Truncation Of Space Research Articles

Improving bird abundance estimates in harvested forests with retention by limiting detection radius through sound truncation

ABSTRACT An inherent challenge with acoustically surveying birds is that the distance at which they can be detected depends on how far their song can be heard. We developed a distance-based sound detection space truncation method to correct for variable sampling radii due to surveying in forested or open conditions. The method was pivotal in evaluating bird responses to retention patches; without this methodological advancement, the impact of retention patches on songbird abundance was vastly underestimated. In the boreal forest, these patches of live trees are retained in regenerating harvested forests to provide ecological services for species adapted to natural disturbances. Although we did not verify our a priori assumption with ground observations, our findings suggest that limited-distance sampling better captures the effects of retention patches on bird use of harvested forests. When evaluated using unlimited distance surveys, retained trees had a negligible effect on bird abundance, whereas applying detection distance truncation highlighted the importance of retention on forest birds. We found that early to mid-seral forest songbirds benefited from retention patches, with notable increases in abundance after 10 years of regeneration. The size of retention patches, ranging from 0.1 to 1.2 ha, did not have a linear relationship with bird abundance. Instead, edge effects stemming from the configuration of these patches emerged as key determinants of abundance for the majority of the species studied. Retention patches that were nearest to unharvested forests were used the most, compared to further into harvest areas. Our research not only highlights the underestimated impact of small-scale live tree retention on forest songbirds but also introduces a significant methodological innovation in the field of acoustic monitoring.

Unification of Ewald and shifted force methods to calculate Coulomb interactions in molecular simulations.

Three new Ewald series are derived using a new strategy that does not start with a proposed charge spreading function. Of these, the Ewald series produced using shifted potential interactions for the Ewald real space series converges relatively slowly, while the corresponding expression using a shifted force (SF) interaction does not converge. A comparison is made between several approximations of the Ewald method and the SF route to include Coulomb interactions in molecular dynamics (MD) computer simulations. MD simulations of a model bulk molten salt and water were carried out. The recently derived α' variant of Ewald, by K. D. Hammonds and D. M. Heyes [J. Chem. Phys. 157, 074108 (2022)], has been developed analytically and found to be more accurate and computationally efficient than SF in part due to the smaller real space truncation distance that can be used. In addition, with α', the number of reciprocal lattice vectors required is reduced considerably compared with the standard Ewald implementations to give the same accuracy. The invention of the α' method shifts the computational balance back toward using an Ewald construction. The SF method shows greater errors in the Coulomb pressure and time dependent fluctuation properties compared to α'. It does not conserve the shadow Hamiltonian in a microcanonical MD simulation, whereas the α' method does, which facilitates long time stability and insignificant drift of properties over time. The speed of the Ewald computer code is improved by using a new lookup table method.

Classical and quantum computing of shear viscosity for (2+1)D SU(2) gauge theory

We perform a nonperturbative calculation of the shear viscosity for (2+1)-dimensional SU(2) gauge theory by using the lattice Hamiltonian formulation. The retarded Green’s function of the stress-energy tensor is calculated from real time evolution via exact diagonalization of the lattice Hamiltonian with a local Hilbert space truncation, and the shear viscosity is obtained via the Kubo formula. When taking the continuum limit, we account for the renormalization group flow of the coupling but no additional operator renormalization. We find the ratio of the shear viscosity and the entropy density ηs is consistent with a well-known holographic result 14π at several temperatures on a 4×4 honeycomb lattice with the local electric representation truncated at jmax=12. We also find the ratio of the spectral function and frequency ρxy(ω)ω exhibits a peak structure when the frequency is small. Both the exact diagonalization method and simple matrix product state classical simulation method beyond jmax=12 on bigger lattices require exponentially growing resources. So we develop a quantum computing method to calculate the retarded Green’s function and analyze various systematics of the calculation including jmax truncation and finite size effects, Trotter errors and the thermal state preparation efficiency. Our thermal state preparation method still requires resources that grow exponentially with the lattice size, but with a very small prefactor at high temperature. We test our quantum circuit on both the Quantinuum emulator and the IBM simulator for a small lattice and obtain results consistent with the classical computing ones. Published by the American Physical Society 2024

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We derive the primitive quantum gate sets to simulate lattice quantum chromodynamics (LQCD) in the strong-coupling limit with one flavor of massless staggered quarks. This theory is of interest for studies at non-zero density as the sign problem can be overcome using Monte Carlo methods. In this work, we use it as a testing ground for quantum simulations. The key point is that no truncation of the bosonic Hilbert space is necessary as the theory is formulated in terms of color-singlet degrees of freedom (“baryons” and “mesons”). The baryons become static in the limit of continuous time and decouple, whereas the dynamics of the mesonic theory involves two qubits per lattice site. Lending dynamics also to the “baryons” simply requires to use the derived gate set in its controlled version.

