Density Matrix Research Articles

Correlated pair ansatz with a binary tree structure.

We develop an efficient algorithm to implement the recently introduced binary tree state (BTS) ansatz on a classical computer. BTS allows a simple approximation to permanents arising from the computationally intractable antisymmetric product of interacting geminals and respects size-consistency. We show how to compute BTS overlap and reduced density matrices efficiently. We also explore two routes for developing correlated BTS approaches: Jastrow coupled cluster on BTS and linear combinations of BT states. The resulting methods show great promise in benchmark applications to the reduced Bardeen-Cooper-Schrieffer Hamiltonian and the one-dimensional XXZ Heisenberg Hamiltonian.

Unified construction of relativistic Hamiltonians.

It is shown that the four-component (4C), quasi-four-component (Q4C), and exact two-component (X2C) relativistic Hartree-Fock equations can be implemented in a unified manner by making use of the atomic nature of the small components of molecular 4-spinors. A model density matrix approximation can first be invoked for the small-component charge/current density functions, which gives rise to a static, pre-molecular mean field to be combined with the one-electron term. As a result, only the nonrelativistic-like two-electron term of the 4C/Q4C/X2C Fock matrix needs to be updated during the iterations. A "one-center small-component" approximation can then be invoked in the evaluation of relativistic integrals, that is, all atom-centered small-component basis functions are regarded as extremely localized near the position of the atom to which they belong such that they have vanishing overlaps with all small- or large-component functions centered at other nuclei. Under these approximations, the 4C, Q4C, and X2C mean-field and many-electron Hamiltonians share precisely the same structure and accuracy. Beyond these is the effective quantum electrodynamics Hamiltonian that can be constructed in the same way. Such approximations lead to errors that are orders of magnitude smaller than other sources of errors (e.g., truncation errors in the one- and many-particle bases as well as uncertainties of experimental measurements) and are, hence, safe to use for whatever purposes. The quaternion forms of the 4C, Q4C, and X2C equations are also presented in the most general way, based on which the corresponding Kramers-restricted open-shell variants are formulated for "high-spin" open-shell systems.

The Physical Mechanism of Linear and Nonlinear Optical Properties of Nanographene-Induced Chiral Inversion.

Based on density functional theory (DFT) and wave function analysis, the ultraviolet and visible spectrophotometry (UV-Vis) spectra and Raman spectra of 1-meso and 1-rac obtained by the chiral separation of chiral nanographenes are theoretically investigated. The electron excitation properties of 1-meso and 1-rac are studied by means of transition density matrix (TDM) and charge density difference (CDD) diagrams. The intermolecular interaction is discussed based on an independent gradient model based on Hirshfeld partition (IGMH). The interaction of 1-meso and 1-rac with the external environment is studied using the electrostatic potential (ESP), and the electron delocalization degree of 1-meso and 1-rac is studied based on the magnetically induced current under the external magnetic field. Through the chiral separation of 1-rac, two enantiomers, 1-(P, P) and 1-(M, M), were obtained. The electrical-magnetic interaction of the molecule is revealed by analyzing the electron circular dichroism (ECD) spectra of 1-meso, 1-(P, P) and 1-(M, M), the transition electric dipole moment (TEDM) and the transition magnetic dipole moment (TMDM). It is found that 1-(P, P) and 1-(M, M) have opposite chiral properties due to the inversion of the structure.

Commercial hydrogel product for drug delivery based on route of administration.

Hydrogels are hydrophilic, three-dimensional, cross-linked polymers that absorb significant amounts of biological fluids or water. Hydrogels possess several favorable properties, including flexibility, stimulus-responsiveness, versatility, and structural composition. They can be categorized according to their sources, synthesis route, response to stimulus, and application. Controlling the cross-link density matrix and the hydrogels' attraction to water while they're swelling makes it easy to change their porous structure, which makes them ideal for drug delivery. Hydrogel in drug delivery can be achieved by various routes involving injectable, oral, buccal, vaginal, ocular, and transdermal administration routes. The hydrogel market is expected to grow from its 2019 valuation of USD 22.1 billion to USD 31.4 billion by 2027. Commercial hydrogels are helpful for various drug delivery applications, such as transdermal patches with controlled release characteristics, stimuli-responsive hydrogels for oral administration, and localized delivery via parenteral means. Here, we are mainly focused on the commercial hydrogel products used for drug delivery based on the described route of administration.

