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In this paper, we investigate the time evolution of quantum coherence—the off-diagonal elements of the density matrix of a multistate quantum system—from the perspective of the Wigner–Moyal formalism. This approach provides an exact phase space representation of quantum mechanics. We consider the coherent evolution of nuclear wavepackets in a molecule with two electronic states. For harmonic potentials, the problem is analytically soluble for both a fully quantum mechanical description and a semiclassical description. We highlight the serious deficiencies of the semiclassical treatment of coherence for general systems and illustrate how even qualitative accuracy requires higher order terms in the Moyal expansion to be included. The model provides an experimentally relevant example of a molecular Schrödinger's cat state. The alive and dead cats of the exact two-state quantum evolution collapse into a "zombie" cat in the semiclassical limit—an averaged behavior, neither alive nor dead, leading to significant errors. The inclusion of the Moyal correction restores a faithful simultaneously alive and dead representation of the cat that is experimentally observable. [ABSTRACT FROM AUTHOR]

Fewest-switches surface hopping (FSSH) has emerged as one of the leading methods for modeling the quantum dynamics of molecular systems. While its original formulation was limited to adiabatic populations, the growing interest in the application of FSSH to coherent phenomena prompts the question of how one should construct a complete density matrix based on FSSH trajectories. A straightforward solution is to define adiabatic coherences based on wavefunction coefficients. In this paper, we demonstrate that inconsistencies introduced in the density matrix through such treatment may lead to a violation of positivity. We furthermore show that a recently proposed coherent generalization of FSSH results in density matrices that satisfy positivity while yielding improved accuracy throughout much (but not all) of parameter space. [ABSTRACT FROM AUTHOR]

The approach to question answering is challenging because it usually requires finding useful information from within and between question and answer sentences for sentence semantic matching. The key information mined from existing question and answer sentences, as a supplement to semantic information, maybe helpful for this task. However, capturing the intra-sentence and inter-sentence semantic interactions is somewhat difficult given the implicit interrelationships between question and answer sentences. Although the learning effect of multi-layer neural network is good, it lacks explanatory and theoretical support. This paper mainly studies how to select the best answer sentence from a set of question and answer sentences, mine information more effectively, perform semantic matching, and have a certain interpretability. Therefore, we propose a hierarchical attention network (QHAN) based on the mathematical framework of quantum theory, which integrates the attention mechanism under quantum measurement and density matrix (DMATT) and the attention mechanism under quantum weak measurement and weak value (WMATT) in one in a unified model framework. QHAN can not only discover key sentences in a set of question and answer sentences and key words in a sentence, but also perform sentence semantic matching quickly and accurately. Furthermore, QHAN has the advantage of interpretability in terms of models due to the physical meaning and attentional full weight distribution implied by quantum theory. Extensive experiments on the question answering dataset show that our method is comparable to the baselines and can explain why the selected question and answer sentence is the best option in terms of intra-sentence and inter-sentence attention distributions. [ABSTRACT FROM AUTHOR]

The generalized quantum master equation (GQME) provides a general and formally exact framework for simulating the reduced dynamics of open quantum systems. The recently introduced modified approach to the GQME (M-GQME) corresponds to a specific implementation of the GQME that is geared toward simulating the dynamics of the electronic reduced density matrix in systems governed by an excitonic Hamiltonian. Such a Hamiltonian, which is often used for describing energy and charge transfer dynamics in complex molecular systems, is given in terms of diabatic electronic states that are coupled to each other and correspond to different nuclear Hamiltonians. Within the M-GQME approach, the effect of the nuclear degrees of freedom on the time evolution of the electronic density matrix is fully captured by a memory kernel superoperator, which can be obtained from short-lived (compared to the time scale of energy/charge transfer) projection-free inputs. In this paper, we test the ability of the M-GQME to predict the energy transfer dynamics within a seven-state benchmark model of the Fenna–Matthews–Olson (FMO) complex, with the short-lived projection-free inputs obtained via the Ehrenfest method. The M-GQME with Ehrenfest-based inputs is shown to yield accurate results across a wide parameter range. It is also found to dramatically outperform the direct application of the Ehrenfest method and to provide better-behaved convergence with respect to memory time in comparison to an alternative implementation of the GQME approach previously applied to the same FMO model. [ABSTRACT FROM AUTHOR]

