematical induction. We also derive a formula for the coefficients of the expansion in terms of the number of bosons and the commutation relation between the creation and annihilation operators. Our results have important applications in the study of many-body systems in quantum mechanics, such as in the calculation of correlation functions and the evaluation of the partition function. The general expansion presented in this paper provides a powerful tool for analyzing and understanding the behavior of bosonic systems, and can be applied to a wide range of physical problems.

We show that quantum graph parameters for finite, simple, undirected graphs encode winning strategies for all possible synchronous non-local games. Given a synchronous game $\mathcal{G}=(I,O,\lambda)$ with $|I|=n$ and $|O|=k$, we demonstrate what we call a weak $*$-equivalence between $\mathcal{G}$ and a $3$-coloring game on a graph with at most $3+n+9n(k-2)+6|\lambda^{-1}(\{0\})|$ vertices, strengthening and simplifying work implied by Z. Ji (arXiv:1310.3794) for winning quantum strategies for synchronous non-local games. As an application, we obtain a quantum version of L. Lov\'{a}sz's reduction (Proc. 4th SE Conf. on Comb., Graph Theory & Computing, 1973) of the $k$-coloring problem for a graph $G$ with $n$ vertices and $m$ edges to the $3$-coloring problem for a graph with $3+n+9n(k-2)+6mk$ vertices. We also show that, for ``graph of the game" $X(\mathcal{G})$ associated to $\mathcal{G}$ from A. Atserias et al (J. Comb. Theory Series B, Vol. 136, 2019), the independence number game $\text{Hom}(K_{|I|},\overline{X(\mathcal{G})})$ is hereditarily $*$-equivalent to $\mathcal{G}$, so that the possibility of winning strategies is the same in both games for all models, except the game algebra. Thus, the quantum versions of the chromatic number, independence number and clique number encode winning strategies for all synchronous games in all quantum models.

This work aims to shed some light on the meaning of the positive energy assumption in relativistic quantum theory and its relation to questions of localization of quantum systems. It is shown that the positive energy property of solutions of relativistic wave equations (such as the Dirac equation) is very fragile with respect to state transformations beyond free time evolution. Paying attention to the connection between negative energy Dirac wave functions and pair creation processes in second quantization, this analysis leads to a better understanding of a class of problems known as the localization problem of relativistic quantum theory (associated for instance with famous results of Newton and Wigner, Reeh and Schlieder, Hegerfeldt or Malament). Finally, this analysis is reflected from the perspective of a Bohmian quantum field theory.

We compare the lower and higher order non-classicality of a class of the photon-added Bell-type entangled coherent states (PBECS) got from Bell-type entangled coherent states using creation operators. We obtained lower and higher order criteria namely Mandel's $Q_m^l$, antibunching $d_h^{l-1}$, Subpoissioning photon statistics $D_h(l-1)$ and Squeezing $S(l)$ for the states obtained. Further we observe that first three criteria does not gives non-classicality for any state and higher order criteria gives very high positive values for all values of parameters. Also the fourth or last criterion $S(l)$ gives non-classicality for lower order as well as higher order.

We present a systematic study of the nonlinear thermal Hall responses in bosonic systems using the quantum kinetic theory framework. We demonstrate the existence of an intrinsic nonlinear boson thermal current, arising from the quantum metric which is a wavefunction dependent band geometric quantity. In contrast to the nonlinear Drude and nonlinear anomalous Hall contributions, the intrinsic nonlinear thermal conductivity is independent of the scattering timescale. We demonstrate the dominance of this intrinsic thermal Hall response in topological magnons in a two-dimensional ferromagnetic honeycomb lattice without Dzyaloshinskii-Moriya interaction. Our findings highlight the significance of band geometry induced nonlinear thermal transport and motivate experimental probe of the intrinsic nonlinear thermal Hall response with implications for quantum magnonics.

The controlled-SWAP and controlled-controlled-NOT gates are at the heart of the original proposal of reversible classical computation by Fredkin and Toffoli. Their widespread use in quantum computation, both in the implementation of classical logic subroutines of quantum algorithms and in quantum schemes with no direct classical counterparts, have made it imperative early on to pursue their efficient decomposition in terms of the lower-level gate sets native to different physical platforms. Here, we add to this body of literature by providing several logically equivalent CNOT-count-optimal circuits for the Toffoli and Fredkin gates under all-to-all and linear qubit connectivity, the latter with two different routings for control and target qubits. We then demonstrate how these decompositions can be employed on near-term quantum computers to mitigate coherent errors via equivalent circuit averaging. We also consider the case where the three qubits on which the Toffoli or Fredkin gates act nontrivially are not adjacent, proposing a novel scheme to reorder them that saves one CNOT for every SWAP. This scheme also finds use in the shallow implementation of long-range CNOTs. Our results highlight the importance of considering different entanglement structures and connectivity constraints when designing efficient quantum circuits.

We study the entanglement dynamics of quantum automaton (QA) circuits in the presence of U(1) symmetry. We find that the second R\'enyi entropy grows diffusively with a logarithmic correction as $\sqrt{t\ln{t}}$, saturating the bound established by Huang [IOP SciNotes 1, 035205 (2020)]. Thanks to the special feature of QA circuits, we understand the entanglement dynamics in terms of a classical bit string model. Specifically, we argue that the diffusive dynamics stems from the rare slow modes containing extensively long domains of spin 0s or 1s. Additionally, we investigate the entanglement dynamics of monitored QA circuits by introducing a composite measurement that preserves both the U(1) symmetry and properties of QA circuits. We find that as the measurement rate increases, there is a transition from a volume-law phase where the second R\'enyi entropy persists the diffusive growth (up to a logarithmic correction) to a critical phase where it grows logarithmically in time. This interesting phenomenon distinguishes QA circuits from non-automaton circuits such as U(1)-symmetric Haar random circuits, where a volume-law to an area-law phase transition exists, and any non-zero rate of projective measurements in the volume-law phase leads to a ballistic growth of the R\'enyi entropy.

