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Lin Lin

Publications and source records attributed to Lin Lin.

At least 127 records · Page 7Linked to original sources
arXiv2024

CSST Strong Lensing Preparation: a Framework for Detecting Strong Lenses in the Multi-color Imaging Survey by the China Survey Space Telescope (CSST)

Strong gravitational lensing is a powerful tool for investigating dark matter and dark energy properties. With the advent of large-scale sky surveys, we can discover strong lensing systems on an unprecedented scale, which requires efficient tools to extract them from billions of astronomical objects. The existing mainstream lens-finding tools are based on machine learning algorithms and applied to cut-out-centered galaxies. However, according to the design and survey strategy of optical surveys by CSST, preparing cutouts with multiple bands requires considerable efforts. To overcome these challenges, we have developed a framework based on a hierarchical visual Transformer with a sliding window technique to search for strong lensing systems within entire images. Moreover, given that multi-color images of strong lensing systems can provide insights into their physical characteristics, our framework is specifically crafted to identify strong lensing systems in images with any number of channels. As evaluated using CSST mock data based on an Semi-Analytic Model named CosmoDC2, our framework achieves precision and recall rates of 0.98 and 0.90, respectively. To evaluate the effectiveness of our method in real observations, we have applied it to a subset of images from the DESI Legacy Imaging Surveys and media images from Euclid Early Release Observations. 61 new strong lensing system candidates are discovered by our method. However, we also identified false positives arising primarily from the simplified galaxy morphology assumptions within the simulation. This underscores the practical limitations of our approach while simultaneously highlighting potential avenues for future improvements.

astro-ph.IM↗
arXiv2024

Energy Allocation for Multi-User Cooperative Molecular Communication Systems in the Internet of Bio-Nano Things

Cooperative molecular communication (MC) is a promising technology for facilitating communication between nanomachines in the Internet of Bio-Nano Things (IoBNT) field. However, the performance of IoBNT is limited by the availability of energy for cooperative MC. This paper presents a novel transmitter design scheme that utilizes molecule movement between reservoirs, creating concentration differences through the consumption of free energy, and encoding information on molecule types. The performance of the transmitter is primarily influenced by energy costs, which directly impact the overall IoBNT system performance. To address this, the paper focuses on optimizing energy allocation in cooperative MC for enhanced transmitter performance. Theoretical analysis is conducted for two transmitters. For scenarios with more than two users, a genetic algorithm is employed in the energy allocation to minimize the total bit error rate (BER). Finally, numerical results show the effectiveness of the proposed energy allocation strategies in the considered cooperative MC system.

cs.IT↗
arXiv2024

Inverse Volume Scaling of Finite-Size Error in Periodic Coupled Cluster Theory

Coupled cluster theory is one of the most popular post-Hartree-Fock methods for ab initio molecular quantum chemistry. The finite-size error of the correlation energy in periodic coupled cluster calculations for three-dimensional insulating systems has been observed to satisfy the inverse volume scaling, even in the absence of any correction schemes. This is surprising, as simpler theories that utilize only a subset of the coupled cluster diagrams exhibit much slower decay of the finite-size error, which scales inversely with the length of the system. In this study, we review the current understanding of finite-size error in quantum chemistry methods for periodic systems. We introduce new tools that elucidate the mechanisms behind this phenomenon in the context of coupled cluster doubles calculations. This reconciles some seemingly paradoxical statements related to finite-size scaling. Our findings also show that singularity subtraction can be a powerful method to effectively reduce finite-size errors in practical quantum chemistry calculations for periodic systems.

math.NA↗
arXiv2024

On the Hartree-Fock Ground State Manifold in Magic Angle Twisted Graphene Systems

