Searcharxiv⌕ Search

arXiv subjects

Di Luo

Publications and source records attributed to Di Luo.

At least 73 records · Page 4Linked to original sources
arXiv2024

Autoregressive Transformer Neural Network for Simulating Open Quantum Systems via a Probabilistic Formulation

The theory of open quantum systems lays the foundations for a substantial part of modern research in quantum science and engineering. Rooted in the dimensionality of their extended Hilbert spaces, the high computational complexity of simulating open quantum systems calls for the development of strategies to approximate their dynamics. In this paper, we present an approach for tackling open quantum system dynamics. Using an exact probabilistic formulation of quantum physics based on positive operator-valued measure (POVM), we compactly represent quantum states with autoregressive transformer neural networks; such networks bring significant algorithmic flexibility due to efficient exact sampling and tractable density. We further introduce the concept of String States to partially restore the symmetry of the autoregressive transformer neural network and improve the description of local correlations. Efficient algorithms have been developed to simulate the dynamics of the Liouvillian superoperator using a forward-backward trapezoid method and find the steady state via a variational formulation. Our approach is benchmarked on prototypical one and two-dimensional systems, finding results which closely track the exact solution and achieve higher accuracy than alternative approaches based on using Markov chain Monte Carlo to sample restricted Boltzmann machines. Our work provides general methods for understanding quantum dynamics in various contexts, as well as techniques for solving high-dimensional probabilistic differential equations in classical setups.

cond-mat.str-el↗
arXiv2024

Gauge Invariant and Anyonic Symmetric Transformer and RNN Quantum States for Quantum Lattice Models

Symmetries such as gauge invariance and anyonic symmetry play a crucial role in quantum many-body physics. We develop a general approach to constructing gauge invariant or anyonic symmetric autoregressive neural network quantum states, including a wide range of architectures such as Transformer and recurrent neural network (RNN), for quantum lattice models. These networks can be efficiently sampled and explicitly obey gauge symmetries or anyonic constraint. We prove that our methods can provide exact representation for the ground and excited states of the 2D and 3D toric codes, and the X-cube fracton model. We variationally optimize our symmetry incorporated autoregressive neural networks for ground states as well as real-time dynamics for a variety of models. We simulate the dynamics and the ground states of the quantum link model of $\text{U(1)}$ lattice gauge theory, obtain the phase diagram for the 2D $\mathbb{Z}_2$ gauge theory, determine the phase transition and the central charge of the $\text{SU(2)}_3$ anyonic chain, and also compute the ground state energy of the SU(2) invariant Heisenberg spin chain. Our approach provides powerful tools for exploring condensed matter physics, high energy physics and quantum information science.

cond-mat.str-el↗
arXiv2024

Stochastic logic in biased coupled photonic probabilistic bits

Optical computing often employs tailor-made hardware to implement specific algorithms, trading generality for improved performance in key aspects like speed and power efficiency. An important computing approach that is still missing its corresponding optical hardware is probabilistic computing, used e.g. for solving difficult combinatorial optimization problems. In this study, we propose an experimentally viable photonic approach to solve arbitrary probabilistic computing problems. Our method relies on the insight that coherent Ising machines composed of coupled and biased optical parametric oscillators can emulate stochastic logic. We demonstrate the feasibility of our approach by using numerical simulations equivalent to the full density matrix formulation of coupled optical parametric oscillators.

physics.optics↗
arXiv2024

TENG: Time-Evolving Natural Gradient for Solving PDEs With Deep Neural Nets Toward Machine Precision

Partial differential equations (PDEs) are instrumental for modeling dynamical systems in science and engineering. The advent of neural networks has initiated a significant shift in tackling these complexities though challenges in accuracy persist, especially for initial value problems. In this paper, we introduce the $\textit{Time-Evolving Natural Gradient (TENG)}$, generalizing time-dependent variational principles and optimization-based time integration, leveraging natural gradient optimization to obtain high accuracy in neural-network-based PDE solutions. Our comprehensive development includes algorithms like TENG-Euler and its high-order variants, such as TENG-Heun, tailored for enhanced precision and efficiency. TENG's effectiveness is further validated through its performance, surpassing current leading methods and achieving $\textit{machine precision}$ in step-by-step optimizations across a spectrum of PDEs, including the heat equation, Allen-Cahn equation, and Burgers' equation.