Quantum algorithm for lattice Boltzmann (QALB) simulation of incompressible fluids with a nonlinear collision term

We present a full quantum algorithm for the lattice Boltzmann method for simulating fluid flows, the only such algorithm to implement both the streaming and collision substeps as unitary operators using an efficient number of qubits. We use Hamiltonian simulation as the main route underlying the algorithm, and show that it uses qubits that scale logarithmically in the flow Reynolds number but gates that scale only polynomially. We motivate the discussion by a brief overview of existing attempts at simulating classical fluids on quantum computers and present a pedagogical discussion on assigning quantum operators to classical variables in both the streaming and the collision substeps, after highlighting the incompatibility of the latter with the implementations of the streaming step that exists in the literature. We use the Bhatnagar–Gross–Krook ansatz for the collision term, representing the relaxation toward an equilibrium distribution. For nonlinear collisions, we use Kowalski's framework that links the nonlinear dynamics of a system to the evolution of bosonic modes, assigning a Carleman linearization order to the truncation in the Fock space of the bosons. We present the qubit and gate complexities, in terms of the chosen accuracy and the Reynolds number. In the Appendix, we work out the details of implementing the operators of the truncated bosonic Fock space in terms of single-qubit gates as well as the error scaling for a general polynomial driving function.

Dimensioning the pending interest table in content-centric networks

In chunk-based interest-driven content-centric networks, each interest packet forwarded upstream by a node on a face implies the return of at most one data chunk to the node from that face shortly after. As a consequence, the congestion of the downstream transmission buffer in the data path of the node is highly correlated with the occupancy of the pending interest table (PIT). Therefore a systematic study and analysis of the PIT occupancy are of paramount importance to understanding congestion in CCN. In particular, in this paper, we propose an analytical model to estimate the PIT occupancy distribution via a continuous-time Markov chain (CTMC) model that considers the effects of interest blocking, interest timeout and retries. To validate our model and assumptions, we invoke simulation with realistic traffic streams and show how the filtering effects of caching and interest aggregation make the Markov assumption reasonable in the nodes that are the most susceptible to experiencing congestion. To solve the model numerically, we use two alternative approximations, state space truncation and state aggregation, and then give some numerical results to demonstrate the accuracy of our approximations.

VIDM: Video Implicit Diffusion Models

Diffusion models have emerged as a powerful generative method for synthesizing high-quality and diverse set of images. In this paper, we propose a video generation method based on diffusion models, where the effects of motion are modeled in an implicit condition manner, i.e. one can sample plausible video motions according to the latent feature of frames. We improve the quality of the generated videos by proposing multiple strategies such as sampling space truncation, robustness penalty, and positional group normalization. Various experiments are conducted on datasets consisting of videos with different resolutions and different number of frames. Results show that the proposed method outperforms the state-of-the-art generative adversarial network-based methods by a significant margin in terms of FVD scores as well as perceptible visual quality.

A study of core-excited states of organic molecules computed with the generalized active space driven similarity renormalization group.

This work examines the accuracy and precision of x-ray absorption spectra computed with a multireference approach that combines generalized active space (GAS) references with the driven similarity renormalization group (DSRG). We employ the x-ray absorption benchmark of organic molecule (XABOOM) set, consisting of 116 transitions from mostly organic molecules [Fransson et al., J. Chem. Theory Comput. 17, 1618 (2021)]. Several approximations to a full-valence active space are examined and benchmarked. Absolute excitation energies and intensities computed with the GAS-DSRG truncated to second-order in perturbation theory are found to systematically underestimate experimental and reference theoretical values. Third-order perturbative corrections significantly improve the accuracy of GAS-DSRG absolute excitation energies, bringing the mean absolute deviation from experimental values down to 0.32eV. The ozone molecule and glyoxylic acid are particularly challenging for second-order perturbation theory and are examined in detail to assess the importance of active space truncation and intruder states.

