Symmetry Constraints Research Articles

Symmetry-adapted encodings for qubit number reduction by point-group and other Boolean symmetries

A symmetry-adapted fermion-to-spin mapping or encoding that is able to store information about the occupancy of the n spin-orbitals of a molecular system into a lower number of n − k qubits in a quantum computer (where the number of reduced qubits k ranges from 2 to 5 depending on the symmetry of the system) is introduced. This mapping reduces the computational cost of a quantum computing simulation and at the same time enforces symmetry constraints. These symmetry-adapted encodings (SAEs) can be explicitly seen as a block-diagonalization of the Jordan–Wigner qubit Hamiltonian, followed by an orthogonal projection. We provide the form of the Clifford tableau for a general class of fermion-to-qubit encodings, and then use it to construct the map that block-diagonalizes the Hamiltonian in the SAEs. The algorithm proposed does not require any further computations to obtain this map, which is derived directly from the character table of the molecular point group. An implementation of the algorithm is presented as an open-source Python package, QuantumSymmetry, a user guide and code examples. QuantumSymmetry uses open-source quantum chemistry software PySCF for Hartree–Fock calculations, and is compatible with quantum computing toolsets OpenFermion and Qiskit. QuantumSymmetry takes arbitrary user input such as the molecular geometry and atomic basis set to construct the qubit operators that correspond in the appropriate SAE to fermionic operators on the molecular system, such as the second-quantized electronic structure Hamiltonian. QuantumSymmetry is used to produce numerical examples of variational quantum algorithm simulations to find the ground state energy for a number of example molecules, for both Unitary Coupled Clusters with Singles and Doubles and Adaptive Derivative Assembled Pseudo-Trotter Variational Quantum Eigensolver ansätze. We show that, beyond the advantage given by the lower qubit count, the proposed encodings consistently result in shallower and less complex circuits with a reduced number of variational parameters that are able to reach convergence faster and without any loss of computed accuracy.

Hybrid-order topological odd-parity superconductors via Floquet engineering

Having the potential for performing quantum computation, topological superconductors have been generalized to the second-order case. The hybridization of different orders of topological superconductors is attractive because it facilitates the simultaneous utilization of their respective advantages. However, previous studies found that they cannot coexist in one system due to the constraint of symmetry. We propose a Floquet engineering scheme to generate two-dimensional (2D) hybrid-order topological superconductors in an odd-parity superconductor system. Exotic hybrid-order phases exhibiting the coexisting gapless chiral edge states and gapped Majorana corner states not only in two different quasienergy gaps but also in one single quasienergy gap are created by periodic driving. The generalization of this scheme to the 3D system allows us to discover a second-order Dirac superconductor featuring coexisting surface and hinge Majorana Fermi arcs. Our results break a fundamental limitation on topological phases and open a feasible avenue to realize topological superconductor phases without static analogs.

Suppression of the Talbot effect in Fourier transform acousto-optic imaging.

We report on the observation and correction of an imaging artifact attributed to the Talbot effect in the context of acousto-optic imaging using structured acoustic waves. When ultrasound waves are emitted with a periodic structure, the Talbot effect produces π-phase shifts of that periodic structure at every half of the Talbot distance in propagation. This unwanted artifact is detrimental to the image reconstruction, which assumes near-field diffraction is negligible. Here, we demonstrate both theoretically and experimentally how imposing an additional phase modulation on the acoustic periodic structure induces a symmetry constraint leading to the annihilation of the Talbot effect. This will significantly improve the acousto-optic image reconstruction quality and allows for an improvement of the reachable spatial resolution of the image.

Introducing a novel C50N10 azafullerene with chained nitrogen atoms on a buckyball pole: structure, stability, vibration, and electronic properties.