cs.LG↗
arXiv2024

Operator Learning Renormalization Group

In this paper, we present a general framework for quantum many-body simulations called the operator learning renormalization group (OLRG). Inspired by machine learning perspectives, OLRG is a generalization of Wilson's numerical renormalization group and White's density matrix renormalization group, which recursively builds a simulatable system to approximate a target system of the same number of sites via operator maps. OLRG uses a loss function to minimize the error of a target property directly by learning the operator map in lieu of a state ansatz. This loss function is designed by a scaling consistency condition that also provides a provable bound for real-time evolution. We implement two versions of the operator maps for classical and quantum simulations. The former, which we call the Operator Matrix Map, can be implemented via neural networks on classical computers. The latter, which we call the Hamiltonian Expression Map, generates device pulse sequences to leverage the capabilities of quantum computing hardware. We illustrate the performance of both maps for calculating time-dependent quantities in the quantum Ising model Hamiltonian.

quant-ph↗
arXiv2024

Leveraging 2D Information for Long-term Time Series Forecasting with Vanilla Transformers

Time series prediction is crucial for understanding and forecasting complex dynamics in various domains, ranging from finance and economics to climate and healthcare. Based on Transformer architecture, one approach involves encoding multiple variables from the same timestamp into a single temporal token to model global dependencies. In contrast, another approach embeds the time points of individual series into separate variate tokens. The former method faces challenges in learning variate-centric representations, while the latter risks missing essential temporal information critical for accurate forecasting. In our work, we introduce GridTST, a model that combines the benefits of two approaches using innovative multi-directional attentions based on a vanilla Transformer. We regard the input time series data as a grid, where the $x$-axis represents the time steps and the $y$-axis represents the variates. A vertical slicing of this grid combines the variates at each time step into a \textit{time token}, while a horizontal slicing embeds the individual series across all time steps into a \textit{variate token}. Correspondingly, a \textit{horizontal attention mechanism} focuses on time tokens to comprehend the correlations between data at various time steps, while a \textit{vertical}, variate-aware \textit{attention} is employed to grasp multivariate correlations. This combination enables efficient processing of information across both time and variate dimensions, thereby enhancing the model's analytical strength. % We also integrate the patch technique, segmenting time tokens into subseries-level patches, ensuring that local semantic information is retained in the embedding. The GridTST model consistently delivers state-of-the-art performance across various real-world datasets.

cs.LG↗
arXiv2024

QuACK: Accelerating Gradient-Based Quantum Optimization with Koopman Operator Learning

Quantum optimization, a key application of quantum computing, has traditionally been stymied by the linearly increasing complexity of gradient calculations with an increasing number of parameters. This work bridges the gap between Koopman operator theory, which has found utility in applications because it allows for a linear representation of nonlinear dynamical systems, and natural gradient methods in quantum optimization, leading to a significant acceleration of gradient-based quantum optimization. We present Quantum-circuit Alternating Controlled Koopman learning (QuACK), a novel framework that leverages an alternating algorithm for efficient prediction of gradient dynamics on quantum computers. We demonstrate QuACK's remarkable ability to accelerate gradient-based optimization across a range of applications in quantum optimization and machine learning. In fact, our empirical studies, spanning quantum chemistry, quantum condensed matter, quantum machine learning, and noisy environments, have shown accelerations of more than 200x speedup in the overparameterized regime, 10x speedup in the smooth regime, and 3x speedup in the non-smooth regime. With QuACK, we offer a robust advancement that harnesses the advantage of gradient-based quantum optimization for practical benefits.

quant-ph↗
arXiv2024

ANTN: Bridging Autoregressive Neural Networks and Tensor Networks for Quantum Many-Body Simulation