Recent experiments have shown that magic angle twisted bilayer graphene (MATBG) can exhibit correlated insulator behavior at half-filling. Seminal theoretical results towards understanding this phase in MATBG has shown that Hartree-Fock ground states (with a positive charge gap) can be exact many-body ground states of an idealized flat band interacting (FBI) Hamiltonian. We prove that in the absence of spin and valley degrees of freedom, the only Hartree-Fock ground states of the FBI Hamiltonian for MATBG are two ferromagnetic Slater determinants. Incorporating spin and valley degrees of freedom, we provide a complete characterization of the Hartree-Fock ground state manifold, which is generated by a ${\rm U}(4) \times {\rm U}(4)$ hidden symmetry group acting on five elements. We also introduce new tools for ruling out translation symmetry breaking in the Hartree-Fock ground state manifold, which may be of independent interest.

math-ph↗
arXiv2024

Forklens: Accurate weak-lensing shear measurement with deep learning

Weak gravitational lensing is one of the most important probes of the nature of dark matter and dark energy. In order to extract cosmological information from next-generation weak lensing surveys (e.g., Euclid, Roman, LSST, and CSST) as much as possible, accurate measurements of weak lensing shear are required. There are existing algorithms to measure the weak lensing shear on imaging data, which have been successfully applied in previous surveys. In the meantime, machine learning (ML) has been widely recognized in various astrophysics applications in modeling and observations. In this work, we present a fully deep-learning-based approach to measuring weak lensing shear accurately. Our approach comprises two modules. The first one contains a convolutional neural network (CNN) with two branches for taking galaxy images and point spread function (PSF) simultaneously, and the output of this module includes the galaxy's magnitude, size, and shape. The second module includes a multiple-layer neural network (NN) to calibrate weak-lensing shear measurements. We name the program Forklens and make it publicly available online. Applying Forklens to CSST-like mock images, we achieve consistent accuracy with traditional approaches (such as moment-based measurement and forward model fitting) on the sources with high signal-to-noise ratios (S/N, > 20). For the sources with S/N < 10, Forklens exhibits an $\sim 36\%$ higher Pearson coefficient on galaxy ellipticity measurements. After adopting galaxy weighting, the shear measurements with Forklens deliver accuracy levels to $0.2\%$. The whole procedure of Forklens is automated and costs about $0.7$ milliseconds per galaxy, which is appropriate for adequately taking advantage of the sky coverage and depth of the upcoming weak lensing surveys.

astro-ph.CO↗
arXiv2024

Robust ground-state energy estimation under depolarizing noise

We present a novel ground-state energy estimation algorithm that is robust under global depolarizing error channels. Building upon the recently developed Quantum Exponential Least Squares (QCELS) algorithm, our new approach incorporates significant advancements to ensure robust estimation while maintaining a polynomial cost in precision. By leveraging the spectral gap of the Hamiltonian effectively, our algorithm overcomes limitations observed in previous methods like quantum phase estimation (QPE) and robust phase estimation (RPE). Going beyond global depolarizing error channels, our work underscores the significance and practical advantages of utilizing randomized compiling techniques to tailor quantum noise towards depolarizing error channels. Our research demonstrates the feasibility of ground-state energy estimation in the presence of depolarizing noise, offering potential advancements in error correction and algorithmic-level error mitigation for quantum algorithms.

quant-ph↗
arXiv2024

Even shorter quantum circuit for phase estimation on early fault-tolerant quantum computers with applications to ground-state energy estimation

We develop a phase estimation method with a distinct feature: its maximal runtime (which determines the circuit depth) is $δ/ε$, where $ε$ is the target precision, and the preconstant $δ$ can be arbitrarily close to $0$ as the initial state approaches the target eigenstate. The total cost of the algorithm satisfies the Heisenberg-limited scaling $\widetilde{\mathcal{O}}(ε^{-1})$. As a result, our algorithm may significantly reduce the circuit depth for performing phase estimation tasks on early fault-tolerant quantum computers. The key technique is a simple subroutine called quantum complex exponential least squares (QCELS). Our algorithm can be readily applied to reduce the circuit depth for estimating the ground-state energy of a quantum Hamiltonian, when the overlap between the initial state and the ground state is large. If this initial overlap is small, we can combine our method with the Fourier filtering method developed in [Lin, Tong, PRX Quantum 3, 010318, 2022], and the resulting algorithm provably reduces the circuit depth in the presence of a large relative overlap compared to $ε$. The relative overlap condition is similar to a spectral gap assumption, but it is aware of the information in the initial state and is therefore applicable to certain Hamiltonians with small spectral gaps. We observe that the circuit depth can be reduced by around two orders of magnitude in numerical experiments under various settings.