Fullerenes are of high significance due to their unique chemical properties and various applications in technology, particularly materials science, drug delivery, electronics, and nanoelectronics. In the recent years, many attempts have been focused to introduce new heteroatom-doped fullerenes having advanced chemical properties and tunable electronic traits, which make them a potential candidate for application in many branches of sciences. In this study, a novel C50N10 azafullerene with a fascinating structure of chained nitrogen atoms on a buckyball pole, with different electronic and optical properties compared to its other analogs, is introduced and trace of N-N substructures on the surface of C60 fullerene cage is investigated. For this molecule, four structural isomers including 3 structures with chain N atoms on a fullerene buckyball pole (NP isomers) and one isomer with separated N atoms (SN isomer) have been studied. All isomers have been studied with and without symmetry constraints, and the symmetry influence on the structure and stability of each isomer has been investigated. Although the studied NP structures have lower stability than the SN isomer, some reasons (such as their more all-carbon hexagonal rings, breaking some of their N-N bonds for partial opening of the cage and creating bigger rings in order to get rid of the unfavorable strain, as well as decreasing the N-N lone pair repulsions) lead to the acceptable stability of these structures with the bonded N atoms. The results of atomization energy and vibrational frequency calculations indicate that isomers with the bonded N atoms have acceptable stabilities and do not decompose into their constituent components. Investigation on the structural parameters demonstrates important roles of the number of all-carbon hexagonal rings, the number of N-N junction, and the molecule symmetry in the stability of the structures with the bonded N atoms. Study on the electronic and optical properties indicates that the target structures exhibit high electronic polarizability, relatively small HOMO/LUMO gap, high first- and second-order hyperpolarizability, and also large third-order nonlinear optical properties. All calculations have been performed using Gaussian G09 software using density functional theory (DFT) approach. Three-parameter Beck hybrid exchange functional (B3) hybridized with nonlocal correlation functional of Lee, Yang, and Parr (LYP) has been employed as the level of DFT calculations. All optimizations have been performed at double-zeta polarized (DZP) split valence 6-31G(d,p) and also at split valence TZP 6-311G(d,p) basis sets. The global minimum structures have been confirmed by frequency calculations at the same level of optimizations. The natural bond orbital (NBO) analyses, frontier orbital surfaces imaging, atomic charges, and charge transfer analyses have been achieved by GenNBO program package.

Transition Metal Dichalcogenides Heterostructures Nanoribbons

The integration of two-dimensional van der Waals (vdW) heterostructures breaks through the constraints of lattice matching and symmetry, offering substantial opportunities in the development of advanced materials. After the width is reduced, one-dimensional vdW heterostructures show rich band structures and strong spin–orbit coupling behaviors, widening the applications in optoelectronics and spintronics. However, the synthesis of one-dimensional vdW heterostructure nanoribbons has rarely been reported yet. Herein, we report a general approach to realizing transition metal dichalcogenide (TMD) heterostructure nanoribbons for the first time by unzipping self-assembled TMD heterostructure nanoscrolls. As demonstrated by MoS2/WS2 nanoribbons, the obtained TMD heterostructure nanoribbons with alternating stacked layers possess flat edge structures and high quality. Meanwhile, this strategy can be extended to create diverse vdW TMD nanoribbons, demonstrating its versatility. Our work thus shows great potential to prepare TMD heterostructure nanoribbons with various compositions and stacking modes, and new structures can be customized with targeted properties.

Translational Boundaries as Incipient Ferrielectric Domains in Antiferroelectric PbZrO_{3}.

In the archetypal antiferroelectric PbZrO_{3}, antiparallel electric dipoles cancel each other, resulting in zero spontaneous polarization at the macroscopic level. Yet in actual hysteresis loops, the cancellation is rarely perfect and some remnant polarization is often observed, suggesting the metastability of polar phases in this material. In this work, using aberration-corrected scanning transmission electron microscopy methods on a PbZrO_{3} single crystal, we uncover the coexistence of the common antiferroelectric phase and a ferrielectric phase featuring an electric dipole pattern of ↓↑↓. This dipole arrangement, predicted by Aramberri etal. to be the ground state of PbZrO_{3} at 0K, appears at room temperature in the form of translational boundaries. The dual nature of the ferrielectric phase, both a distinct phase and a translational boundary structure, places important symmetry constraints on its growth. These are overcome by sideways motion of the boundaries, which aggregate to form arbitrarily wide stripe domains of the polar phase embedded within the antiferroelectric matrix.