The time dependent density matrix renormalization group (TD-DMRG) has become one of the cutting edge methods of quantum dynamics for complex systems. In this paper, we comparatively study the accuracy of three time evolution schemes in the TD-DMRG, the global propagation and compression method with the Runge-Kutta algorithm (P&C-RK), the time dependent variational principle based methods with the matrix unfolding algorithm (TDVP-MU), and with the projector-splitting algorithm (TDVP-PS), by performing benchmarks on the exciton dynamics of the Fenna-Matthews-Olson complex. We show that TDVP-MU and TDVP-PS yield the same result when the time step size is converged and they are more accurate than P&C-RK4, while TDVP-PS tolerates a larger time step size than TDVP-MU. We further adopt the graphical processing units to accelerate the heavy tensor contractions in the TD-DMRG, and it is able to speed up the TDVP-MU and TDVP-PS schemes by up to 73 times. [ABSTRACT FROM AUTHOR]

The molecular dynamics following the electronic B Π u 3 0 + ⟵ X Σ g + 1 photoexcitation of the iodine molecule embedded in solid krypton are studied quantum mechanically using the Gaussian variant of the multiconfigurational time-dependent Hartree method (G-MCTDH). The accuracy of the Gaussian wave packet approximation is validated against numerically exact MCTDH simulations for a fully anharmonic seven-dimensional model of the I2Kr18 cluster in a crystal Kr cage. The linear absorption spectrum, time-evolving vibrational probability densities, and I2 energy expectation value are accurately reproduced by the numerically efficient G-MCTDH approach. The reduced density matrix of the chromophore is analyzed in the coordinate, Wigner and energy representations, so as to obtain a multifaceted dynamical view of the guest-host interactions. Vibrational coherences extending over the bond distance range 2.7 Å < RI–I < 4.0 Å are found to survive for several vibrational periods, despite extensive dissipation. The present results prepare the ground for the simulation of time-resolved coherent Raman spectroscopy of the I2-krypton system addressed in Paper II. [ABSTRACT FROM AUTHOR]

The density matrix model described in an earlier paper "Model Dynamics for Quantum Computing" is applied to the case of two qubits. The earlier paper provided a density matrix dynamics with unitary time-dependent gates including qubit energy splitting, entropy constraints, external bath and noise effects. The Lindblad formulation as extended by Beretta was adopted in designing this model. Visualization was provided by examining the time-evolution of the polarization vector. In this paper, the same ideas are applied to two-qubit systems, where there are now 15 time-dependent observables; namely, six polarization vectors ( P → A , P → B) , and nine spin-correlations (T ↔). These time-dependent observables provide ready visualization of two qubit dynamics. Special emphasis is placed on the CNOT gate, which is implemented following recent outstanding developments in using silicon-based dots. By invoking a different splitting for each qubit, plus a spin–spin interaction and a carefully designed Rabi oscillation, a CNOT gate is generated. Careful analysis of the time-dependence of these aspects provides insight into CNOT dynamics. The model can be used to ascertain the sensitivity and efficacy of such a CNOT gate when subject to external environmental effects such as noise disturbances, and noise compensation, using the single-system formulation of steepest-entropy-ascent (SEA) non-equilibrium quantum thermodynamics, suitable to model controlled-gate implementations as long as the two qubits remain localized and effectively behave as a single physical four-level system. The role of careful timing in constructing an efficient CNOT gate is illustrated. The formation of Bell states and the evolution of entanglement including noise, bath and entropy considerations are examined. Extensions to the two-qubit swap, and to the three-qubit Toffoli gate dynamics are outlined. It is also shown that a simple Lindblad form can be used to introduce weak and distinct qubit noise pulses. A simple scheme for noise compensation is designed to increase purity and decrease entropy, without invocation of quantum correction methodology. It is based on using the preexisting entanglement of the environment with the quantum system and carefully designed non-Hermitian Lindblad pulses. • Density matrix evolution with dissipation and entropy. • Control gates for two qubits. • Noise and Noise Compensation using Lindblad operators. • Steepest-entropy-ascent quantum thermodynamics. • Equilibrium in quantum thermodynamics. [ABSTRACT FROM AUTHOR]

