arXiv subjects

Shi-Ju Ran

Publications and source records attributed to Shi-Ju Ran.

At least 37 records · Page 2Linked to original sources

arXiv2023

Nature of the 1/9-magnetization plateau in the spin-1/2 kagome Heisenberg antiferromagnet

The nature of the 1/9-magnetization plateau of the spin-1/2 kagome Heisenberg antiferromagnet remains controversial due to the exotic physical properties and high complexity induced by the geometrical frustration. Instead of a Z3 quantum spin liquid revealed on a cylinder, we show on an infinite-size lattice that the 1/9 plateau can be described by a valence bond crystal (VBC) that breaks spatial translational invariance. Consistent results are achieved by two accurate tensor network methods, namely the full-update infinite projected-entangled pair states and the projected-entangled simplex states. The VBC exhibits an hourglass pattern with $\sqrt{3}\times\sqrt{3}$ spatial symmetry, demonstrated by magnetizations, bond energies, and three-body correlators. The spatial inversion symmetry in the $\sqrt{3}\times\sqrt{3}$ VBC is instantly broken with the presence of the difference between the coupling strengths in the up and down triangles, suggesting the existence of gapless excitations. The gapless nature of the 1/9 plateau is further indicated by the scaling behaviors of the entanglement entropy and the correlation length, which indicate a c=1 conformal field theory.

cond-mat.str-el↗

arXiv2023

Quantum compiling with a variational instruction set for accurate and fast quantum computing

The quantum instruction set (QIS) is defined as the quantum gates that are physically realizable by controlling the qubits in quantum hardware. Compiling quantum circuits into the product of the gates in a properly defined QIS is a fundamental step in quantum computing. We here propose the quantum variational instruction set (QuVIS) formed by flexibly designed multi-qubit gates for higher speed and accuracy of quantum computing. The controlling of qubits for realizing the gates in a QuVIS is variationally achieved using the fine-grained time optimization algorithm. Significant reductions in both the error accumulation and time cost are demonstrated in realizing the swaps of multiple qubits and quantum Fourier transformations, compared with the compiling by a standard QIS such as the quantum microinstruction set (QuMIS, formed by several one- and two-qubit gates including one-qubit rotations and controlled-NOT gates). With the same requirement on quantum hardware, the time cost for QuVIS is reduced to less than one half of that for QuMIS. Simultaneously, the error is suppressed algebraically as the depth of the compiled circuit is reduced. As a general compiling approach with high flexibility and efficiency, QuVIS can be defined for different quantum circuits and be adapted to the quantum hardware with different interactions.

quant-ph↗

arXiv2023

Intelligent diagnostic scheme for lung cancer screening with Raman spectra data by tensor network machine learning

Artificial intelligence (AI) has brought tremendous impacts on biomedical sciences from academic researches to clinical applications, such as in biomarkers' detection and diagnosis, optimization of treatment, and identification of new therapeutic targets in drug discovery. However, the contemporary AI technologies, particularly deep machine learning (ML), severely suffer from non-interpretability, which might uncontrollably lead to incorrect predictions. Interpretability is particularly crucial to ML for clinical diagnosis as the consumers must gain necessary sense of security and trust from firm grounds or convincing interpretations. In this work, we propose a tensor-network (TN)-ML method to reliably predict lung cancer patients and their stages via screening Raman spectra data of Volatile organic compounds (VOCs) in exhaled breath, which are generally suitable as biomarkers and are considered to be an ideal way for non-invasive lung cancer screening. The prediction of TN-ML is based on the mutual distances of the breath samples mapped to the quantum Hilbert space. Thanks to the quantum probabilistic interpretation, the certainty of the predictions can be quantitatively characterized. The accuracy of the samples with high certainty is almost 100$\%$. The incorrectly-classified samples exhibit obviously lower certainty, and thus can be decipherably identified as anomalies, which will be handled by human experts to guarantee high reliability. Our work sheds light on shifting the ``AI for biomedical sciences'' from the conventional non-interpretable ML schemes to the interpretable human-ML interactive approaches, for the purpose of high accuracy and reliability.

q-bio.QM↗

arXiv2022

Characterizing the quantum field theory vacuum using temporal Matrix Product states