Qubitization strategies for bosonic field theories

Quantum simulations of bosonic field theories require a truncation in field space to map the theory onto finite quantum registers. Ideally, the truncated theory preserves the symmetries of the original model and has a critical point in the same universality class. In this paper, we explore two different truncations that preserve the symmetries of the 1+1-dimensional $O(3)$ non-linear $\sigma$-model - one that truncates the Hilbert space for the unit sphere by setting an angular momentum cutoff and a fuzzy sphere truncation inspired by non-commutative geometry. We compare the spectrum of the truncated theories in a finite box with the full theory. We use open boundary conditions, a novel method that improves on the correlation lengths accessible in our calculations. We provide evidence that the angular-momentum truncation fails to reproduce the $\sigma$-model and that the anti-ferromagnetic fuzzy model agrees with the full theory.

Gauge-invariant theory of truncated quantum light-matter interactions in arbitrary media

The loss of gauge invariance in models of light-matter interaction which arises from material and photonic space truncation can pose significant challenges to conventional quantum optical models when matter and light strongly hybridize. In structured photonic environments, necessary in practice to achieve strong light-matter coupling, a rigorous model of field quantization within the medium is also needed. Here we use the framework of macroscopic QED by quantizing the fields in an arbitrary material system, with a spatially dependent dispersive and absorptive dielectric, starting from a fundamental light-matter action. We truncate the material and mode degrees of freedom while respecting the gauge principle by imposing a partial gauge-fixing constraint during canonical quantization, which admits a large number of gauges including the Coulomb and multipolar gauges commonly used in quantum optics. We also consider gauge conditions with explicit time dependence, enabling us to unambiguously introduce additional phenomenologically time-dependent light-matter interactions in any gauge. Our results allow one to derive rigorous nonrelativistic models of ultrastrong light-matter interactions in structured photonic environments with no gauge ambiguity. Results for two-level systems and the dipole approximation are discussed, as well as how to go beyond the dipole approximation for effective single-particle models. By comparing with the limiting case of an inhomogeneous dielectric, where dispersion and absorption can be neglected and the fields can be expanded in terms of the generalized transverse eigenfunctions of the dielectric, we show how lossy systems can introduce an additional gauge ambiguity, which we resolve and predict to have fundamental implications for open quantum system models. Finally, we show how observables in mode-truncated systems can be calculated without ambiguity by using a simple gauge-invariant model of photodetection.

Correction of residual errors in configuration interaction electronic structure calculations.

Methods for correcting residual energy errors of configuration interaction (CI) calculations of molecules and other electronic systems are discussed based on the assumption that the energy defect can be mapped onto atomic regions. The methods do not consider the detailed nature of excitations but instead define a defect energy per electron that is unique to a specific atom. Defect energy contributions are determined from calculations on diatomic and hydride molecules and then applied to other systems. Calculated energies are compared with experimental thermodynamic and spectroscopic data for a set of 41 mainly organic molecules representing a wide range of bonding environments. The most stringent test is based on a severely truncated virtual space in which higher spherical harmonic basis functions are removed. The errors of the initial CI calculations are large, but in each case, including defect corrections brings calculated CI energies into agreement with experimental values. The method is also applied to a NIST compilation of coupled cluster calculations that employ a larger basis set and no truncation of the virtual space. The corrections show excellent consistency with total energies in very good agreement with experimental values. An extension of the method is applied to dmsn states of Sc, Ti, V, Mn, Cr, Fe, Co, Ni, and Cu, significantly improving the agreement of calculated transition energies with spectroscopic values.

Errors in approximate ionization energies due to the one-electron space truncation of the EKT eigenproblem.