The modular path integral (MPI) formulation offers a numerically exact, versatile, and highly efficient approach to the quantum dynamics of extended systems characterised by a single-file arrangement of units with short-range interactions, such as hydrocarbons, molecular aggregates with exciton couplings, or spin chains. Rather than propagating the many-particle wavefunction or density matrix in time in the usual stepwise fashion, the MPI scheme proceeds by sequentially integrating over each unit after linking its quantum paths to those of its neighbour and leads to linear scaling with system length. This paper shows that the linking matrix can be further decomposed into a diagonal matrix and a product of low-dimensional matrices, which can be applied sequentially. This factorisation changes the cost scaling from L2 to L log ⁡ L , where L is the number of quantum paths, leading to dramatic savings that are analogous to those attained by the fast Fourier transform algorithm and allowing application of the MPI procedure to systems with larger units and to longer propagation times. Applications to spin chains and to electron-vibration dynamics in a large molecular aggregate illustrate the efficiency of the algorithm. [ABSTRACT FROM AUTHOR]

Sentiment analysis, which can discriminate the sentiment tendency of subjective texts, is one of the important research works in the field of natural language processing. Sentiment analysis can be divided into explicit sentiment analysis and implicit sentiment analysis according to whether the text contains explicit sentiment words. Most of the current research work focuses on explicit sentiment analysis, while implicit sentiment analysis has become one of the most challenging research tasks because the sentiment characteristics are too implicit. In this paper, "Fused with Sememe Knowledge Quantum-like Chinese Implicit Sentiment Analysis (FSKQ)" is proposed, which introduces the density matrix in quantum theory and takes sememe, the smallest common sense semantic unit in natural language, as an external knowledge base to build a sememe-based density matrix. The matrix can be regarded as a complete knowledge system with strong generalization, which models the global information of the most fine-grained semantic knowledge. Its incorporation into the text vector results in a high quality of text representation, which effectively improves the performance of the model in Chinese implicit sentiment analysis. Ablation experiments and comparison experiments are conducted in the SMP ECISA2019 dataset, and the results show that the F1 score of the model is improved by 2.6% compared with the best model, which proves the effectiveness and superiority of the idea. In addition, in order to verify the performance of the proposed method in terms of text representation quality, it is also applied to existing models in the aspect-level sentiment analysis and event detection, and it is compared with the original model without using the idea and the baseline model on Twitter, Lap14, Rest14/15/16 and ACE2005 datasets. The results show that compared with the original model and the baseline model in this field, the model combined with the idea improves the accuracy and F1 score, which further proves the effectiveness, superiority and generalization of the FSKQ model. [ABSTRACT FROM AUTHOR]

The nonequilibrium dynamics in chaotic quantum systems denies a fully understanding up to now, even if thermalization in the long-time asymptotic state has been explained by the eigenstate thermalization hypothesis which assumes a universal form of the observable matrix elements in the eigenbasis of Hamiltonian. It was recently proposed that the density matrix elements have also a universal form, which can be used to understand the nonequilibrium dynamics at the whole time scale, from the transient regime to the long-time steady limit. In this paper, we numerically test these assumptions for density matrix in the models of spins. [ABSTRACT FROM AUTHOR]