In this paper we construct the continuous Matrix Product State (MPS) representation of the vacuum of the field theory corresponding to the continuous limit of an Ising model. We do this by exploiting the observation made by Hastings and Mahajan in [Phys. Rev. A \textbf{91}, 032306 (2015)] that the Euclidean time evolution generates a continuous MPS along the time direction. We exploit this fact, together with the emerging Lorentz invariance at the critical point in order to identify the matrix product representation of the quantum field theory (QFT) vacuum with the continuous MPS in the time direction (tMPS). We explicitly construct the tMPS and check these statements by comparing the physical properties of the tMPS with those of the standard ground MPS. We furthermore identify the QFT that the tMPS encodes with the field theory emerging from taking the continuous limit of a weakly perturbed Ising model by a parallel field first analyzed by Zamolodchikov.

cond-mat.stat-mech↗

arXiv2022

Unsupervised Recognition of Informative Features via Tensor Network Machine Learning and Quantum Entanglement Variations

Given an image of a white shoe drawn on a blackboard, how are the white pixels deemed (say by human minds) to be informative for recognizing the shoe without any labeling information on the pixels? Here we investigate such a ``white shoe'' recognition problem from the perspective of tensor network (TN) machine learning and quantum entanglement. Utilizing a generative TN that captures the probability distribution of the features as quantum amplitudes, we propose an unsupervised recognition scheme of informative features with the variations of entanglement entropy (EE) caused by designed measurements. In this way, a given sample, where the values of its features are statistically meaningless, is mapped to the variations of EE that statistically characterize the gain of information. We show that the EE variations identify the features that are critical to recognize this specific sample, and the EE itself reveals the information distribution of the probabilities represented by the TN model. The signs of the variations further reveal the entanglement structures among the features. We test the validity of our scheme on a toy dataset of strip images, the MNIST dataset of hand-drawn digits, the fashion-MNIST dataset of the pictures of fashion articles, and the images of brain cells. Our scheme opens the avenue to the quantum-inspired and interpreted unsupervised learning, which can be applied to, e.g., image segmentation and object detection.

quant-ph↗

arXiv2022

Deep Machine Learning Reconstructing Lattice Topology with Strong Thermal Fluctuations

Applying artificial intelligence to scientific problems (namely AI for science) is currently under hot debate. However, the scientific problems differ much from the conventional ones with images, texts, and etc., where new challenges emerges with the unbalanced scientific data and complicated effects from the physical setups. In this work, we demonstrate the validity of the deep convolutional neural network (CNN) on reconstructing the lattice topology (i.e., spin connectivities) in the presence of strong thermal fluctuations and unbalanced data. Taking the kinetic Ising model with Glauber dynamics as an example, the CNN maps the time-dependent local magnetic momenta (a single-node feature) evolved from a specific initial configuration (dubbed as an evolution instance) to the probabilities of the presences of the possible couplings. Our scheme distinguishes from the previous ones that might require the knowledge on the node dynamics, the responses from perturbations, or the evaluations of statistic quantities such as correlations or transfer entropy from many evolution instances. The fine tuning avoids the "barren plateau" caused by the strong thermal fluctuations at high temperatures. Accurate reconstructions can be made where the thermal fluctuations dominate over the correlations and consequently the statistic methods in general fail. Meanwhile, we unveil the generalization of CNN on dealing with the instances evolved from the unlearnt initial spin configurations and those with the unlearnt lattices. We raise an open question on the learning with unbalanced data in the nearly "double-exponentially" large sample space.

stat.ML↗

arXiv2022

Accurate simulation and thermal tuning by temperature-adaptive boundary interactions on quantum many-body systems

Constructing quantum Hamiltonians for simulating and controlling the exotic physics of many-body systems belongs to the most important topics of condensed matter physics and quantum technologies. The main challenge that hinders the future investigations is the extremely high complexity for either their numerical simulations or experimental realizations. In this work, we propose the temperature-adaptive entanglement simulator (TAES) that mimics and tunes the thermodynamics of the one-dimensional (1D) many-body system by embedding a small-size model in an entanglement bath. The entanglement bath is described by the interactions located at the boundaries of the small-size model, whose coupling constants are optimized by means of differentiable tensor network at target temperatures. With the benchmark on 1D spin chains, TAES surpasses the state-of-the-art accuracy compared with the existing finite-temperature approaches such as linearized and differential tensor renormalization group algorithms. By tuning the couplings of the entanglement bath with the temperature fixed, the bulk entropy exhibits similar behavior compared to that obtained by tuning the temperature. Our work provides novel opportunities of engineering the distribution of fluctuations and mimicking the non-equilibrium phenomena in a uniform temperature within the canonical ensemble framework using the optimized boundary interactions.