Unless the approximate wavefunction of the parent system is expressed in terms of explicitly correlated basis functions, the finite size of the generalized Fock matrix is unlikely to be the leading source of the truncation error in the ionization energy E produced by the EKT (extended Koopmans' theorem) formalism. This conclusion is drawn from a rigorous analysis that involves error partitioning into the parent- and ionized-system contributions, the former being governed by asymptotic power laws when the underlying wavefunction is assembled from a large number of spinorbitals and the latter arising from the truncation of the infinite-dimensional matrix V whose elements involve the 1-, 2-, and 3-matrices of the parent system. Quite surprisingly, the decay of the second contribution with the number n of the natural spinorbitals (NOs) employed in the construction of the truncated V turns out to be strongly system-dependent even in the simplest case of the 1S states of two-electron systems, following the n-5 power law for the helium atom while exhibiting an erratic behavior for the H- anion. This phenomenon, which stems from the presence of the so-called solitonic natural spinorbitals among the NOs, renders the extrapolation of the EKT approximates of E to the complete-basis-set limit generally unfeasible. However, attaining that limit is not contingent upon attempted reproduction of the ill-defined one-electron function known as "the removal orbital," which does not have to be invoked in the derivation of EKT and whose expansion in terms of the NOs diverges.

QuGIT: A numerical toolbox for Gaussian quantum states

Simulating quantum states on a classical computer is hard, typically requiring prohibitive resources in terms of memory and computational power. Efficient simulation, however, can be achieved for certain classes of quantum states, in particular the so-called Gaussian quantum states of continuous variable systems. In this work we introduce QuGIT - a python numerical toolbox based on symplectic methods specialized in efficiently simulating multimode Gaussian states and operations. QuGIT is exact, requiring no truncation of Hilbert space, and provides a wide range of Gaussian operations on arbitrary Gaussian states, including unitaries, partial traces, tensor products, general-dyne measurements, conditional and unconditional dynamics. To illustrate the toolbox, several examples of usage relevant to quantum optics and optomechanics are described. Program summaryProgram Title: QuGIT: Quantum Gaussian Information ToolboxCPC Library link to program files:https://doi.org/10.17632/tp4s84yc5d.1Developer's repository link:https://github.com/IgorBrandao42/Quantum-Gaussian-Information-ToolboxLicensing provisions: CC By 4.0Programming language: PythonExternal routines/libraries: NumPy, SciPyNature of problem: Conditional and unconditional dynamics of Gaussian quantum systems.Solution method: Numerical simulation of symplectic representation of Gaussian states.Additional comments including restrictions and unusual features: Problems must deal with Gaussian states following Gaussian preserving dynamics.

Anyons in conformal Hilbert spaces: Statistics and dynamics of gapless excitations in fractional quantum Hall systems

This paper reviews some of the recent progresses in understanding the dynamical and statistical properties of anyons in fractional quantum Hall (FQH) systems. These are strongly interacting topological systems for electrons confined to a two-dimensional manifold, and anyons are fundamental particles emerging from the truncation of the Hilbert space as a result of both the kinetic and interaction energies. We introduce the concept of the conformal Hilbert spaces (CHS) from such Hilbert space truncation, and the hierarchy of these Hilbert spaces allows us to understand the internal structures of the anyons that can strongly affect their dynamics. The bulk-edge correspondence and the conformal mapping of the CHS also enable us to derive a rigorous bosonization scheme for anyons in these two-dimensional systems, and to capture the statistical interaction between anyons in the form of microscopic interaction Hamiltonians. Examples about the fractionalization of Laughlin quasiholes and a new family of bosonic FQH phases as the dual descriptions of the well-known fermionic FQH phases are given, as applications to the proposed theoretical constructions in this work.

Vulnerability to climate change of species in protected areas in Thailand

Although 23% of Thailand’s land is in protected areas, these are vulnerable to climate change. We used spatial distribution modelling for 866 vertebrate and 591 plant species to understand potential climate change impacts on species in protected areas. Most mammals, birds, and plants were projected to decline by 2070, but most amphibians and reptiles were projected to increase. By 2070 under RCP8.5, 54% of modeled species will be threatened and 11 nationally extinct. However, SDMs are sensitive to truncation of the climate space currently occupied by habitat loss and hunting, and apparent truncation by data limitations. In Thailand, lowland forest clearance has biased records for forest-dependent species to cooler uplands (> 250 m a.s.l.) and hunting has confined larger vertebrates to well-protected areas. In contrast, available data is biased towards lowland non-forest taxa for amphibians and reptiles. Niche truncation may therefore have resulted in overestimation of vulnerability for some mammal and plant species, while data limitations have likely led to underestimation of the threat to forest-dependent amphibians and reptiles. In view of the certainty of climate change but the many uncertainties regarding biological responses, we recommend regular, long-term monitoring of species and communities to detect early signals of climate change impacts.