Quantum many-body physics simulation has important impacts on understanding fundamental science and has applications to quantum materials design and quantum technology. However, due to the exponentially growing size of the Hilbert space with respect to the particle number, a direct simulation is intractable. While representing quantum states with tensor networks and neural networks are the two state-of-the-art methods for approximate simulations, each has its own limitations in terms of expressivity and inductive bias. To address these challenges, we develop a novel architecture, Autoregressive Neural TensorNet (ANTN), which bridges tensor networks and autoregressive neural networks. We show that Autoregressive Neural TensorNet parameterizes normalized wavefunctions, allows for exact sampling, generalizes the expressivity of tensor networks and autoregressive neural networks, and inherits a variety of symmetries from autoregressive neural networks. We demonstrate our approach on quantum state learning as well as finding the ground state of the challenging 2D $J_1$-$J_2$ Heisenberg model with different systems sizes and coupling parameters, outperforming both tensor networks and autoregressive neural networks. Our work opens up new opportunities for quantum many-body physics simulation, quantum technology design, and generative modeling in artificial intelligence.

quant-ph↗
arXiv2024

Photonic probabilistic machine learning using quantum vacuum noise

Probabilistic machine learning utilizes controllable sources of randomness to encode uncertainty and enable statistical modeling. Harnessing the pure randomness of quantum vacuum noise, which stems from fluctuating electromagnetic fields, has shown promise for high speed and energy-efficient stochastic photonic elements. Nevertheless, photonic computing hardware which can control these stochastic elements to program probabilistic machine learning algorithms has been limited. Here, we implement a photonic probabilistic computer consisting of a controllable stochastic photonic element - a photonic probabilistic neuron (PPN). Our PPN is implemented in a bistable optical parametric oscillator (OPO) with vacuum-level injected bias fields. We then program a measurement-and-feedback loop for time-multiplexed PPNs with electronic processors (FPGA or GPU) to solve certain probabilistic machine learning tasks. We showcase probabilistic inference and image generation of MNIST-handwritten digits, which are representative examples of discriminative and generative models. In both implementations, quantum vacuum noise is used as a random seed to encode classification uncertainty or probabilistic generation of samples. In addition, we propose a path towards an all-optical probabilistic computing platform, with an estimated sampling rate of ~ 1 Gbps and energy consumption of ~ 5 fJ/MAC. Our work paves the way for scalable, ultrafast, and energy-efficient probabilistic machine learning hardware.

physics.optics↗
arXiv2024

Classical Shadows for Quantum Process Tomography on Near-term Quantum Computers

Quantum process tomography is a powerful tool for understanding quantum channels and characterizing properties of quantum devices. Inspired by recent advances using classical shadows in quantum state tomography [H.-Y. Huang, R. Kueng, and J. Preskill, Nat. Phys. 16, 1050 (2020).], we have developed ShadowQPT, a classical shadow method for quantum process tomography. We introduce two related formulations with and without ancilla qubits. ShadowQPT stochastically reconstructs the Choi matrix of the device allowing for an a-posteri classical evaluation of the device on arbitrary inputs with respect to arbitrary outputs. Using shadows we then show how to compute overlaps, generate all $k$-weight reduced processes, and perform reconstruction via Hamiltonian learning. These latter two tasks are efficient for large systems as the number of quantum measurements needed scales only logarithmically with the number of qubits. A number of additional approximations and improvements are developed including the use of a pair-factorized Clifford shadow and a series of post-processing techniques which significantly enhance the accuracy for recovering the quantum channel. We have implemented ShadowQPT using both Pauli and Clifford measurements on the IonQ trapped ion quantum computer for quantum processes up to $n=4$ qubits and achieved good performance.

quant-ph↗
arXiv2023

Variational Neural-Network Ansatz for Continuum Quantum Field Theory

Physicists dating back to Feynman have lamented the difficulties of applying the variational principle to quantum field theories. In non-relativistic quantum field theories, the challenge is to parameterize and optimize over the infinitely many $n$-particle wave functions comprising the state's Fock space representation. Here we approach this problem by introducing neural-network quantum field states, a deep learning ansatz that enables application of the variational principle to non-relativistic quantum field theories in the continuum. Our ansatz uses the Deep Sets neural network architecture to simultaneously parameterize all of the $n$-particle wave functions comprising a quantum field state. We employ our ansatz to approximate ground states of various field theories, including an inhomogeneous system and a system with long-range interactions, thus demonstrating a powerful new tool for probing quantum field theories.

