Han Zheng, Christopher Kang, Gokul Subramanian Ravi et al. · mit
We propose SnCQA, a set of hardware-efficient variational circuits of equivariant quantum convolutional circuits respective to permutation symmetries and spatial lattice symmetries with the number of qubits $n$. By exploiting permutation symmetries of the system, such as lattice Hamiltonians common to many quantum many-body and quantum chemistry problems, Our quantum neural networks are suitable for solving machine learning problems where permutation symmetries are present, which could lead to significant savings of computational costs. Aside from its theoretical novelty, we find our simulations perform well in practical instances of learning ground states in quantum computational chemistry, where we could achieve comparable performances to traditional methods with few tens of parameters. Compared to other traditional variational quantum circuits, such as the pure hardware-efficient ansatz (pHEA), we show that SnCQA is more scalable, accurate, and noise resilient (with $20\times$ better performance on $3 \times 4$ square lattice and $200\% - 1000\%$ resource savings in various lattice sizes and key criterions such as the number of layers, parameters, and times to converge in our cases), suggesting a potentially favorable experiment on near-time quantum devices.
Many fundamental properties of a quantum system are captured by its Hamiltonian and ground state. Despite the significance of ground states preparation (GSP), this task is classically intractable for large-scale Hamiltonians. Quantum neural networks (QNNs), which exert the power of modern quantum machines, have emerged as a leading protocol to conquer this issue. As such, how to enhance the performance of QNNs becomes a crucial topic in GSP. Empirical evidence showed that QNNs with handcraft symmetric ansatzes generally experience better trainability than those with asymmetric ansatzes, while theoretical explanations have not been explored. To fill this knowledge gap, here we propose the effective quantum neural tangent kernel (EQNTK) and connect this concept with over-parameterization theory to quantify the convergence of QNNs towards the global optima. We uncover that the advance of symmetric ansatzes attributes to their large EQNTK value with low effective dimension, which requests few parameters and quantum circuit depth to reach the over-parameterization regime permitting a benign loss landscape and fast convergence. Guided by EQNTK, we further devise a symmetric pruning (SP) scheme to automatically tailor a symmetric ansatz from an over-parameterized and asymmetric one to greatly improve the performance of QNNs when the explicit symmetry information of Hamiltonian is unavailable. Extensive numerical simulations are conducted to validate the analytical results of EQNTK and the effectiveness of SP.
Large machine learning models are revolutionary technologies of artificial intelligence whose bottlenecks include huge computational expenses, power, and time used both in the pre-training and fine-tuning process. In this work, we show that fault-tolerant quantum computing could possibly provide provably efficient resolutions for generic (stochastic) gradient descent algorithms, scaling as O(T^2 polylog(n)), where n is the size of the models and T is the number of iterations in the training, as long as the models are both sufficiently dissipative and sparse, with small learning rates. Based on earlier efficient quantum algorithms for dissipative differential equations, we find and prove that similar algorithms work for (stochastic) gradient descent, the primary algorithm for machine learning. In practice, we benchmark instances of large machine learning models from 7 million to 103 million parameters. We find that, in the context of sparse training, a quantum enhancement is possible at the early stage of learning after model pruning, motivating a sparse parameter download and re-upload scheme. Our work shows solidly that fault-tolerant quantum algorithms could potentially contribute to most state-of-the-art, large-scale machine-learning problems.
Quantum computing is expected to have transformative influences on many domains, but its practical deployments on industry problems are underexplored. We focus on applying quantum computing to operations management problems in industry, and in particular, supply chain management. Many problems in supply chain management involve large state and action spaces and pose computational challenges on classic computers. We develop a quantized policy iteration algorithm to solve an inventory control problem and demonstrative its effectiveness. We also discuss in-depth the hardware requirements and potential challenges on implementing this quantum algorithm in the near term. Our simulations and experiments are powered by \texttt{IBM Qiskit} and the \texttt{qBraid} system.
Junyu Liu, Frederik Wilde, Antonio Anna Mele et al.
Saddle points constitute a crucial challenge for first-order gradient descent algorithms. In notions of classical machine learning, they are avoided for example by means of stochastic gradient descent methods. In this work, we provide evidence that the saddle points problem can be naturally avoided in variational quantum algorithms by exploiting the presence of stochasticity. We prove convergence guarantees and present practical examples in numerical simulations and on quantum hardware. We argue that the natural stochasticity of variational algorithms can be beneficial for avoiding strict saddle points, i.e., those saddle points with at least one negative Hessian eigenvalue. This insight that some levels of shot noise could help is expected to add a new perspective to notions of near-term variational quantum algorithms.
We introduce a framework of the equivariant convolutional quantum algorithms which is tailored for a number of machine-learning tasks on physical systems with arbitrary SU$(d)$ symmetries. It allows us to enhance a natural model of quantum computation -- permutational quantum computing (PQC) -- and define a more powerful model: PQC+. While PQC was shown to be efficiently classically simulatable, we exhibit a problem which can be efficiently solved on PQC+ machine, whereas no classical polynomial time algorithm is known; thus providing evidence against PQC+ being classically simulatable. We further discuss practical quantum machine learning algorithms which can be carried out in the paradigm of PQC+.
In this paper, we propose the Quantum Data Center (QDC), an architecture combining Quantum Random Access Memory (QRAM) and quantum networks. We give a precise definition of QDC, and discuss its possible realizations and extensions. We discuss applications of QDC in quantum computation, quantum communication, and quantum sensing, with a primary focus on QDC for $T$-gate resources, QDC for multi-party private quantum communication, and QDC for distributed sensing through data compression. We show that QDC will provide efficient, private, and fast services as a future version of data centers.