quant-ph↗

arXiv2022

Efficient Simulation of Quantum Many-body Thermodynamics by Tailoring Zero-temperature Tensor Network

Numerical annealing and renormalization group have conceived various successful approaches to study the thermodynamics of strongly-correlated systems where perturbation or expansion theories fail to work. As the process of lowering the temperatures is usually involved in different manners, these approaches in general become much less efficient or accurate at the low temperatures. In this work, we propose to access the finite-temperature properties from the tensor network (TN) representing the zero-temperature partition function. We propose to "scissor" a finite part from such an infinite-size TN, and "stitch" it to possess the periodic boundary condition along the imaginary-time direction. We dub this approach as TN tailoring. Exceptional accuracy is achieved with a fine-tune process, surpassing the previous methods including the linearized tensor renormalization group [Phys. Rev. Lett. 106, 127202 (2011)], continuous matrix product operator [Phys. Rev. Lett. 125, 170604 (2020)], and etc. High efficiency is demonstrated, where the time cost is nearly independent of the target temperature including the extremely-low temperatures. The proposed idea can be extended to higher-dimensional systems of bosons and fermions.

quant-ph↗

arXiv2022

Functional Tensor Network Solving Many-body Schrödinger Equation

Schrödinger equation belongs to the most fundamental differential equations in quantum physics. However, the exact solutions are extremely rare, and many analytical methods are applicable only to the cases with small perturbations or weak correlations. Solving the many-body Schrödinger equation in the continuous spaces with the presence of strong correlations is an extremely important and challenging issue. In this work, we propose the functional tensor network (FTN) approach to solve the many-body Schrödinger equation. Provided the orthonormal functional bases, we represent the coefficients of the many-body wave-function as tensor network. The observables, such as energy, can be calculated simply by tensor contractions. Simulating the ground state becomes solving a minimization problem defined by the tensor network. An efficient gradient-decent algorithm based on the automatically differentiable tensors is proposed. We here take matrix product state (MPS) as an example, whose complexity scales only linearly with the system size. We apply our approach to solve the ground state of coupled harmonic oscillators, and achieve high accuracy by comparing with the exact solutions. Reliable results are also given with the presence of three-body interactions, where the system cannot be decoupled to isolated oscillators. Our approach is simple and with well-controlled error, superior to the highly-nonlinear neural-network solvers. Our work extends the applications of tensor network from quantum lattice models to the systems in the continuous space. FTN can be used as a general solver of the differential equations with many variables. The MPS exemplified here can be generalized to, e.g., the fermionic tensor networks, to solve the electronic Schrödinger equation.

quant-ph↗

arXiv2022

Experimental realization of a quantum image classifier via tensor-network-based machine learning

Quantum machine learning aspires to overcome intractability that currently limits its applicability to practical problems. However, quantum machine learning itself is limited by low effective dimensions achievable in state-of-the-art experiments. Here we demonstrate highly successful classifications of real-life images using photonic qubits, combining a quantum tensor-network representation of hand-written digits and entanglement-based optimization. Specifically, we focus on binary classification for hand-written zeroes and ones, whose features are cast into the tensor-network representation, further reduced by optimization based on entanglement entropy and encoded into two-qubit photonic states. We then demonstrate image classification with a high success rate exceeding 98%, through successive gate operations and projective measurements. Although we work with photons, our approach is amenable to other physical realizations such as nitrogen-vacancy centers, nuclear spins and trapped ions, and our scheme can be scaled to efficient multi-qubit encodings of features in the tensor-product representation, thereby setting the stage for quantum-enhanced multi-class classification.