In the Color Glass Condensate (CGC) effective theory, the physics of valence gluons with large longitudinal momentum is reflected in the distribution of color charges in the transverse plane. Averaging over the valence degrees of freedom is effected by integrating over classical color charges with some quasi probability weight functional W [j] whose evolution with rapidity is governed by the JIMWLK equation. In this paper, we reformulate this setup in terms of effective quantum field theory on valence Hilbert space governed by the reduced density matrix ρ ̂ for hard gluons, which is obtained after properly integrating out the soft gluon "environment". We show that the evolution of this density matrix with rapidity in the dense and dilute limits has the form of Lindblad equation. The quasi probability distribution (weight) functional W is directly related to the reduced density matrix ρ ̂ through the generalization of the Wigner-Weyl quantum-classical correspondence, which reformulates quantum dynamics on Hilbert space in terms of classical dynamics on the phase space. In the present case the phase space is non Abelian and is spanned by the components of transverse color charge density j. The same correspondence maps the Lindblad equation for ρ ̂ into the JIMWLK evolution equation for W. [ABSTRACT FROM AUTHOR]

In this paper we review an approach to the dynamics of open quantum systems based of non-Hermitian Hamiltonians. Non-Hermitian Hamiltonians arise naturally when one wish to study a subsystem interacting with a continuum of states. Moreover, quantum subsystems with probability sinks or sources are naturally described by non-Hermitian Hamiltonians. Herein, we discuss a non-Hermitian formalism based on the density matrix. We show both how to derive the equations of motion of the density matrix and how to define statistical averages properly. It turns out that the laws of evolution of the normalized density matrix are intrinsically non-linear. We also show how to define correlation functions and a non-Hermitian entropy with a non zero production rate. The formalism has been generalized to the case of hybrid quantum-classical systems using a partial Wigner representation. The equations of motion and the statistical averages are defined analogously to the pure quantum case. However, the definition of the entropy requires to introduce a non-Hermitian linear entropy functional. [ABSTRACT FROM AUTHOR]

In this series of papers, we investigate the projective framework initiated by Kijowski (1977) and Okołów (2009, 2014, 2013), which describes the states of a quantum theory as projective families of density matrices. A short reading guide to the series can be found in Lanéry (2016). After discussing the formalism at the classical level in a first paper (Lanéry, 2017), the present second paper is devoted to the quantum theory. In particular, we inspect in detail how such quantum projective state spaces relate to inductive limit Hilbert spaces and to infinite tensor product constructions (Lanéry, 2016, subsection 3.1) [1] . Regarding the quantization of classical projective structures into quantum ones, we extend the results by Okołów (2013), that were set up in the context of linear configuration spaces, to configuration spaces given by simply-connected Lie groups, and to holomorphic quantization of complex phase spaces (Lanéry, 2016, subsection 2.2) [1] . [ABSTRACT FROM AUTHOR]

Abstract Multimodal sentiment analysis aims to capture diversified sentiment information implied in data that are of different modalities (e.g., an image that is associated with a textual description or a set of textual labels). The key challenge is rooted on the "semantic gap" between different low-level content features and high-level semantic information. Existing approaches generally utilize a combination of multimodal features in a somehow heuristic way. However, how to employ and combine multiple information from different sources effectively is still an important yet largely unsolved problem. To address the problem, in this paper, we propose a Quantum-inspired Multimodal Sentiment Analysis (QMSA) framework. The framework consists of a Quantum-inspired Multimodal Representation (QMR) model (which aims to fill the "semantic gap" and model the correlations between different modalities via density matrix), and a Multimodal decision Fusion strategy inspired by Quantum Interference (QIMF) in the double-slit experiment (in which the sentiment label is analogous to a photon, and the data modalities are analogous to slits). Extensive experiments are conducted on two large scale datasets, which are collected from the Getty Images and Flickr photo sharing platform. The experimental results show that our approach significantly outperforms a wide range of baselines and state-of-the-art methods. [ABSTRACT FROM AUTHOR]

We have already derived the criteria for thermal stability of charged rotating quantum black holes, for horizon areas that are large relative to the Planck area. The derivation is done by using results of loop quantum gravity and equilibrium statistical mechanics of the grand canonical ensemble. We have also showed that in four-dimensional spacetime, quantum AdS Kerr–Newman black hole and asymptotically AdS dyonic black hole with electric and magnetic charge are thermally stable within certain range of its parameters. In this paper, the expectation values of fluctuations and correlations among horizon area, electric charge and angular momentum (magnetic charge) of these black holes are calculated within their range of stability. Interestingly, it is found that leading order fluctuations of electric charge and angular momentum (magnetic charge), in large horizon area limit, are independent of the values of electric charge and angular momentum (magnetic charge) at equilibrium. [ABSTRACT FROM AUTHOR]