quant-ph↗
arXiv2023

Lift Yourself Up: Retrieval-augmented Text Generation with Self Memory

With direct access to human-written reference as memory, retrieval-augmented generation has achieved much progress in a wide range of text generation tasks. Since better memory would typically prompt better generation~(we define this as primal problem). The traditional approach for memory retrieval involves selecting memory that exhibits the highest similarity to the input. However, this method is constrained by the quality of the fixed corpus from which memory is retrieved. In this paper, by exploring the duality of the primal problem: better generation also prompts better memory, we propose a novel framework, selfmem, which addresses this limitation by iteratively employing a retrieval-augmented generator to create an unbounded memory pool and using a memory selector to choose one output as memory for the subsequent generation round. This enables the model to leverage its own output, referred to as self-memory, for improved generation. We evaluate the effectiveness of selfmem on three distinct text generation tasks: neural machine translation, abstractive text summarization, and dialogue generation, under two generation paradigms: fine-tuned small model and few-shot LLM. Our approach achieves state-of-the-art results in four directions in JRC-Acquis, XSum (50.3 ROUGE-1), and BigPatent (62.9 ROUGE-1), demonstrating the potential of self-memory in enhancing retrieval-augmented generation models. Furthermore, we conduct thorough analyses of each component in the selfmem framework to identify bottlenecks and provide insights for future research.

cs.CL↗
arXiv2023

Pairing-based graph neural network for simulating quantum materials

We develop a pairing-based graph neural network for simulating quantum many-body systems. Our architecture augments a BCS-type geminal wavefunction with a generalized pair amplitude parameterized by a graph neural network. Variational Monte Carlo with our neural network simultaneously provides an accurate, flexible, and scalable method for simulating many-electron systems. We apply this method to two-dimensional semiconductor electron-hole bilayers and obtain accurate results on a variety of interaction-induced phases, including the exciton Bose-Einstein condensate, electron-hole superconductor, and bilayer Wigner crystal. Our study demonstrates the potential of physically-motivated neural network wavefunctions for quantum materials simulations.

cond-mat.str-el↗
arXiv2023

Infinite Neural Network Quantum States: Entanglement and Training Dynamics

We study infinite limits of neural network quantum states ($\infty$-NNQS), which exhibit representation power through ensemble statistics, and also tractable gradient descent dynamics. Ensemble averages of Renyi entropies are expressed in terms of neural network correlators, and architectures that exhibit volume-law entanglement are presented. A general framework is developed for studying the gradient descent dynamics of neural network quantum states (NNQS), using a quantum state neural tangent kernel (QS-NTK). For $\infty$-NNQS the training dynamics is simplified, since the QS-NTK becomes deterministic and constant. An analytic solution is derived for quantum state supervised learning, which allows an $\infty$-NNQS to recover any target wavefunction. Numerical experiments on finite and infinite NNQS in the transverse field Ising model and Fermi Hubbard model demonstrate excellent agreement with theory. $\infty$-NNQS opens up new opportunities for studying entanglement and training dynamics in other physics applications, such as in finding ground states.

quant-ph↗
arXiv2023

Enhancing Job Recommendation through LLM-based Generative Adversarial Networks

Recommending suitable jobs to users is a critical task in online recruitment platforms, as it can enhance users' satisfaction and the platforms' profitability. While existing job recommendation methods encounter challenges such as the low quality of users' resumes, which hampers their accuracy and practical effectiveness. With the rapid development of large language models (LLMs), utilizing the rich external knowledge encapsulated within them, as well as their powerful capabilities of text processing and reasoning, is a promising way to complete users' resumes for more accurate recommendations. However, directly leveraging LLMs to enhance recommendation results is not a one-size-fits-all solution, as LLMs may suffer from fabricated generation and few-shot problems, which degrade the quality of resume completion. In this paper, we propose a novel LLM-based approach for job recommendation. To alleviate the limitation of fabricated generation for LLMs, we extract accurate and valuable information beyond users' self-description, which helps the LLMs better profile users for resume completion. Specifically, we not only extract users' explicit properties (e.g., skills, interests) from their self-description but also infer users' implicit characteristics from their behaviors for more accurate and meaningful resume completion. Nevertheless, some users still suffer from few-shot problems, which arise due to scarce interaction records, leading to limited guidance for the models in generating high-quality resumes. To address this issue, we propose aligning unpaired low-quality with high-quality generated resumes by Generative Adversarial Networks (GANs), which can refine the resume representations for better recommendation results. Extensive experiments on three large real-world recruitment datasets demonstrate the effectiveness of our proposed method.