Surface Topological Plexcitons: Strong Coupling in a Bi2Se3 Topological Insulator Nanoparticle-Quantum Dot Molecule

Strong coupling of quantum states with electromagnetic modes of topological matter offer an interesting platform for the exploration of new physics and applications. In this work, we report a novel hybrid mode, a surface topological plexciton, arising from strong coupling between the surface topological plasmon mode of a Bi2Se3 topological insulator nanoparticle and the exciton of a two-level quantum emitter. We study the power absorption spectrum of the system by working within the dipole and rotating-wave approximations, using a density matrix approach for the emitter, and a classical dielectric-function approach for the topological-insulator nanoparticle. We show that a Rabi-type splitting can appear in the spectrum suggesting the presence of strong coupling. Furthermore, we study the dependence of the splitting on the separation of the two nanoparticles as well as the dipole moment of the quantum emitter. These results can be useful for exploring exotic phases of matter, furthering research in topological insulator plasmonics, as well as for applications in the far-infrared and quantum computing.

On lower density operators

Abstract The classical density topology is an extension of the natural topology on the real line, as the interior of arbitrary Lebesgue measurable set A is contained in the set of density points of A. Also each density point of A belongs to the closure of A for arbitrary measurable set A. In this paper, we concentrate on lower density operators for which the inclusions mentioned above are not fulfilled. In the first part, examples of such lower density operators generated by measure-preserving bijections are given. There are introduced three conditions to investigate lower density operators for which only the second inclusion holds. In the second part, the concept of operator D introduced by K. Kuratowski is applied to the characterization of such operators.

Variational quantum algorithms for simulation of Lindblad dynamics

We introduce variational hybrid classical-quantum algorithms to simulate the Lindblad master equation and its adjoint for time-evolving Markovian open quantum systems and quantum observables. Our methods are based on a direct representation of density matrices and quantum observables as quantum superstates. We design and optimize low-depth variational quantum circuits that efficiently capture the unitary and non-unitary dynamics of the solutions. We benchmark and test the algorithms on different models and system sizes, showing their potential for utility with near-future hardware.

Partially reflecting jamming objects in correlation-enhanced target detection with entangled photons

In the optical detection of distant objects, one can benefit from quantum light properties over those of classical light. Two-beam correlation-enhanced protocols can improve imaging or target detection even under strong background noise and in the low photon flux regime. We demonstrate that a partially reflecting jamming object introduces noise to these protocols, including quantum illumination. In contrast to background noise, the signal radiation reflected from the jammer is correlated with the corresponding idler beam. We analyze the means to mitigate this noise and introduce an indistinguishability parameter μ, showing how efficiently the jammer can be distinguished from the target. We use the quantum Chernoff bound and the density matrix orthogonalization procedure to separate the contributions from the target, the background, and the jammer. We illustrate our findings with an experiment using optical entangled photon pairs at 800 nm. Our results can be applied to the design of target detection protocols and advanced imaging techniques.

Development of ultra-high energy storage density and ultra-wide operating temperature behavior of a lead-free capacitor sensor; (Bi1/2 K1/2) (Fe1/3Mn1/3W1/3)O3

In the present report, attention has been focused on the development of electronic components of a high-energy storage density in small dimensions using ceramic technology and standard techniques. The detailed studies of electrical and dielectric properties of a potassium, manganese, and tungsten modified complex perovskite with a chemical composition: (Bi1/2K1/2) (Fe1/3Mn1/3W1/3)O3 (by solid-state reaction route) have been attempted for the purpose. Through the analysis of structural X-ray diffraction and micro-structural properties, the quality of the developed material has been verified. These methods have provided a crystallite size of 97 nm, and micro-strain (0.0027) and a grain size of 9.83 μm. Studies of frequency and temperature dependent dielectric and complex impedance support the divergence of dielectric dispersion and relaxation from Debye-type behavior. The nature of conductivity of the material of semiconductor type suggests its potential use in optoelectronic component. The temperature coefficient of resistance of −1.3491% confirms that it is a contender for thermistor devices applications. These findings indicate that material with high energy storage density and minimal energy loss could be used for energy storage devices. The dielectric constant and efficiency of 671 and 70.44%, respectively with a maximum power density (0.16 MW/cm3) at 1 kHz is achieved for the devices.

Accelerating Quantum Algorithms with Precomputation

Real-world applications of computing can be extremely time-sensitive. It would be valuable if we could accelerate such tasks by performing some of the work ahead of time. Motivated by this, we propose a cost model for quantum algorithms that allows quantum precomputation; i.e., for a polynomial amount of ``free'' computation before the input to an algorithm is fully specified, and methods for taking advantage of it. We analyze two families of unitaries that are asymptotically more efficient to implement in this cost model than in the standard one. The first example of quantum precomputation, based on density matrix exponentiation, could offer an exponential advantage under certain conditions. The second example uses a variant of gate teleportation to achieve a quadratic advantage when compared with implementing the unitaries directly. These examples hint that quantum precomputation may offer a new arena in which to seek quantum advantage.