Bound on the central charge of CFTs in large dimension

In this paper, we use crossing symmetry and unitarity constraints to put a lower bound on the central charge of conformal field theories in large space-time dimensions D. Specifically, we work with the four-point function of identical scalars ϕ with scaling dimension ∆ϕ, and use a certain class of analytic functionals to show that the OPE coefficient squared {c}_{phi phi {T}^{mu nu}}^2 must be exponentially small in D. For this to hold, we need to make a certain assumption about the nature of the spectrum below 2∆ϕ. Our argument is robust and can be applied to any OPE coefficient squared {c}_{phi phi O}^2 with ∆O< 2∆ϕ. This suggests that conformal field theories in large dimensions (if they exist) must be exponentially close to generalized free field theories.

Direct reduction approach and soliton solutions for the integrable space–time shifted nonlocal Sasa-Satsuma equation

This paper investigates the space–time shifted nonlocal Sasa-Satsuma equation which is constructed by imposing a space–time shifted symmetry constraint on the two-component Sasa-Satsuma system. By applying the direct reduction approach, specific parameter values are determined to obtain N-soliton solutions of the shifted nonlocal equation. The resulting one-soliton and two-soliton solutions are analyzed both theoretically and graphically. Additionally, the asymptotic behavior of two-soliton solution with two purely imaginary eigenvalues is studied. The findings shed light on the mathematical properties and dynamic behaviors of shifted nonlocal integrable systems.

Polar magneto-optic Kerr and Faraday effects in finite periodic PT -symmetric systems

We discuss the anomalous behavior of the Faraday (transmission) and polar Kerr (reflection) rotation angles of the propagating light, in finite periodic parity-time ($\mathcal{P}\mathcal{T}$) symmetric structures, consisting of $N$ cells. The unit cell potential is two complex $\delta$-potentials placed on both boundaries of the ordinary dielectric slab. It is shown that, for a given set of parameters describing the system, a phase transition-like anomalous behavior of Faraday and Kerr rotation angles in a parity-time symmetric systems can take place. In the anomalous phase the value of one of the Faraday and Kerr rotation angles can become negative, and both angles suffer from spectral singularities and give a strong enhancement near the singularities. We also shown that the real part of the complex angle of KR, $\theta^{R}_1$, is always equal to the $\theta^{T}_1$ of FR, no matter what phase the system is in due to the symmetry constraints. The imaginary part of KR angles $\theta^{R^{r/l}}_2$ are related to the $\theta^{T}_2$ of FR by parity-time symmetry. Calculations based on the approach of the generalized nonperturbative characteristic determinant, which is valid for a layered system with randomly distributed delta potentials, show that the Faraday and Kerr rotation spectrum in such structures has several resonant peaks. Some of them coincide with transmission peaks, providing simultaneous large Faraday and Kerr rotations enhanced by an order one or two of magnitude. We provide a recipe for funding a one-to-one relation in between KR and FR.

Bootstrapping multi-field inflation: non-Gaussianities from light scalars revisited