cs.IR↗
arXiv2023

Q-Flow: Generative Modeling for Differential Equations of Open Quantum Dynamics with Normalizing Flows

Studying the dynamics of open quantum systems can enable breakthroughs both in fundamental physics and applications to quantum engineering and quantum computation. Since the density matrix $ρ$, which is the fundamental description for the dynamics of such systems, is high-dimensional, customized deep generative neural networks have been instrumental in modeling $ρ$. However, the complex-valued nature and normalization constraints of $ρ$, as well as its complicated dynamics, prohibit a seamless connection between open quantum systems and the recent advances in deep generative modeling. Here we lift that limitation by utilizing a reformulation of open quantum system dynamics to a partial differential equation (PDE) for a corresponding probability distribution $Q$, the Husimi Q function. Thus, we model the Q function seamlessly with off-the-shelf deep generative models such as normalizing flows. Additionally, we develop novel methods for learning normalizing flow evolution governed by high-dimensional PDEs based on the Euler method and the application of the time-dependent variational principle. We name the resulting approach $Q$-$Flow$ and demonstrate the scalability and efficiency of Q-Flow on open quantum system simulations, including the dissipative harmonic oscillator and the dissipative bosonic model. Q-Flow is superior to conventional PDE solvers and state-of-the-art physics-informed neural network solvers, especially in high-dimensional systems.

quant-ph↗
arXiv2023

Quantum Computation and Simulation using Fermion-Pair Registers

We propose and analyze an approach to realize quantum computation and simulation using fermionic particles under quantum gas microscopes. Our work is inspired by a recent experimental demonstration of large-scale quantum registers, where tightly localized fermion pairs are used to encode qubits exhibiting long coherence time and robustness against laser intensity noise. We describe how to engineer the SWAP gate and high-fidelity controlled-phase gates by adjusting the fermion hopping as well as Feshbach interaction strengths. Combined with previously demonstrated single-qubit rotations, these gates establish the computational universality of the system. Furthermore, we show that 2D quantum Ising Hamiltonians with tunable transverse and longitudinal fields can be efficient simulated by modulating Feshbach interaction strengths. We present a sample-efficient protocol to characterize engineered gates and Hamiltonian dynamics based on an improved classical shadow process tomography that requires minimal experimental controls. Our work opens up new opportunities to harness existing ultracold quantum gases for quantum information sciences.

quant-ph↗
arXiv2023

Enhancement of Fusion Reactivity under Non-Maxwellian Distributions: Effects of Drift-Ring-Beam, Slowing-Down, and Kappa Super-Thermal Distributions

Non-Maxwellian distributions of particles are commonly observed in fusion studies, especially for magnetic confinement fusion plasmas. The particle distribution has a direct effect on fusion reactivity, which is the focus of this study. We investigate the effects of three types of non-Maxwellian distributions, namely drift-ring-beam, slowing-down, and kappa super-thermal distributions, on the fusion reactivities of D-T (Deuterium-Trillium) and p-B11 (proton-Boron) using a newly developed program, where the enhancement of fusion reactivity relative to the Maxwellian distribution is computed while keeping the total kinetic energy constant. The calculation results show that for the temperature ranges of interest to us, namely 5-50 keV for D-T and 100-500 keV for p-B11, these non-Maxwellian distributions can enhance the fusion reactivities. In the case of the drift-ring-beam distribution, the enhancement factors for both reactions are affected by the perpendicular ring beam velocity, leading to decreased enhancement in low temperature range and increased enhancement in high temperature range. However, this effect is favorable for p-B11 fusion reaction and unfavorable for D-T fusion reaction. In the slowing-down distribution, the birth speed plays a crucial role in both reactions, and increasing birth speed leads to a shift in the enhancement ranges towards lower temperatures, which is beneficial for both reactions. Finally, the kappa super-thermal distribution results in a relatively large enhancement in the low temperature range with a small high energy power-law index κ. Overall, this study provides insight into the effects of non-Maxwellian distributions on fusion reactivity and highlights potential opportunities for enhancing fusion efficiency.

physics.plasm-ph↗