quant-ph↗

arXiv2021

Residual Matrix Product State for Machine Learning

Tensor network, which originates from quantum physics, is emerging as an efficient tool for classical and quantum machine learning. Nevertheless, there still exists a considerable accuracy gap between tensor network and the sophisticated neural network models for classical machine learning. In this work, we combine the ideas of matrix product state (MPS), the simplest tensor network structure, and residual neural network and propose the residual matrix product state (ResMPS). The ResMPS can be treated as a network where its layers map the "hidden" features to the outputs (e.g., classifications), and the variational parameters of the layers are the functions of the features of the samples (e.g., pixels of images). This is different from neural network, where the layers map feed-forwardly the features to the output. The ResMPS can equip with the non-linear activations and dropout layers, and outperforms the state-of-the-art tensor network models in terms of efficiency, stability, and expression power. Besides, ResMPS is interpretable from the perspective of polynomial expansion, where the factorization and exponential machines naturally emerge. Our work contributes to connecting and hybridizing neural and tensor networks, which is crucial to further enhance our understand of the working mechanisms and improve the performance of both models.

cs.LG↗

arXiv2021

Preparation of Many-body Ground States by Time Evolution with Variational Microscopic Magnetic Fields and Incomplete Interactions

State preparation is of fundamental importance in quantum physics, which can be realized by constructing the quantum circuit as a unitary that transforms the initial state to the target, or implementing a quantum control protocol to evolve to the target state with a designed Hamiltonian. In this work, we study the latter on quantum many-body systems by the time evolution with fixed couplings and variational magnetic fields. In specific, we consider to prepare the ground states of the Hamiltonians containing certain interactions that are missing in the Hamiltonians for the time evolution. An optimization method is proposed to optimize the magnetic fields by "fine-graining" the discretization of time, in order to gain high precision and stability. The back propagation technique is utilized to obtain the gradients of the fields against the logarithmic fidelity. Our method is tested on preparing the ground state of Heisenberg chain with the time evolution by the XY and Ising interactions, and its performance surpasses two baseline methods that use local and global optimization strategies, respectively. Our work can be applied and generalized to other quantum models such as those defined on higher dimensional lattices. It enlightens to reduce the complexity of the required interactions for implementing quantum control or other tasks in quantum information and computation by means of optimizing the magnetic fields.

quant-ph↗

arXiv2021

Non-parametric Semi-Supervised Learning in Many-body Hilbert Space with Rescaled Logarithmic Fidelity

In quantum and quantum-inspired machine learning, the very first step is to embed the data in quantum space known as Hilbert space. Developing quantum kernel function (QKF), which defines the distances among the samples in the Hilbert space, belongs to the fundamental topics for machine learning. In this work, we propose the rescaled logarithmic fidelity (RLF) and non-parametric semi-supervised learning in the quantum space, which we name as RLF-NSSL. The rescaling takes advantage of the non-linearity of the kernel to tune the mutual distances of samples in the Hilbert space, and meanwhile avoids the exponentially-small fidelities between quantum many-qubit states. Being non-parametric excludes the possible effects from the variational parameters, and evidently demonstrates the advantages from the space itself. We compare RLF-NSSL with several well-known non-parametric algorithms including naive Bayes classifiers, k-nearest neighbors, and spectral clustering. Our method exhibits better accuracy particularly for the unsupervised case with no labeled samples and the few-shot cases with small numbers of labeled samples. With the visualizations by t-stochastic neighbor embedding, our results imply that the machine learning in the Hilbert space complies with the principles of maximal coding rate reduction, where the low-dimensional data exhibit within-class compressibility, between-class discrimination, and overall diversity. Our proposals can be applied to other quantum and quantum-inspired machine learning, including the methods using the parametric models such as tensor networks, quantum circuits, and quantum neural networks.

quant-ph↗

arXiv2021

Predicting Quantum Potentials by Deep Neural Network and Metropolis Sampling

The hybridizations of machine learning and quantum physics have caused essential impacts to the methodology in both fields. Inspired by quantum potential neural network, we here propose to solve the potential in the Schrodinger equation provided the eigenstate, by combining Metropolis sampling with deep neural network, which we dub as Metropolis potential neural network (MPNN). A loss function is proposed to explicitly involve the energy in the optimization for its accurate evaluation. Benchmarking on the harmonic oscillator and hydrogen atom, MPNN shows excellent accuracy and stability on predicting not just the potential to satisfy the Schrodinger equation, but also the eigen-energy. Our proposal could be potentially applied to the ab-initio simulations, and to inversely solving other partial differential equations in physics and beyond.