Derivation of the non-stationary Schrödinger equation from the stationary one

A derivation of the time-dependent Schrödinger equation from the time-independent one is considered. Instead of time, the coordinate of an additional degree of freedom, the clock, is introduced into the original time-independent Schrödinger equation. It is shown that the standard time-dependent Schrödinger equation can be obtained for the semiclassical clock only. For elucidation of the physical meaning of the equation obtained in this way, various types of clocks are discussed. In addition, the corresponding equation for the density matrix and formulas for the mean values of operators are derived.

Renormalized-Residue-Based Multireference Configuration Interaction Method for Strongly Correlated Systems.

The implementation of multireference configuration interaction (MRCI) methods in quantum systems with large active spaces is hindered by the expansion of configuration bases or the intricate handling of reduced density matrices (RDMs). In this work, we present a spin-adapted renormalized-residue-based MRCI (RR-MRCI) approach that leverages renormalized residues to effectively capture the entanglement between active and inactive orbitals. This approach is reinforced by a novel efficient algorithm, which also facilitates an efficient deployment of spin-adapted matrix product state MRCI (MPS-MRCI). The RR-MRCI framework possesses several advantages: (1) It considers the orbital entanglement and utilizes highly compressed MPS structure, improving computational accuracy and efficiency compared with internally contracted (ic) MRCI. (2) Utilizing small-sized buffer environments of a few external orbitals as probes based on quantum information theory, it enhances computational efficiency over MPS-MRCI and offers potential application to large molecular systems. (3) The RR framework can be implemented in conjunction with ic-MRCI, eliminating the need for high-rank RDMs, by using distinct renormalized residues. We evaluated this method across nine diverse molecular systems, including Cu2O22+ with an active space of (24e,24o) and two complexes of lanthanide and actinide with active space (38e,36o), demonstrating the method's versatility and efficacy.

Positivity preserving density matrix minimization at finite temperatures via square root.

We present a Wave Operator Minimization (WOM) method for calculating the Fermi-Dirac density matrix for electronic structure problems at finite temperature while preserving physicality by construction using the wave operator, i.e., the square root of the density matrix. WOM models cooling a state initially at infinite temperature down to the desired finite temperature. We consider both the grand canonical (constant chemical potential) and canonical (constant number of electrons) ensembles. Additionally, we show that the number of steps required for convergence is independent of the number of atoms in the system. We hope that the discussion and results presented in this article reinvigorate interest in density matrix minimization methods.

Not All Probability Density Functions Are Tomograms.

This paper delves into the significance of the tomographic probability density function (pdf) representation of quantum states, shedding light on the special classes of pdfs that can be tomograms. Instead of using wave functions or density operators on Hilbert spaces, tomograms, which are the true pdfs, are used to completely describe the states of quantum systems. Unlike quasi-pdfs, like the Wigner function, tomograms can be analysed using all the tools of classical probability theory for pdf estimation, which can allow a better quality of state reconstruction. This is particularly useful when dealing with non-Gaussian states where the pdfs are multi-mode. The knowledge of the family of distributions plays an important role in the application of both parametric and nonparametric density estimation methods. We show that not all pdfs can play the role of tomograms of quantum states and introduce the conditions that must be fulfilled by pdfs to be "quantum".

High-Density CoSe2 Sites Embedded within 2D Porous N-Doped Carbon for High-Performance Oxygen Reduction Reaction Electrocatalysis.

Designing and fabricating efficient and stable nonprecious metal-based oxygen reduction reaction (ORR) electrocatalysts is a pressing and challenging task for the pursuit of sustainable new energy devices. Herein, porous P-CoSe2@NC electrocatalysts with high-density carbon-coated CoSe2 sites were successfully fabricated based on a pyridyl-porphyrinic metal-organic framework (Co-TPyP MOF) via a molten salt-assisted synthesis method. The hierarchical pore and N-doping carbon substrate of P-CoSe2@NC promotes mass transfer and electron-transfer efficiency, which is beneficial to maximize CoSe2 site utilization. Well-designed P-CoSe2@NC exhibits efficient ORR catalytic activity with a high half-wave potential of 0.863 V and excellent catalytic stability. Meanwhile, rechargeable aqueous primary/quasi-solid-state ZABs based on a P-CoSe2@NC air cathode show a high peak power density and exceptional operating stability, catering to the demands of practical applications. The qualified performance and structure stability of the electrocatalytic system may be mainly attributed to the protection of the CoSe2 nanoparticle by the coated carbon layer. Given the rational design of the structure and the component of the electrocatalyst with enhanced ORR activity, we believe that this work has provided a reliable pathway to the development of high-performance transition-metal chalcogenides for energy-storage and -conversion devices.

