arXiv subjects

Tong Liu

Publications and source records attributed to Tong Liu.

At least 199 records · Page 11Linked to original sources

arXiv2023

Relative Fontaine-Messing theory over power series rings

Let $k$ be a perfect field of characteristic $p>2$, $R := W(k)[\![t_1, \dots, t_d]\!]$ be the power series ring over the Witt vectors, and $X$ be a smooth proper scheme over $R$. The main goal of this article is to extend classical Fontaine-Messing theory to the setting where the base ring is $R$. In particular, we obtain comparison theorems between torsion crystalline cohomology of $X/R$ and torsion étale cohomology in this setting.

math.NT↗

arXiv2023

Training Multi-layer Neural Networks on Ising Machine

As a dedicated quantum device, Ising machines could solve large-scale binary optimization problems in milliseconds. There is emerging interest in utilizing Ising machines to train feedforward neural networks due to the prosperity of generative artificial intelligence. However, existing methods can only train single-layer feedforward networks because of the complex nonlinear network topology. This paper proposes an Ising learning algorithm to train quantized neural network (QNN), by incorporating two essential techinques, namely binary representation of topological network and order reduction of loss function. As far as we know, this is the first algorithm to train multi-layer feedforward networks on Ising machines, providing an alternative to gradient-based backpropagation. Firstly, training QNN is formulated as a quadratic constrained binary optimization (QCBO) problem by representing neuron connection and activation function as equality constraints. All quantized variables are encoded by binary bits based on binary encoding protocol. Secondly, QCBO is converted to a quadratic unconstrained binary optimization (QUBO) problem, that can be efficiently solved on Ising machines. The conversion leverages both penalty function and Rosenberg order reduction, who together eliminate equality constraints and reduce high-order loss function into a quadratic one. With some assumptions, theoretical analysis shows the space complexity of our algorithm is $\mathcal{O}(H^2L + HLN\log H)$, quantifying the required number of Ising spins. Finally, the algorithm effectiveness is validated with a simulated Ising machine on MNIST dataset. After annealing 700 ms, the classification accuracy achieves 98.3%. Among 100 runs, the success probability of finding the optimal solution is 72%. Along with the increasing number of spins on Ising machine, our algorithm has the potential to train deeper neural networks.

cs.LG↗

arXiv2023

Spatio-Temporal Similarity Measure based Multi-Task Learning for Predicting Alzheimer's Disease Progression using MRI Data

Identifying and utilising various biomarkers for tracking Alzheimer's disease (AD) progression have received many recent attentions and enable helping clinicians make the prompt decisions. Traditional progression models focus on extracting morphological biomarkers in regions of interest (ROIs) from MRI/PET images, such as regional average cortical thickness and regional volume. They are effective but ignore the relationships between brain ROIs over time, which would lead to synergistic deterioration. For exploring the synergistic deteriorating relationship between these biomarkers, in this paper, we propose a novel spatio-temporal similarity measure based multi-task learning approach for effectively predicting AD progression and sensitively capturing the critical relationships between biomarkers. Specifically, we firstly define a temporal measure for estimating the magnitude and velocity of biomarker change over time, which indicate a changing trend(temporal). Converting this trend into the vector, we then compare this variability between biomarkers in a unified vector space(spatial). The experimental results show that compared with directly ROI based learning, our proposed method is more effective in predicting disease progression. Our method also enables performing longitudinal stability selection to identify the changing relationships between biomarkers, which play a key role in disease progression. We prove that the synergistic deteriorating biomarkers between cortical volumes or surface areas have a significant effect on the cognitive prediction.

cs.LG↗

arXiv2023

Probability Thermodynamics and Probability Quantum Field

We introduce probability thermodynamics and probability quantum fields. By probability we mean that there is an unknown operator, physical or nonphysical, whose eigenvalues obey a certain statistical distribution. Eigenvalue spectra define spectral functions. Various thermodynamic quantities in thermodynamics and effective actions in quantum field theory are all spectral functions. In the scheme, eigenvalues obey a probability distribution, so a probability distribution determines a family of spectral functions in thermodynamics and quantum field theory. This leads to probability thermodynamics and probability quantum fields determined by a probability distribution. In constructing spectral functions, we encounter a problem. The conventional definition of spectral functions applies only to lower bounded spectra. In our scheme, however, there are two types of spectra: lower bounded spectra, corresponding to the probability distribution with nonnegative random variables, and the lower unbounded spectra, corresponding to probability distributions with negative random variables. To take the lower unbounded spectra into account, we generalize the definition of spectral functions by analytical continuation. In some cases, we encounter divergences. We remove the divergence by a renormalization procedure. Moreover, in virtue of spectral theory in physics, we generalize some concepts in probability theory. For example, the moment-generating function in probability theory does not always exist. We redefine the moment-generating function as the generalized heat kernel introduced in this paper, which makes the concept definable when the definition in probability theory fails. Thermodynamic quantities, vacuum amplitudes, one-loop effective actions, and vacuum energies for various probability distributions are presented.