Primordial non-Gaussianities from multi-field inflation are a leading target for cosmological observations, because of the possible large correlations generated between long and short distances.These signatures are captured by the local shape of the scalar bispectrum. In this paper, we revisit the nonlinearities of the conversion process from additional light scalars into curvature perturbations during inflation.We provide analytic templates for correlation functions valid at any kinematical configuration, using the cosmological bootstrap as a main computational tool. Our results include the possibility of large breaking of boost symmetry, in the form of small speeds of sound for both the inflaton and the mediators.We consider correlators coming from the tree-level exchange of a massless scalar field.By introducing a late-time cutoff, we identify that the symmetry constraints on the correlators are modified. This leads to anomalous conformal Ward identities, and consequently the bootstrap differential equations acquire a source term that depends on this cutoff.The solutions to the differential equations are scalar seed functions that incorporate these late-time growth effects. Applying weight-shifting operators to auxiliary “seed” functions, we obtain a systematic classification of shapes of non-Gaussianity coming from massless exchange.For theories with de Sitter symmetry, we compare the resulting shapes with the ones obtained via the δN formalism, identifying missing contributions away from the squeezed limit. For boost-breaking scenarios, we derive a novel class of shape functions with phenomenologically distinct features in scale-invariant theories.Specifically, the new shape provides a simple extension of equilateral non-Gaussianity: the signal peaks at a geometric configuration controlled by the ratio of the sound speeds of the mediator and the inflaton.

Irregular universe in the Nieh-Yan modified teleparallel gravity

The Nieh-Yan modified teleparallel gravity is a model which modifies the general relativity equivalent teleparallel gravity by a coupling between the Nieh-Yan density and an axion-like field. This model predicts parity violations in the gravitational waves if the axion-like field has a non-trivial background, and more importantly it is ghost free and avoids the pathologies presented in other parity-violating gravity models. The cosmological dynamics and perturbations of the Nieh-Yan modified teleparallel gravity have been investigated in detail, but all these previous investigations rely on the symmetry requirement that in the background universe both the metric and affine connection are homogeneous and isotropic. In this paper we relax the symmetry constraint on the connection and leave it arbitrary at the beginning, after all the cosmological principle only needs the metric of the background spacetime to meet the symmetry requirement. We find a new flat universe solution for the Nieh-Yan modified teleparallel gravity, for which the background dynamics itself is unchanged but the perturbations around it present a new feature that the scalar and tensor perturbations are coupled together at the linear level. The implications of this peculiar feature in primordial perturbations from inflation are also discussed.

Quantum kinetic theory of nonlinear optical currents: Finite Fermi surface and Fermi sea contributions

The quantum kinetic framework provides a versatile method for investigating the dynamical optical and transport currents of crystalline solids. In this paper, starting from the density-matrix equations of motion, we present a general theoretical path to obtain the nonlinear optical response in an elegant and transparent manner. We devise an extensive kinetic theory that can be applied to materials with arbitrary band structures and captures intraband and interband coherence effects, finite Fermi surfaces, and disorder effects. We present a classification of the nonlinear optical currents arising from the interference of the interband and intraband components of the density matrix with distinct symmetry and quantum geometrical origin for each contribution. In this context, we report the following four primary findings: (i) The Fermi golden rule approach is insufficient to derive the correct expression for the injection current, a shortcoming that we remedy in our theory while associating the injection current with the intraband-interband contribution to the second-order density matrix. (ii) The interband-intraband contribution yields a resonant current that survives irrespective of any symmetry constraint in addition to the well-known anomalous nonlinear current (nonresonant), which requires time-reversal symmetry. (iii) Quite generally, the nonlinear current is significantly enhanced by contributions arising from the finite Fermi surface. (iv) The finite Fermi surface and Fermi sea additionally lead to sizable novel nonlinear effects via contributions we term double resonant and higher-order pole. We investigate such effects in sum frequency and difference frequency generation. As an illustration, we compute the nonlinear response of the topological antiferromagnet CuMnAs and thin film tilted Weyl semimetals as model systems dominated by interband coherence contributions. We find that the nonlinear response of CuMnAs is responsive to the direction of the finite magnetization field and the response of Weyl semimetal to the tilt. In addition, the choice of the polarization angle of the beam is crucial to have a nonlinear current in CuMnAs, while it is not the case for Weyl semimetals.

Design and Development of a Spherical 5-Bar Thumb Exoskeleton Mechanism for Poststroke Rehabilitation.