quant-ph↗
arXiv2024

Concise Spectrotemporal Studies of Magnetar SGR J1935+2154 Bursts

SGR J1935+2154 has truly been the most prolific magnetar over the last decade: It has been entering into burst active episodes once every 1-2 years since its discovery in 2014, it emitted the first Galactic fast radio burst associated with an X-ray burst in 2020, and has emitted hundreds of energetic short bursts. Here, we present the time-resolved spectral analysis of 51 bright bursts from SGR J1935+2154. Unlike conventional time-resolved X-ray spectroscopic studies in the literature, we follow a two-step approach to probe true spectral evolution. For each burst, we first extract spectral information from overlapping time segments, fit them with three continuum models, and employ a machine learning based clustering algorithm to identify time segments that provide the largest spectral variations during each burst. We then extract spectra from those non-overlapping (clustered) time segments and fit them again with the three models: the cutoff power-law model, the sum of two blackbody functions, and the model considering the emission of a modified black body undergoing resonant cyclotron scattering, which is applied systematically at this scale for the first time. Our novel technique allowed us to establish the genuine spectral evolution of magnetar bursts. We discuss the implications of our results and compare their collective behavior with the average burst properties of other magnetars.

astro-ph.HE↗
arXiv2024

An Efficient Quantum Circuit for Block Encoding a Pairing Hamiltonian

We present an efficient quantum circuit for block encoding pairing Hamiltonian often studied in nuclear physics. Our block encoding scheme does not require mapping the creation and annihilation operators to the Pauli operators and representing the Hamiltonian as a linear combination of unitaries. Instead, we show how to encode the Hamiltonian directly using controlled swap operations. We analyze the gate complexity of the block encoding circuit and show that it scales polynomially with respect to the number of qubits required to represent a quantum state associated with the pairing Hamiltonian. We also show how the block encoding circuit can be combined with the quantum singular value transformation to construct an efficient quantum circuit for approximating the density of states of a pairing Hamiltonian. The techniques presented can be extended to encode more general second-quantized Hamiltonians.

nucl-th↗
arXiv2024

The Staggered Mesh Method: Accurate Exact Exchange towards the Thermodynamic Limit for Solids

In periodic systems, the Hartree-Fock (HF) exchange energy exhibits the slowest convergence of all HF energy components as the system size approaches the thermodynamic limit. We demonstrate that the recently proposed staggered mesh method for Fock exchange energy [Xing, Li, and Lin, Math. Comp., 2024], which is specifically designed to sidestep certain singularities in exchange energy evaluation, can expedite the finite-size convergence rate for the exact exchange energy across a range of insulators and semiconductors when compared to the regular and truncated Coulomb methods. This remains true even for two computationally cheaper versions of this new method, which we call Non-SCF and Split-SCF staggered mesh. Additionally, a sequence of numerical tests on simple solids showcases the staggered mesh method's ability to improve convergence towards the thermodynamic limit for band gaps, bulk moduli, equilibrium lattice dimensions, energies, and phonon force constants.

physics.comp-ph↗
arXiv2023

Exact ground state of interacting electrons in magic angle graphene

One of the most remarkable theoretical findings in magic angle twisted bilayer graphene (TBG) is the emergence of ferromagnetic Slater determinants as exact ground states for the interacting Hamiltonian at the chiral limit. This discovery provides an explanation for the correlated insulating phase which has been experimentally observed at half filling. This work is the first mathematical study of interacting models in magic angle graphene systems. These include not only TBG but also TBG-like systems featuring four flat bands per valley, and twisted trilayer graphene (TTG) systems with equal twist angles. We identify symmetries of the Bistritzer-MacDonald Hamiltonian that are responsible for characterizing the Hartree-Fock ground states as zero energy many-body ground states. Furthermore, for a general class of Hamiltonian, we establish criteria that the ferromagnetic Slater determinants are the unique ground states within the class of uniformly half-filled, translation invariant Slater determinants. We then demonstrate that these criteria can be explicitly verified for TBG and TBG-like systems at the chiral limit, using properties of Jacobi-$θ$ and Weierstrass-$\wp$ functions.