cond-mat.stat-mech↗

arXiv2023

ITRE: Low-light Image Enhancement Based on Illumination Transmission Ratio Estimation

Noise, artifacts, and over-exposure are significant challenges in the field of low-light image enhancement. Existing methods often struggle to address these issues simultaneously. In this paper, we propose a novel Retinex-based method, called ITRE, which suppresses noise and artifacts from the origin of the model, prevents over-exposure throughout the enhancement process. Specifically, we assume that there must exist a pixel which is least disturbed by low light within pixels of same color. First, clustering the pixels on the RGB color space to find the Illumination Transmission Ratio (ITR) matrix of the whole image, which determines that noise is not over-amplified easily. Next, we consider ITR of the image as the initial illumination transmission map to construct a base model for refined transmission map, which prevents artifacts. Additionally, we design an over-exposure module that captures the fundamental characteristics of pixel over-exposure and seamlessly integrate it into the base model. Finally, there is a possibility of weak enhancement when inter-class distance of pixels with same color is too small. To counteract this, we design a Robust-Guard module that safeguards the robustness of the image enhancement process. Extensive experiments demonstrate the effectiveness of our approach in suppressing noise, preventing artifacts, and controlling over-exposure level simultaneously. Our method performs superiority in qualitative and quantitative performance evaluations by comparing with state-of-the-art methods.

cs.CV↗

arXiv2023

How to predict critical state: Invariance of Lyapunov exponent in dual spaces

The critical state in disordered systems, a fascinating and subtle eigenstate, has attracted a lot of research interest. However, the nature of the critical state is difficult to describe quantitatively. Most of the studies focus on numerical verification, and cannot predict the system in which the critical state exists. In this work, we propose an explicit and universal criterion that for the critical state Lyapunov exponent should be 0 simultaneously in dual spaces, namely Lyapunov exponent remains invariant under Fourier transform. With this criterion, we exactly predict a specific system hosting a large number of critical states for the first time. Then, we perform numerical verification of the theoretical prediction, and display the self-similarity and scale invariance of the critical state. Finally, we conjecture that there exist some kind of connection between the invariance of the Lyapunov exponent and conformal invariance.

cond-mat.dis-nn↗

arXiv2023

Real eigenvalues are determined by the recursion of eigenstates

Quantum physics is generally concerned with real eigenvalues due to the unitarity of time evolution. With the introduction of $\mathcal{PT}$ symmetry, a widely accepted consensus is that, even if the Hamiltonian of the system is not Hermitian, the eigenvalues can still be pure real under specific symmetry. Hence, great enthusiasm has been devoted to exploring the eigenvalue problem of non-Hermitian systems. In this work, from a distinct perspective, we demonstrate that real eigenvalues can also emerge under the appropriate recursive condition of eigenstates. Consequently, our findings provide another path to extract the real energy spectrum of non-Hermitian systems, which guarantees the conservation of probability and stimulates future experimental observations.

quant-ph↗

arXiv2023

Adaptive Encoding Strategies for Erasing-Based Lossless Floating-Point Compression

Lossless floating-point time series compression is crucial for a wide range of critical scenarios. Nevertheless, it is a big challenge to compress time series losslessly due to the complex underlying layouts of floating-point values. The state-of-the-art erasing-based compression algorithm Elf demonstrates a rather impressive performance. We give an in-depth exploration of the encoding strategies of Elf, and find that there is still much room for improvement. In this paper, we propose Elf*, which employs a set of optimizations for leading zeros, center bits and sharing condition. Specifically, we develop a dynamic programming algorithm with a set of pruning strategies to compute the adaptive approximation rules efficiently. We theoretically prove that the adaptive approximation rules are globally optimal. We further extend Elf* to Streaming Elf*, i.e., SElf*, which achieves almost the same compression ratio as Elf*, while enjoying even higher efficiency in streaming scenarios. We compare Elf* and SElf* with 8 competitors using 22 datasets. The results demonstrate that SElf* achieves 9.2% relative compression ratio improvement over the best streaming competitor while maintaining similar efficiency, and that Elf* ranks among the most competitive batch compressors. All source codes are publicly released.

cs.DS↗

arXiv2023

Cognitive Mirage: A Review of Hallucinations in Large Language Models

As large language models continue to develop in the field of AI, text generation systems are susceptible to a worrisome phenomenon known as hallucination. In this study, we summarize recent compelling insights into hallucinations in LLMs. We present a novel taxonomy of hallucinations from various text generation tasks, thus provide theoretical insights, detection methods and improvement approaches. Based on this, future research directions are proposed. Our contribution are threefold: (1) We provide a detailed and complete taxonomy for hallucinations appearing in text generation tasks; (2) We provide theoretical analyses of hallucinations in LLMs and provide existing detection and improvement methods; (3) We propose several research directions that can be developed in the future. As hallucinations garner significant attention from the community, we will maintain updates on relevant research progress.