Quantum splines are curves in a Hilbert space or, equivalently, in the corresponding Hilbert projective space, which generalize the notion of Riemannian cubic splines to the quantum domain. In this paper, we present a generalization of this concept to general density matrices with a Hamiltonian approach and using a geometrical formulation of quantum mechanics. Our main goal is to formulate an optimal control problem for a nonlinear system on 𝔲 ∗ ( n ) which corresponds to the variational problem of quantum splines. The corresponding Hamiltonian equations and interpolation conditions are derived. The results are illustrated with some examples and the corresponding quantum splines are computed with the implementation of a suitable iterative algorithm. [ABSTRACT FROM AUTHOR]

Substantial progress of the time-dependent density matrix renormalisation group (t-DMRG) method in the recent 15 years is reviewed in this paper. By integrating the time evolution with the sweep procedures in density matrix renormalisation group (DMRG), t-DMRG provides an efficient tool for real-time simulations of the quantum dynamics for one-dimensional (1D) or quasi-1D strongly correlated systems with a large number of degrees of freedom. In the illustrative applications, the t-DMRG approach is applied to investigate the nonadiabatic processes in realistic chemical systems, including exciton dissociation and triplet fission in polymers and molecular aggregates as well as internal conversion in pyrazine molecule. [ABSTRACT FROM AUTHOR]

This paper revisits the classical problem of representing a thermal bath interacting with a system as a large collection of harmonic oscillators initially in thermal equilibrium. As is well known, the system then obeys an equation, which in the bulk and in the suitable limit tends to the Kramers-Langevin equation of physical kinetics. I consider time-dependent system-bath coupling and show that this leads to an additional harmonic force acting on the system. When the coupling is switched on and switched off rapidly, the force has delta-function support at the initial and final time. I further show that the work and heat functionals as recently defined in stochastic thermodynamics at strong coupling contain additional terms depending on the time derivative of the system-bath coupling. I discuss these terms and show that while they can be very large if the system-bath coupling changes quickly, they only give a finite contribution to the work that enters in Jarzynski's equality. I also discuss that these corrections to standard work and heat functionals provide an explanation for non-standard terms in the change of the von Neumann entropy of a quantum bath interacting with a quantum system found in an earlier contribution (Aurell and Eichhorn, 2015). [ABSTRACT FROM AUTHOR]

We present analytical formulas for the Sommerfeld corrections to the annihilation of massive colored particles into quarks and gluons through the strong interaction. These corrections are essential to accurately compute the darkmatter relic density for coannihilationwith colored partners. Our formulas allow us to compute the Sommerfeld effect, not only for the lowest term in the angular momentum expansion of the amplitude, but for all orders in the partial wave expansion. In particular, we carefully account for the effects of the spin of the annihilating particle on the symmetry of the two-particle wave function. This work focuses on strongly interacting particles of arbitrary spin in the triplet, sextet and octet color representations. For typical velocities during freeze-out, we find that including Sommerfeld corrections on the next-to-leading order partial wave leads to modifications of up to 10 to 20 percent on the total annihilation cross section. Complementary to QCD, we generalize our results to particles charged under an arbitrary unbroken SU(N) gauge group, as encountered in dark glueball models. In connection with this paper a Mathematica notebook is provided to compute the Sommerfeld corrections for colored particles up to arbitrary order in the angular momentum expansion. [ABSTRACT FROM AUTHOR]

The density matrix formalism and the equation of motion approach are two semi-analytical methods that can be used to compute the non-equilibrium dynamics of correlated systems. While for a bilinear Hamiltonian both formalisms yield the exact result, for any non-bilinear Hamiltonian a truncation is necessary. Due to the fact that the commonly used truncation schemes differ for these two methods, the accuracy of the obtained results depends significantly on the chosen approach. In this paper, both formalisms are applied to the quantum Rabi model. This allows us to compare the approximate results and the exact dynamics of the system and enables us to discuss the accuracy of the approximations as well as the advantages and the disadvantages of both methods. It is shown to which extent the results fulfill physical requirements for the observables and which properties of the methods lead to unphysical results. [ABSTRACT FROM AUTHOR]