math-ph↗
arXiv2023

Unified analysis of finite-size error for periodic Hartree-Fock and second order Møller-Plesset perturbation theory

Despite decades of practice, finite-size errors in many widely used electronic structure theories for periodic systems remain poorly understood. For periodic systems using a general Monkhorst-Pack grid, there has been no comprehensive and rigorous analysis of the finite-size error in the Hartree-Fock theory (HF) and the second order Møller-Plesset perturbation theory (MP2), which are the simplest wavefunction based method, and the simplest post-Hartree-Fock method, respectively. Such calculations can be viewed as a multi-dimensional integral discretized with certain trapezoidal rules. Due to the Coulomb singularity, the integrand has many points of discontinuity in general, and standard error analysis based on the Euler-Maclaurin formula gives overly pessimistic results. The lack of analytic understanding of finite-size errors also impedes the development of effective finite-size correction schemes. We propose a unified analysis to obtain sharp convergence rates of finite-size errors for the periodic HF and MP2 theories. Our main technical advancement is a generalization of the result of [Lyness, 1976] for obtaining sharp convergence rates of the trapezoidal rule for a class of non-smooth integrands. Our result is applicable to three-dimensional bulk systems as well as low dimensional systems (such as nanowires and 2D materials). Our unified analysis also allows us to prove the effectiveness of the Madelung-constant correction to the Fock exchange energy, and the effectiveness of a recently proposed staggered mesh method for periodic MP2 calculations [Xing, Li, Lin, J. Chem. Theory Comput. 2021]. Our analysis connects the effectiveness of the staggered mesh method with integrands with removable singularities, and suggests a new staggered mesh method for reducing finite-size errors of periodic HF calculations.

physics.comp-ph↗
arXiv2023

Linear combination of Hamiltonian simulation for nonunitary dynamics with optimal state preparation cost

We propose a simple method for simulating a general class of non-unitary dynamics as a linear combination of Hamiltonian simulation (LCHS) problems. LCHS does not rely on converting the problem into a dilated linear system problem, or on the spectral mapping theorem. The latter is the mathematical foundation of many quantum algorithms for solving a wide variety of tasks involving non-unitary processes, such as the quantum singular value transformation (QSVT). The LCHS method can achieve optimal cost in terms of state preparation. We also demonstrate an application for open quantum dynamics simulation using the complex absorbing potential method with near-optimal dependence on all parameters.

quant-ph↗
arXiv2023

Simultaneous estimation of multiple eigenvalues with short-depth quantum circuit on early fault-tolerant quantum computers

We introduce a multi-modal, multi-level quantum complex exponential least squares (MM-QCELS) method to simultaneously estimate multiple eigenvalues of a quantum Hamiltonian on early fault-tolerant quantum computers. Our theoretical analysis demonstrates that the algorithm exhibits Heisenberg-limited scaling in terms of circuit depth and total cost. Notably, the proposed quantum circuit utilizes just one ancilla qubit, and with appropriate initial state conditions, it achieves significantly shorter circuit depths compared to circuits based on quantum phase estimation (QPE). Numerical results suggest that compared to QPE, the circuit depth can be reduced by around two orders of magnitude under several settings for estimating ground-state and excited-state energies of certain quantum systems.

quant-ph↗
arXiv2023

Efficient anti-symmetrization of a neural network layer by taming the sign problem