cs.CL↗

arXiv2023

Simulating Chern insulators on a superconducting quantum processor

The quantum Hall effect, fundamental in modern condensed matter physics, continuously inspires new theories and predicts emergent phases of matter. Here we experimentally demonstrate three types of Chern insulators with synthetic dimensions on a programable 30-qubit-ladder superconducting processor. We directly measure the band structures of the 2D Chern insulator along synthetic dimensions with various configurations of Aubry-André-Harper chains and observe dynamical localisation of edge excitations. With these two signatures of topology, our experiments implement the bulk-edge correspondence in the synthetic 2D Chern insulator. Moreover, we simulate two different bilayer Chern insulators on the ladder-type superconducting processor. With the same and opposite periodically modulated on-site potentials for two coupled chains, we simulate topologically nontrivial edge states with zero Hall conductivity and a Chern insulator with higher Chern numbers, respectively. Our work shows the potential of using superconducting qubits for investigating different intriguing topological phases of quantum matter.

quant-ph↗

arXiv2023

Observation of multiple steady states with engineered dissipation

Simulating the dynamics of open quantum systems is essential in achieving practical quantum computation and understanding novel nonequilibrium behaviors. However, quantum simulation of a many-body system coupled to an engineered reservoir has yet to be fully explored in present-day experiment platforms. In this work, we introduce engineered noise into a one-dimensional ten-qubit superconducting quantum processor to emulate a generic many-body open quantum system. Our approach originates from the stochastic unravellings of the master equation. By measuring the end-to-end correlation, we identify multiple steady states stemmed from a strong symmetry, which is established on the modified Hamiltonian via Floquet engineering. Furthermore, we find that the information saved in the initial state maintains in the steady state driven by the continuous dissipation on a five-qubit chain. Our work provides a manageable and hardware-efficient strategy for the open-system quantum simulation.

quant-ph↗

arXiv2023

Modulating magnetic and electronic properties of lead-apatite Pb$_{10}$(PO$_4$)$_6$O via different transition metal doping

Based on the first-principles electronic structure calculations, we investigate the magnetic and electronic properties of transition-metal-doped Pb$_{10}$(PO$_4$)$_6$O with the Pb atom substituted by various transition metals. The $3d$ orbitals of the doped transition metals are distributed near the Fermi energy and exhibit strong spin-polarization, resulting in the local magnetic moment. With the doped metal varying from V, Cr, Mn, Fe, Co, Ni, Cu, to Zn, the moment changes gradually from 3.0, 4.0, 5.0, 4.0, 3.0, 2.0, 1.0, to 0 $μ_B$, while the electronic structure is modulated progressively due to the continuous change of total charge. Moreover, the flat bands near the Fermi energy are also found in the V, Cr, and Fe-doped lead-apatite, similar to the Cu-doped system. Our work not only provides the critical comparative information for investigating the Cu-doped lead-apatite, but also suggest a category of diluted magnetic semiconductor.

cond-mat.mtrl-sci↗

arXiv2023

iEDA: An Open-Source Intelligent Physical Implementation Toolkit and Library

Open-source EDA shows promising potential in unleashing EDA innovation and lowering the cost of chip design. This paper presents an open-source EDA project, iEDA, aiming for building a basic infrastructure for EDA technology evolution and closing the industrial-academic gap in the EDA area. iEDA now covers the whole flow of physical design (including Floorplan, Placement, CTS, Routing, Timing Optimization etc.), and part of the analysis tools (Static Timing Analysis and Power Analysis). To demonstrate the effectiveness of iEDA, we implement and tape out three chips of different scales (from 700k to 1.5M gates) on different process nodes (110nm and 28nm) with iEDA. iEDA is publicly available from the project home page http://ieda.oscc.cc.

cs.AR↗

arXiv2023

A prismatic approach to $(φ, \hat G)$-modules and $F$-crystals

We give a new construction of $(φ, \hat G)$-modules using the theory of prisms developed by Bhatt and Scholze. As an application, we give a new proof about the equivalence between the category of prismatic $F$-crystals in finite locally free $\mathcal{O}_Δ$-modules over $(\mathcal{O}_K)_Δ$ and the category of lattices in crystalline representations of $G_K$, where $K$ is a complete discretely valued field of mixed characteristic with perfect residue field. We also generalize this result to semi-stable representations using the absolute logarithmic prismatic site defined by Koshikawa.

math.NT↗

arXiv2023

Quantum simulation of topological zero modes on a 41-qubit superconducting processor