Nowadays, there are plenty of separability criteria which are used to detect entanglement. Many of them are limited to apply for some cases. In this paper, we propose a separability criterion for arbitrary multipartite pure state which is based on the rank of reduced density matrix. It is proved that the rank of reduced density matrices of a multipartite state is closely related to entanglement. In fact it can be used to characterize entanglement. Our separability criterion is a necessary and sufficient condition for detecting entanglement. Furthermore, it is able to help us find the completely separable form of a multipartite pure state according to some explicit examples. Finally it demonstrates that our method are more suitable for some specific case. Our separability criterion are simple to understand and it is operational. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of open systems out of equilibrium. An analytical expression for a time-dependent density matrix of two arbitrarily coupled identical quantum oscillators interacting with separate reservoirs is derived using path integral methods. The temporal behavior of spatial variances and of covariance from given initial values up to stationary values is investigated. It is shown that at comparatively low coupling strengths, the asymptotic variances in the long-time limit achieve steady states independently of initial values. Stationary variances differ from the case of total equilibrium due to their coupling with separate thermal reservoirs of different temperatures. The larger the difference in temperatures of thermal baths, the larger is the difference of the stationary values of variances of coupled oscillators compared with values given by the fluctuation dissipation theorem. At strong couplings the variances have divergent character in the framework of the accepted model. Otherwise, in the weak coupling limit the asymptotic stationary variances are always in accordance with the fluctuation dissipation theorem with some accuracy. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of relaxation of open quantum systems. Using the path integral methods, we found an analytical expression for the time-dependent density matrix of two coupled quantum oscillators interacting with different baths of oscillators. The expression for density matrix was found in the linear regime with respect to the coupling constant between selected oscillators. Time dependent spatial variances and covariances were investigated analytically and numerically. It was shown that asymptotic variances in the long-time limit are always in accordance with the fluctuation dissipation theorem despite their initial values. In the weak coupling approach there is good reason to believe that subsystems are asymptotically in equilibrium at their own temperatures despite the arbitrary difference in temperatures within the whole system. [ABSTRACT FROM AUTHOR]

• This paper presents a new framework to describe non-Markovian dynamics in open quantum systems. • Two flexible descriptions are formulated, one in terms of the wave functions, and the other using the density matrix. • The spectral properties of the bath are realized by using correlated OU processes. It ensures accuracy in predicting long-time dynamics. We present embedding procedures for the non-Markovian stochastic Schrödinger equations, arising from studies of quantum systems coupled with bath environments. By introducing auxiliary wave functions, it is demonstrated that the non-Markovian dynamics can be embedded in extended, but Markovian, stochastic models. Two embedding procedures are presented. The first method leads to nonlinear stochastic equations, the implementation of which is much more efficient than the non-Markovian stochastic Schrödinger equations. The stochastic Schrödinger equations obtained from the second procedure involve more auxiliary wave functions, but the equations are linear, and a closed-form generalized quantum master equation for the density-matrix can be obtained. The accuracy of the embedded models is ensured by fitting to the power spectrum. The stochastic force is represented using a linear superposition of Ornstein-Uhlenbeck processes, which are incorporated as multiplicative noise in the auxiliary Schrödinger equations. It is shown that the asymptotic behavior of the spectral density in the low frequency regime, which is responsible for the long-time behavior of the quantum dynamics, can be preserved by using correlated stochastic processes. The approximations are verified by using a spin-boson system as a test example. [ABSTRACT FROM AUTHOR]