Explicit antisymmetrization of a neural network is a potential candidate for a universal function approximator for generic antisymmetric functions, which are ubiquitous in quantum physics. However, this procedure is a priori factorially costly to implement, making it impractical for large numbers of particles. The strategy also suffers from a sign problem. Namely, due to near-exact cancellation of positive and negative contributions, the magnitude of the antisymmetrized function may be significantly smaller than before anti-symmetrization. We show that the anti-symmetric projection of a two-layer neural network can be evaluated efficiently, opening the door to using a generic antisymmetric layer as a building block in anti-symmetric neural network Ansatzes. This approximation is effective when the sign problem is controlled, and we show that this property depends crucially the choice of activation function under standard Xavier/He initialization methods. As a consequence, using a smooth activation function requires re-scaling of the neural network weights compared to standard initializations.

cs.LG↗
arXiv2023

A radio pulsar phase from SGR J1935+2154 provides clues to the magnetar FRB mechanism

The megajansky radio burst, FRB 20200428, and other bright radio bursts detected from the Galactic source SGR J1935+2154 suggest that magnetars can make fast radio bursts (FRBs), but the emission site and mechanism of FRB-like bursts are still unidentified. Here we report the emergence of a radio pulsar phase of the magnetar five months after FRB 20200428. 795 pulses were detected in 16.5 hours over 13 days by the Five-hundred-meter Aperture Spherical Radio telescope, with luminosities about eight decades fainter than FRB 20200428. The pulses were emitted in a narrow phase window anti-aligned with the X-ray pulsation profile observed by the X-ray telescopes. The bursts, conversely, appear in random phases. This dichotomy suggests that radio pulses originate from a fixed region within the magnetosphere, but bursts occur in random locations and are possibly associated with explosive events in a dynamically evolving magnetosphere. This picture reconciles the lack of periodicity in cosmological repeating FRBs within the magnetar engine model.

astro-ph.HE↗
arXiv2023

Robust iterative method for symmetric quantum signal processing in all parameter regimes

This paper addresses the problem of solving nonlinear systems in the context of symmetric quantum signal processing (QSP), a powerful technique for implementing matrix functions on quantum computers. Symmetric QSP focuses on representing target polynomials as products of matrices in SU(2) that possess symmetry properties. We present a novel Newton's method tailored for efficiently solving the nonlinear system involved in determining the phase factors within the symmetric QSP framework. Our method demonstrates rapid and robust convergence in all parameter regimes, including the challenging scenario with ill-conditioned Jacobian matrices, using standard double precision arithmetic operations. For instance, solving symmetric QSP for a highly oscillatory target function $α\cos(1000 x)$ (polynomial degree $\approx 1433$) takes $6$ iterations to converge to machine precision when $α=0.9$, and the number of iterations only increases to $18$ iterations when $α=1-10^{-9}$ with a highly ill-conditioned Jacobian matrix. Leveraging the matrix product states the structure of symmetric QSP, the computation of the Jacobian matrix incurs a computational cost comparable to a single function evaluation. Moreover, we introduce a reformulation of symmetric QSP using real-number arithmetics, further enhancing the method's efficiency. Extensive numerical tests validate the effectiveness and robustness of our approach, which has been implemented in the QSPPACK software package.

quant-ph↗
arXiv2023

A theory of quantum subspace diagonalization

Quantum subspace diagonalization methods are an exciting new class of algorithms for solving large\rev{-}scale eigenvalue problems using quantum computers. Unfortunately, these methods require the solution of an ill-conditioned generalized eigenvalue problem, with a matrix pair corrupted by a non-negligible amount of noise that is far above the machine precision. Despite pessimistic predictions from classical \rev{worst-case} perturbation theories, these methods can perform reliably well if the generalized eigenvalue problem is solved using a standard truncation strategy. By leveraging and advancing classical results in matrix perturbation theory, we provide a theoretical analysis of this surprising phenomenon, proving that under certain natural conditions, a quantum subspace diagonalization algorithm can accurately compute the smallest eigenvalue of a large Hermitian matrix. We give numerical experiments demonstrating the effectiveness of the theory and providing practical guidance for the choice of truncation level. Our new results can also be of independent interest to solving eigenvalue problems outside the context of quantum computation.

quant-ph↗