Quantum simulation of different exotic topological phases of quantum matter on a noisy intermediate-scale quantum (NISQ) processor is attracting growing interest. Here, we develop a one-dimensional 43-qubit superconducting quantum processor, named as Chuang-tzu, to simulate and characterize emergent topological states. By engineering diagonal Aubry-Andr$\acute{\mathrm{e}}$-Harper (AAH) models, we experimentally demonstrate the Hofstadter butterfly energy spectrum. Using Floquet engineering, we verify the existence of the topological zero modes in the commensurate off-diagonal AAH models, which have never been experimentally realized before. Remarkably, the qubit number over 40 in our quantum processor is large enough to capture the substantial topological features of a quantum system from its complex band structure, including Dirac points, the energy gap's closing, the difference between even and odd number of sites, and the distinction between edge and bulk states. Our results establish a versatile hybrid quantum simulation approach to exploring quantum topological systems in the NISQ era.

quant-ph↗

arXiv2023

Super-resolution imaging through a multimode fiber: the physical upsampling of speckle-driven

Following recent advancements in multimode fiber (MMF), miniaturization of imaging endoscopes has proven crucial for minimally invasive surgery in vivo. Recent progress enabled by super-resolution imaging methods with a data-driven deep learning (DL) framework has balanced the relationship between the core size and resolution. However, most of the DL approaches lack attention to the physical properties of the speckle, which is crucial for reconciling the relationship between the magnification of super-resolution imaging and the quality of reconstruction quality. In the paper, we find that the interferometric process of speckle formation is an essential basis for creating DL models with super-resolution imaging. It physically realizes the upsampling of low-resolution (LR) images and enhances the perceptual capabilities of the models. The finding experimentally validates the role played by the physical upsampling of speckle-driven, effectively complementing the lack of information in data-driven. Experimentally, we break the restriction of the poor reconstruction quality at great magnification by inputting the same size of the speckle with the size of the high-resolution (HR) image to the model. The guidance of our research for endoscopic imaging may accelerate the further development of minimally invasive surgery.

physics.optics↗

arXiv2023

Long-duration Gamma-ray Burst Progenitors and Magnetar Formation

Millisecond magnetars produced in the center of dying massive stars are one prominent model to power gamma-ray bursts (GRBs). However, their detailed nature remains a mystery. To explore the effects of the initial mass, rotation rate, wind mass loss, and metallicity on the GRB progenitors and the newborn magnetar properties, we evolve 227 of $10-30~M_\odot$ single star models from the pre-main-sequence to core collapse by using the stellar evolution code MESA. The pre-supernova properties, the compactness parameter, and magnetar characteristics of models with different initial parameters are presented. The compactness parameter remains a non-monotonic function of the initial mass and initial rotation rate when the effects of vary metallicity and ``Dutch'' wind scale factor are taken into account. We find that the initial rotation rate and mass play the dominant roles in whether a star can evolve into a GRB progenitor. The minimum rotation rate necessary to generate a magnetar gradually reduces as the initial mass increases. The greater the initial metallicity and ``Dutch'' wind scale factor, the larger the minimum rotation rate required to produce a magnetar. In other words, massive stars with low metallicity are more likely to harbor magnetars. Furthermore, we present the estimated period, magnetic field strength, and masses of magnetars in all cases. The typical rotational energy of these millisecond magnetars is sufficient to power long-duration GRBs.

astro-ph.HE↗

arXiv2023

Tunable Coupling Architectures with Capacitively Connecting Pads for Large-Scale Superconducting Multi-Qubit Processors

We have proposed and experimentally verified a tunable inter-qubit coupling scheme for large-scale integration of superconducting qubits. The key feature of the scheme is the insertion of connecting pads between qubit and tunable coupling element. In such a way, the distance between two qubits can be increased considerably to a few millimeters, leaving enough space for arranging control lines, readout resonators and other necessary structures. The increased inter-qubit distance provides more wiring space for flip-chip process and reduces crosstalk between qubits and from control lines to qubits. We use the term Tunable Coupler with Capacitively Connecting Pad (TCCP) to name the tunable coupling part that consists of a transmon coupler and capacitively connecting pads. With the different placement of connecting pads, different TCCP architectures can be realized. We have designed and fabricated a few multi-qubit devices in which TCCP is used for coupling. The measured results show that the performance of the qubits coupled by the TCCP, such as $T_1$ and $T_2$, was similar to that of the traditional transmon qubits without TCCP. Meanwhile, our TCCP also exhibited a wide tunable range of the effective coupling strength and a low residual ZZ interaction between the qubits by properly tuning the parameters on the design. Finally, we successfully implemented an adiabatic CZ gate with TCCP. Furthermore, by introducing TCCP, we also discuss the realization of the flip-chip process and tunable coupling qubits between different chips.

quant-ph↗