quant-ph↗

arXiv2021

Deep learning Local Reduced Density Matrices for Many-body Hamiltonian Estimation

Human experts cannot efficiently access the physical information of quantum many-body states by simply "reading" the coefficients, but have to reply on the previous knowledge such as order parameters and quantum measurements. In this work, we demonstrate that convolutional neural network (CNN) can learn from the coefficients of local reduced density matrices to estimate the physical parameters of the many-body Hamiltonians, such as coupling strengths and magnetic fields, provided the states as the ground states. We propose QubismNet that consists of two main parts: the Qubism map that visualizes the ground states (or the purified reduced density matrices) as images, and a CNN that maps the images to the target physical parameters. By assuming certain constraints on the training set for the sake of balance, QubismNet exhibits impressive powers of learning and generalization on several quantum spin models. While the training samples are restricted to the states from certain ranges of the parameters, QubismNet can accurately estimate the parameters of the states beyond such training regions. For instance, our results show that QubismNet can estimate the magnetic fields near the critical point by learning from the states away from the critical vicinity. Our work illuminates a data-driven way to infer the Hamiltonians that give the designed ground states, and therefore would benefit the existing and future generalizations of quantum technologies such as Hamiltonian-based quantum simulations and state tomography.

quant-ph↗

arXiv2021

Cold atoms meet lattice gauge theory

The central idea of this review is to consider quantum field theory models relevant for particle physics and replace the fermionic matter in these models by a bosonic one. This is mostly motivated by the fact that bosons are more ``accessible'' and easier to manipulate for experimentalists, but this ``substitution'' also leads to new physics and novel phenomena. It allows us to gain new information about among other things confinement and the dynamics of the deconfinement transition. We will thus consider bosons in dynamical lattices corresponding to the bosonic Schwinger or Z$_2$ Bose-Hubbard models. Another central idea of this review concerns atomic simulators of paradigmatic models of particle physics theory such as the Creutz-Hubbard ladder, or Gross-Neveu-Wilson and Wilson-Hubbard models. Finally, we will briefly describe our efforts to design experimentally friendly simulators of these and other models relevant for particle physics.

cond-mat.quant-gas↗

arXiv2021

Automatically Differentiable Quantum Circuit for Many-qubit State Preparation

Constructing quantum circuits for efficient state preparation belongs to the central topics in the field of quantum information and computation. As the number of qubits grows fast, methods to derive large-scale quantum circuits are strongly desired. In this work, we propose the automatically differentiable quantum circuit (ADQC) approach to efficiently prepare arbitrary quantum many-qubit states. A key ingredient is to introduce the latent gates whose decompositions give the unitary gates that form the quantum circuit. The circuit is optimized by updating the latent gates using back propagation to minimize the distance between the evolved and target states. Taking the ground states of quantum lattice models and random matrix product states as examples, with the number of qubits where processing the full coefficients is unlikely, ADQC obtains high fidelities with small numbers of layers $N_L \sim O(1)$. Superior accuracy is reached compared with the existing state-preparation approach based on the matrix product disentangler. The parameter complexity of MPS can be significantly reduced by ADQC with the compression ratio $r \sim O(10^{-3})$. Our work sheds light on the "intelligent construction" of quantum circuits for many-qubit systems by combining with the machine learning methods.

quant-ph↗

arXiv2020

Visual configuration segmentation of quantum states for phase identification in many-body systems

Artificial intelligence provides an unprecedented perspective for studying phases of matter in condensed-matter systems. Image segmentation is a basic technique of computer vision that belongs to a branch of artificial intelligence. In this work, we propose a segmentation scheme named visual configuration segmentation (VCS) to unveil quantum phases and quantum phase transitions in many-body systems. By encoding the information of renormalized quantum states into a color image and segmenting the color image through the VCS, the renormalized quantum states can be visualized, from which quantum phase transitions can be revealed and the corresponding critical points can be identified. Our scheme is benchmarked on several strongly correlated spin systems, which does not depend on the priori knowledge of order parameters of quantum phases. This demonstrates the potential to disclose the underlying structure of quantum phases by the techniques of computer vision.

cond-mat.str-el↗