This paper presents the kinematic design and development of a two degree-of-freedom (2DOF) spherical 5-bar thumb exoskeleton to augment the finger individuating grasp exercise robot (FINGER) rehabilitation robot, which assists the index and middle fingers individually in naturalistic grasping. The thumb module expands the capabilities of FINGER, allowing for broader proprioceptive training and assessment of hand function. The design process started by digitizing thumb-grasping motions to the index and the middle fingers separately, recorded from multiple healthy subjects utilizing a motion capture system. Fitting spheres to trajectory data of each subject allowed normalization of all subjects' data to a common center and radius. A two-revolute joint serial-chain mechanism was synthesized (intermediate optimization step) to reach the normalized trajectories. Next, the two resulting grasping trajectories were spatially sampled as targets for the 2DOF spherical 5-bar synthesis. Optimization of the spherical 5-bar included symmetry constraints and cost-function penalties for poor manipulability. The resulting exoskeleton assists both flexion/extension and abduction/adduction of the thumb enabling a wide range of motions. Consistent with FINGER, the parallel structure of the spherical 5-bar places the actuators at the base of the module, allowing for desirable characteristics, including high backdrivability, high controllable bandwidth, and low mechanical impedance. The mechanical design was developed from the kinematic solution, including an adjustable thumb cuff to accommodate different hand sizes. Fit and function of the device were tested on multiple subjects, including survivors of stroke. A proportional-derivative force controller with gravity and friction compensation was implemented to reduce resistance to motion during subject testing.

Structural and thermal properties of H6Ta2O17

The structural, electronic, mechanical, and thermal properties of H6Ta2O17 are studied using density functional theory. The Helmholtz free energy is computed for various symmetry constraints on the H6Ta2O17 structure during lattice structure optimization and atomic configuration relax- ation. The Helmholtz free energies calculated from Γ-point phonon frequencies demonstrate a pref- erence for slightly lowered symmetry, preferring triclinic symmetry rather than the experimentally determined orthorhombic symmetry. Elastic constants are obtained for the symmetry-enforced (i.e., orthorhombic) structure and are used to calculate the structure’s mechanical and thermal properties including its bulk, shear, and Young’s moduli, Poisson ratio, Pugh ratio, longitudinal and shear sound velocities, and Debye temperature. Using the Born criteria, the symmetry-enforced structure is shown to be mechanically stable. The electronic band structure for H6Ta2O17 is pre- sented and found to exhibit a large indirect band gap.

A very simple derivation of Born’s rule from symmetry

We provide a simple derivation of the Born rule for transition probabilities in quantum theory from the requirement of invariance under unitary symmetry and basic probabilistic constraints, improving upon work recently published in this Journal (Hossenfelder, 2021). While this is merely a special case of a classical result by Gleason (Gleason, 1957), it is nevertheless instructive to see how the constraints imposed by unitary symmetry lead to a much simpler derivation.

Tuning the conductance topology in solids

The inertia of trapping and detrapping of nonequilibrium charge carriers affects the electrochemical and transport properties of both bulk and nanoscopic structures in a very peculiar way. An emerging memory response with hysteresis in the current–voltage response and its eventual multiple crossing, produced by this universally available ingredient, are signatures of this process. Here, we deliver a microscopic and analytical solution for these behaviors, understood as the modulation of the topology of the current–voltage loops. Memory emergence thus becomes a characterization tool for intrinsic features that affect the electronic transport of solids such as the nature and number of trapping sites, intrinsic symmetry constraints, and natural relaxation time scales. This method is also able to reduce the seeming complexity of frequency-dependent electrochemical impedance and cyclic voltammetry observable for a variety of systems to a combination of simple microscopic ingredients.

Physics guided deep learning for generative design of crystal materials with symmetry constraints

Discovering new materials is a challenging task in materials science crucial to the progress of human society. Conventional approaches based on experiments and simulations are labor-intensive or costly with success heavily depending on experts’ heuristic knowledge. Here, we propose a deep learning based Physics Guided Crystal Generative Model (PGCGM) for efficient crystal material design with high structural diversity and symmetry. Our model increases the generation validity by more than 700% compared to FTCP, one of the latest structure generators and by more than 45% compared to our previous CubicGAN model. Density Functional Theory (DFT) calculations are used to validate the generated structures with 1869 materials out of 2000 are successfully optimized and deposited into the Carolina Materials Database www.carolinamatdb.org, of which 39.6% have negative formation energy and 5.3% have energy-above-hull less than 0.25 eV/atom, indicating their thermodynamic stability and potential synthesizability.