Cosmological functional renormalization group, extended Galilean invariance, and approximate solutions to the flow equations

The functional renormalisation group is employed to study the non-linear regime of late-time cosmic structure formation. This framework naturally allows for non-perturbative approximation schemes, usually guided by underlying symmetries or a truncation of the theory space. An extended symmetry that is related to Galilean invariance is studied and corresponding Ward identities are derived. These are used to obtain (formally) closed renormalisation group flow equations for two-point correlation functions in the limit of large wave numbers (small scales). The flow equations are analytically solved in an approximation that is connected to the 'sweeping effect' previously described in the context of fluid turbulence.

Diagnosis of information scrambling from Hamiltonian evolution under decoherence

We apply a quantum teleportation protocol based on the Hayden-Preskill thought experiment to quantify how scrambling a given quantum evolution is. It has an advantage over the direct measurement of out-of-time ordered correlators when used to diagnose the information scrambling in the presence of decoherence effects stemming from a noisy quantum device. We demonstrate the protocol by applying it to two physical systems: Ising spin chain and SU(2) lattice Yang-Mills theory. To this end, we numerically simulate the time evolution of the two theories in the Hamiltonian formalism. The lattice Yang-Mills theory is implemented with a suitable truncation of Hilbert space on the basis of the Kogut-Susskind formalism. On a two-leg ladder geometry and with the lowest nontrivial spin representations, it can be mapped to a spin chain, which we call it Yang-Mills-Ising model and is also directly applicable to future digital quantum simulations. We find that the Yang-Mills-Ising model shows the signal of information scrambling at late times.

On the spectrum of the many-body Pauli projector

Spectrum of the Pauli projector of a quantum many-body system is studied using the methods of operator algebra. It is proven that the kernel of the complete many-body projector is identical to the kernel of the sum of two-body projectors. Since the kernel of the many-body Pauli projector defines an allowed subspace of the complete Hilbert space, it is argued that a truncation of the many-body model space following the two-body Pauli projectors is a natural way of solving the Schrödinger equation for the many-body system. These relations clarify the role of many-body Pauli forces in a multicluster system.

Toward simulating superstring/M-theory on a quantum computer

We present a novel framework for simulating matrix models on a quantum computer. Supersymmetric matrix models have natural applications to superstring/M-theory and gravitational physics, in an appropriate limit of parameters. Furthermore, for certain states in the Berenstein-Maldacena-Nastase (BMN) matrix model, several supersymmetric quantum field theories dual to superstring/M-theory can be realized on a quantum device. Our prescription consists of four steps: regularization of the Hilbert space, adiabatic state preparation, simulation of real-time dynamics, and measurements. Regularization is performed for the BMN matrix model with the introduction of energy cut-off via the truncation in the Fock space. We use the Wan-Kim algorithm for fast digital adiabatic state preparation to prepare the low-energy eigenstates of this model as well as thermofield double state. Then, we provide an explicit construction for simulating real-time dynamics utilizing techniques of block-encoding, qubitization, and quantum signal processing. Lastly, we present a set of measurements and experiments that can be carried out on a quantum computer to further our understanding of superstring/M-theory beyond analytic results.

Embedded equation-of-motion coupled-cluster theory for electronic excitation, ionisation, electron attachment, and electronic resonances

The projection-based quantum embedding method is applied to a comprehensive set of electronic states. We embed different variants of equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) theory in density functional theory and investigate electronically excited states of valence, Rydberg, and charge-transfer character, valence- and core-ionised states, as well as bound and temporary radical anions. The latter states, which are unstable towards electron loss, are treated by means of a complex-absorbing potential. Besides transition energies, we present Dyson orbitals and natural transition orbitals for embedded EOM-CCSD. We benchmark the performance of the embedded EOM-CCSD methods against full EOM-CCSD using small organic molecules microsolvated by a varying number of water molecules as test cases. Our results illustrate that embedded EOM-CCSD describes ionisation and valence excitation very well and that these transitions are quite insensitive towards technical details of the embedding procedure. On the contrary, more care is required when dealing with Rydberg excitations or electron attachment. For the latter type of transition in particular, the use of long-range corrected density functionals is mandatory and truncation of the virtual orbital space proves to be difficult.