A multiresolution method for modelling galaxy and massive black hole mergers

ABSTRACT The coalescence of the most massive black hole (MBH) binaries releases gravitational waves (GWs) within the detectable frequency range of pulsar timing arrays (PTAs; 10−9 to 10−6 Hz). The incoherent superposition of GWs from MBH mergers, the stochastic gravitational wave background (GWB), can provide unique information on MBH parameters and the large-scale structure of the Universe. The recent evidence for a GWB reported by the PTAs opens an exciting new window on to MBHs and their host galaxies. However, the astrophysical interpretation of the GWB requires accurate estimations of MBH merger time-scales for a statistically representative sample of galaxy mergers. This is numerically challenging; a high numerical resolution is required to avoid spurious relaxation and stochastic effects, while a large number of simulations are needed to sample a cosmologically representative volume. Here, we present a new multimass modelling method to increase the central resolution of a galaxy model at a fixed particle number. We follow mergers of galaxies hosting central MBHs with the fast multiple method code griffin at two reference resolutions and with two refinement schemes. We show that both refinement schemes are effective at increasing central resolution, reducing spurious relaxation and stochastic effects. A particle number of N ≥ 106 within a radius of five times the sphere of influence of the MBHs is required to reduce numerical scatter in the binary eccentricity and the coalescence time-scale to <30 per cent, a resolution that can only be reached at present with the mass refinement scheme.

Numerical study of the laser isotope separation of optically pumped 102Pd

The feasibility of laser isotope separation of 102Pd through pulsed laser optical pumping followed by isotope selective photoionization has been studied through density matrix formalism. The effect of various parameters such as bandwidth of the excitation lasers, intensity of the lasers and Doppler broadening of the atomic ensemble on the efficiency of optical pumping and isotope selective photoionization have been evaluated. The optimum number density in the laser-atom interaction region has been derived from the studies of the effect of charge exchange collisions on the degree of enrichment. It has been shown that it is possible to enrich 102Pd up to ~ 23.7% at a production rate of 1.1 mg /h. The achievable degree of enrichment through this photoionization scheme is higher than the previously reported laser isotope separation process. The radionuclidic purity of the irradiated enriched mixture has been found to be suitable for medical applications.

Practical quantum protocols for blind millionaires’ problem based on rotation encryption and swap test

Millionaires’ problem, as the most fundamental problem in secure multiparty computation (SMC), has attracted much attention in recent years. Blind millionaires’ problem, an extension of millionaires’ problem, enables to determine the size relationship of the secrets sum. In this paper, two practical quantum protocols based on rotation encryption and swap test are proposed, which can essentially solve the blind millionaires’ problem. To verify the correctness and feasibility, the proposed protocols are simulated on IBM Quantum Platform by designing the corresponding quantum circuits. Compared with the existing quantum solutions for the blind millionaires’ problem, the proposed protocols demonstrate improved performance in terms of feasibility and security, as they utilize Bell states, single-particle measurements, rotation operations and swap tests without necessitating the preparation of d-dimensional quantum states, the shift operation of d-dimensional quantum states, quantum Fourier transform, or the measurement of computational basis and Fourier basis. Security analysis demonstrates that the private data of each participant and the secrets sum remain confidential and undisclosed.

Time evolution of natural orbitals in abinitio molecular dynamics.

This work combines for the first time abinitio molecular dynamics (AIMD) within the Born-Oppenheimer approximation with a global natural orbital functional (GNOF), an approximate functional of the one-particle reduced density matrix. The most prominent feature of GNOF-AIMD is its ability to display the real-time evolution of natural orbitals, providing detailed information on the time-dependent electronic structure of complex systems and processes, including reactive collisions. The quartet ground-state reaction N(4S) + H2(1Σ) → NH(3Σ) + H(2S) is taken as a validation test. Collision energy influences on integral cross sections for different initial rovibrational states of H2 and rotational-state distributions of the NH product are discussed, showing a good agreement with previous high-quality theoretical results.

Excited States by Coupling Piris Natural Orbital Functionals with the Extended Random-Phase Approximation.

In this work, we explore the use of Piris natural orbital functionals (PNOFs) to calculate excited-state energies by coupling their reconstructed second-order reduced density matrix with the extended random-phase approximation (ERPA). We have named the general method PNOF-ERPA, and specific approaches are referred to as PNOF-ERPA0, PNOF-ERPA1, and PNOF-ERPA2, according to the way the excitation operator is built. The implementation has been tested in the first excited states of H2, HeH+, LiH, Li2, and N2 showing good results compared to the configuration interaction (CI) method. As expected, an increase in accuracy is observed on going from ERPA0 to ERPA1 and ERPA2. We also studied the effect of electron correlation included by PNOF5, PNOF7, and the recently proposed global NOF (GNOF) on the predicted excited states. PNOF5 appears to be good and may even provide better results in very small systems, but including more electron correlation becomes important as the system size increases, where GNOF achieves better results. Overall, the extension of PNOF to excited states has been successful, making it a promising method for further applications.