Radiometric and Polarimetric Quality Validation of Gaofen-3 over a Five-Year Operation Period

GaoFen-3 was the first Chinese civilian C-band synthetic aperture radar (SAR) satellite, launched in August 2016. The need for monitoring the satellite’s image quality has been boosted by its widespread applications in various fields. The efficient and scientific assessment of the system’s radiometric and polarimetric performance has been essential in its more than five years of service. The authors collected 90 images of the Inner Mongolia calibration site, 888 images of the Amazon rainforest, and 39,929 images of the Chinese mainland from 2017 to 2021. This was achieved whilst covering the leading imaging modes, such as the spotlight mode, stripmap mode, ultra-fine mode, wave imaging mode, etc. In this study, we derive a framework that incorporates the man-made corner reflectors (CRs) in Mongolia, the traditional Amazon rainforest datasets, and even the long-strip data in the Chinese mainland (known as CRAS) for the purposes of GaoFen-3 radiometric quality analysis and polarimetric validation over its five years of operation. Polarimetric calibration without recourse to the CRs is utilized to measure the polarimetric distortions regardless of the region, and thus requires a higher calibration accuracy for the GaoFen-3 polarimetric monitoring task. Consequently, the modified Quegan method is developed by relaxing the target azimuth symmetry constraint with the Amazon forest datasets. The experiments based on the CRAS demonstrate that the main radiometric characteristics could reach the international level, with an estimated noise-equivalent sigma zero of approximately −30 dB, a radiometric resolution that is better than 2.9 dB, and a single-imagery relative radiation accuracy that is better than 0.51 dB. For polarimetric validation, the modified Quegan method was utilized to measure the crosstalk for quad-pol products to ensure that it was than −40 dB. Meanwhile, non-negligible channel imbalance errors were found in the QPSII and WAV modes, and they were effectively well-calibrated with strip estimators to satisfy the system design.

Utilization of two‐equation model for analysis of flow over a moving needle in the presence of magnetic field

AbstractMany applications of the ocean and aerodynamic engineering, like the design of submarines, missiles, aircraft, rockets, and jet engines, involve flow over surfaces. Moreover, several experimental propulsion methods for seagoing ships, submarines and aerospace crafts are based on magnetohydrodynamics (MHD). This research explores the MHD boundary layer flow over a moving needle (shaped like a paraboloid of revolution). Governing equations are modelled in cylindrical coordinates under axial symmetry constraint, which is then simplified by employing order of magnitude analysis. In the absence of a magnetic field, these equations are self‐similar, and this analysis is already available in the literature. We have applied the local non‐similarity method to derive the boundary layer equations up to the second level of truncation to compute the solutions of non‐similar boundary layer equations. The built‐in MATLAB routine bvp5c is used to solve these equations numerically. This analysis will assist in predicting flow quantities that are important in designing the objects mentioned above.

Disordered structures in ultracold spin-imbalanced Fermi gas

We investigate properties of spin-imbalanced ultracold Fermi gas in a large range of spin polarizations at low temperatures. We present results of microscopic calculations based on mean-field and density functional theory approaches, with no symmetry constraints. At low polarization values we predict the structure of the system as consisting of several spin-polarized droplets. As the polarization increases, the system self-organizes into a disordered structures similar to liquid crystals, and energetically they can compete with ordered structures such as grid-like domain walls. At higher polarizations the system starts to develop regularities that, in principle, can be called supersolid, where periodic density modulation and pairing correlations coexist. The robustness of the results has been checked with respect to temperature effects, dimensionality, and the presence of a trapping potential. Dynamical stability has also been investigated.