Hybrid quantum-classical algorithms are among the most promising systems to implement quantum computing under the Noisy-Intermediate Scale Quantum (NISQ) technology. In this paper, at first, we investigate a quantum dynamics algorithm for the density matrix obeying the von Neumann equation using an efficient Lagrangian-based approach. And then, we consider the dynamics of the ensemble-averaged of disordered quantum systems which is described by Hamiltonian ensemble with a hybrid quantum-classical algorithm. In a recent work (Chen et al. in Phys Rev Lett 120:030403, 2018), the authors concluded that the dynamics of an open system could be simulated by a Hamiltonian ensemble because of nature of the disorder average. We investigate our algorithm to simulating incoherent dynamics (decoherence) of open system using an efficient variational quantum circuit in the form of master equations. Despite the non-unitary evolution of open systems, our method is applicable to a wide range of problems for incoherent dynamics with the unitary quantum operation. [ABSTRACT FROM AUTHOR]

We explore the concept of the reliability theory in the quantum domain, by giving a Hilbert structure to the system states, then utilize a non-Hermitian Schrodinger equation to describe the state evolution and finally derive two new lifetime distributions. Beyond this, the alternative density matrix approach implies that the degradation term can be separated into two parts, one only related to the system properties and the other only influenced by the environment. Applications on six real data sets further show that the proposed models can outperform the existing well-known distributions, which verifies the validity of the proposed method. • This paper firstly applies the quantum approach to the reliability theory. • The causes of degradation separates into system properties and environment effect. • Two new lifetime distributions are derived. • The proposed models can outperforms the existing distributions. [ABSTRACT FROM AUTHOR]

The dynamics of open quantum systems are described using a set of operators called Kraus operators. In this paper, we show how to find system parameters for a closed system of two qubits undergoing quantum multiplexer operations such that Kraus operators can be written for a single open qubit system (the target qubit) when the initial density matrix of the joint system is in any arbitrary mixed state. The strategy used is to extend the single-qubit open system to a larger two-qubit closed system, which can evolve using unitary dynamics. The constructed two-qubit system is evolved using quantum multiplexer operations, and system parameters are derived to implement the operation. To derive the parameters, we use a reduced Hamiltonian technique wherein the qubit of interest (the target) evolves only in subspaces of the second qubit (the control). The main advantage of our scheme is that it is not restricted to separable product states and/or local unitary evolution of the joint system. [ABSTRACT FROM AUTHOR]

The simulation of the physical movement of multi-body systems at an atomistic level, with forces calculated from a quantum mechanical description of the electrons, motivates a graph partitioning problem studied in this article. Several advanced algorithms relying on evaluations of matrix polynomials have been published in the literature for such simulations. We aim to use a special type of graph partitioning to efficiently parallelize these computations. For this, we create a graph representing the zero–nonzero structure of a thresholded density matrix, and partition that graph into several components. Each separate submatrix (corresponding to each subgraph) is then substituted into the matrix polynomial, and the result for the full matrix polynomial is reassembled at the end from the individual polynomials. This paper starts by introducing a rigorous definition as well as a mathematical justification of this partitioning problem. We assess the performance of several methods to compute graph partitions with respect to both the quality of the partitioning and their runtime. [ABSTRACT FROM AUTHOR]

In this paper, we generalize the application of a recently proposed quantum control technique called self-fulfilling prophesy (Uys et al 2018 Phys. Rev. A 97 060102) to achieve high-fidelity target quantum dynamics which are disturbed by unwanted external couplings, based on sequential unsharp measurements and tailored unitary feedback operations. The unsharp measurements are carried out periodically during system evolution, while the feedback operations are well-designed based on the eigenstates of the density matrices of the expected (without external couplings) dynamical states and their corresponding post-measurement states. By means of quantum state estimation, the mechanism of the measurement–feedback scheme is explained generally. For illustrative examples, we show that the dynamical trajectory errors caused by both constant couplings and time-varying couplings are substantially reduced in typical two-level and multi-level systems, i.e. the high-fidelity quantum dynamics are achieved. Furthermore, we discuss the influence of external coupling strength and measurement strength on system dynamics. Crucially, the scheme is universal and can be applied to any dimension systems. Thus, it may find applications in quantum information processing. [ABSTRACT FROM AUTHOR]