Lattice QCD in the strong coupling regime can be formulated in dual variables which are integer-valued. It can be efficiently simulated for modest finite temperatures and finite densities via the Worm algorithm, circumventing the finite density sign problem in this regime. However, the low temperature regime is more expensive to address. As the partition function is solely expressed in terms of integers, it is well suited to be studied on the D-Wave quantum annealer. We will first explain the setup of the system we want to study, and then present its reformulation suitable for a quantum annealer, and in particular the D-Wave. As a proof of concept, we present first results obtained on D-Wave for gauge group $U(1)$ and outline the next steps towards gauge groups $U(3)$ and $SU(3)$. We find that in addition, histogram reweighting greatly improves the accuracy of our observables when compared to analytic results.

Herein, the dynamics of excitons coupled with optical phonons in a triangular system is numerically studied. By representing the excitons by quasi-spin states, the similarity between the chiral spin states and the exciton chiral states is discussed. In particular, the optical control of excitons is discussed, where photoirradiation causes the switching of the exciton states on the ultrafast time scale by Raman scattering. A phase diagram is obtained based on the ground-state properties of the system determined by the magnitudes of the exciton-phonon interactions and exciton transfer energy. By varying the frequency and/or intensity of light, a transition between exciton-phonon composite states is induced, which suggests the possibility of the coherent control of the chiral properties of excitonic systems via phonon excitation.

The realization of quantum gates in topological quantum computation still confronts significant challenges in both fundamental and practical aspects. Here, we propose a deterministic and fully topologically protected measurement-based scheme to realize the issue of implementing Clifford quantum gates on the Majorana qubits. Our scheme is based on rigorous proof that the single-qubit gate can be performed by leveraging the neighboring Majorana qubit but not disturbing its carried quantum information, eliminating the need for ancillary Majorana zero modes (MZMs) in topological quantum computing. Benefiting from the ancilla-free construction, we show the minimum measurement sequences with four steps to achieve two-qubit Clifford gates by constructing their geometric visualization. To avoid the uncertainty of the measurement-only strategy, we propose manipulating the MZMs in their parameter space to correct the undesired measurement outcomes while maintaining complete topological protection, as demonstrated in a concrete Majorana platform. Our scheme identifies the minimal operations of measurement-based topological and deterministic Clifford gates and offers an ancilla-free design of topological quantum computation.

This paper presents a novel approach to probabilistic deep learning (PDL), quantum kernel mixtures, derived from the mathematical formalism of quantum density matrices, which provides a simpler yet effective mechanism for representing joint probability distributions of both continuous and discrete random variables. The framework allows for the construction of differentiable models for density estimation, inference, and sampling, enabling integration into end-to-end deep neural models. In doing so, we provide a versatile representation of marginal and joint probability distributions that allows us to develop a differentiable, compositional, and reversible inference procedure that covers a wide range of machine learning tasks, including density estimation, discriminative learning, and generative modeling. We illustrate the broad applicability of the framework with two examples: an image classification model, which can be naturally transformed into a conditional generative model thanks to the reversibility of our inference procedure; and a model for learning with label proportions, which is a weakly supervised classification task, demonstrating the framework's ability to deal with uncertainty in the training samples.

Understanding the hydrogen atom has been at the heart of modern physics. Exploring the symmetry of the most fundamental two body system has led to advances in atomic physics, quantum mechanics, quantum electrodynamics, and elementary particle physics. In this pedagogic review we present an integrated treatment of the symmetries of the Schrodinger hydrogen atom, including the classical atom, the SO(4) degeneracy group, the non-invariance group or spectrum generating group SO(4,1) and the expanded group SO(4,2). After giving a brief history of these discoveries, most of which took place from 1935-1975, we focus on the physics of the hydrogen atom, providing a background discussion of the symmetries, providing explicit expressions for all the manifestly Hermitian generators in terms of position and momenta operators in a Cartesian space, explaining the action of the generators on the basis states, and giving a unified treatment of the bound and continuum states in terms of eigenfunctions that have the same quantum numbers as the ordinary bound states. We present some new results from SO(4,2) group theory that are useful in a practical application, the computation of the first order Lamb shift in the hydrogen atom. By using SO(4,2) methods, we are able to obtain a generating function for the radiative shift for all levels. Students, non-experts and the new generation of scientists may find the clearer, integrated presentation of the symmetries of the hydrogen atom helpful and illuminating. Experts will find new perspectives, even some surprises.

We present a semiclassical approach for time delay statistics in quantum chaotic systems, in the presence of absorption, for broken time-reversal symmetry. We derive three kinds of expressions for Schur-moments of the time delay operator: as a power series in inverse channel number, $1/M$, whose coefficients are rational functions of absorption time, $\tau_a$; as a power series in $\tau_a$, tailored to strong absorption, whose coefficients are rational functions of $M$; as a power series in $1/\tau_a$, tailored to weak absorption, whose coefficients are rational functions of $M$.