We define \emph{laziness} to describe a large suppression of variational parameter updates for neural networks, classical or quantum. In the quantum case, the suppression is exponential in the number of qubits for randomized variational quantum circuits. We discuss the difference between laziness and \emph{barren plateau} in quantum machine learning created by quantum physicists in \cite{mcclean2018barren} for the flatness of the loss function landscape during gradient descent. We address a novel theoretical understanding of those two phenomena in light of the theory of neural tangent kernels. For noiseless quantum circuits, without the measurement noise, the loss function landscape is complicated in the overparametrized regime with a large number of trainable variational angles. Instead, around a random starting point in optimization, there are large numbers of local minima that are good enough and could minimize the mean square loss function, where we still have quantum laziness, but we do not have barren plateaus. However, the complicated landscape is not visible within a limited number of iterations, and low precision in quantum control and quantum sensing. Moreover, we look at the effect of noises during optimization by assuming intuitive noise models, and show that variational quantum algorithms are noise-resilient in the overparametrization regime. Our work precisely reformulates the quantum barren plateau statement towards a precision statement and justifies the statement in certain noise models, injects new hope toward near-term variational quantum algorithms, and provides theoretical connections toward classical machine learning. Our paper provides conceptual perspectives about quantum barren plateaus, together with discussions about the gradient descent dynamics in \cite{together}.
To simulate bosons on a qubit- or qudit-based quantum computer, one has to regularize the theory by truncating infinite-dimensional local Hilbert spaces to finite dimensions. In the search for practical quantum applications, it is important to know how big the truncation errors can be. In general, it is not easy to estimate errors unless we have a good quantum computer. In this paper, we show that traditional sampling methods on classical devices, specifically Markov Chain Monte Carlo, can address this issue for a rather generic class of bosonic systems with a reasonable amount of computational resources available today. As a demonstration, we apply this idea to the scalar field theory on a two-dimensional lattice, with a size that goes beyond what is achievable using exact diagonalization methods. This method can be used to estimate the resources needed for realistic quantum simulations of bosonic theories, and also, to check the validity of the results of the corresponding quantum simulations.
Random quantum circuits have been utilized in the contexts of quantum supremacy demonstrations, variational quantum algorithms for chemistry and machine learning, and blackhole information. The ability of random circuits to approximate any random unitaries has consequences on their complexity, expressibility, and trainability. To study this property of random circuits, we develop numerical protocols for estimating the frame potential, the distance between a given ensemble and the exact randomness. Our tensor-network-based algorithm has polynomial complexity for shallow circuits and is high-performing using CPU and GPU parallelism. We study 1. local and parallel random circuits to verify the linear growth in complexity as stated by the Brown-Susskind conjecture, and; 2. hardware-efficient ansätze to shed light on its expressibility and the barren plateau problem in the context of variational algorithms. Our work shows that large-scale tensor network simulations could provide important hints toward open problems in quantum information science.
Quantum devices should operate in adherence to quantum physics principles. Quantum random access memory (QRAM), a fundamental component of many essential quantum algorithms for tasks such as linear algebra, data search, and machine learning, is often proposed to offer $\mathcal{O}(\log N)$ circuit depth for $\mathcal{O}(N)$ data size, given $N$ qubits. However, this claim appears to breach the principle of relativity when dealing with a large number of qubits in quantum materials interacting locally. In our study we critically explore the intrinsic bounds of rapid quantum memories based on causality, employing the relativistic quantum field theory and Lieb-Robinson bounds in quantum many-body systems. In this paper, we consider a hardware-efficient QRAM design in hybrid quantum acoustic systems. Assuming clock cycle times of approximately $10^{-3}$ seconds and a lattice spacing of about 1 micrometer, we show that QRAM can accommodate up to $\mathcal{O}(10^7)$ logical qubits in 1 dimension, $\mathcal{O}(10^{15})$ to $\mathcal{O}(10^{20})$ in various 2D architectures, and $\mathcal{O}(10^{24})$ in 3 dimensions. We contend that this causality bound broadly applies to other quantum hardware systems. Our findings highlight the impact of fundamental quantum physics constraints on the long-term performance of quantum computing applications in data science and suggest potential quantum memory designs for performance enhancement.
Climate change is becoming one of the greatest challenges to the sustainable development of modern society. Renewable energies with low density greatly complicate the online optimization and control processes, where modern advanced computational technologies, specifically quantum computing, have significant potential to help. In this paper, we discuss applications of quantum computing algorithms toward state-of-the-art smart grid problems. We suggest potential, exponential quantum speedup by the use of the Harrow-Hassidim-Lloyd (HHL) algorithms for sparse matrix inversions in power-flow problems. However, practical implementations of the algorithm are limited by the noise of quantum circuits, the hardness of realizations of quantum random access memories (QRAM), and the depth of the required quantum circuits. We benchmark the hardware and software requirements from the state-of-the-art power-flow algorithms, including QRAM requirements from hybrid phonon-transmon systems, and explicit gate counting used in HHL for explicit realizations. We also develop near-term algorithms of power flow by variational quantum circuits and implement real experiments for 6 qubits with a truncated version of power flows.
Many learning tasks, including learning potential energy surfaces from ab initio calculations, involve global spatial symmetries and permutational symmetry between atoms or general particles. Equivariant graph neural networks are a standard approach to such problems, with one of the most successful methods employing tensor products between various tensors that transform under the spatial group. However, as the number of different tensors and the complexity of relationships between them increase, maintaining parsimony and equivariance becomes increasingly challenging. In this paper, we propose using fusion diagrams, a technique widely employed in simulating SU($2$)-symmetric quantum many-body problems, to design new equivariant components for equivariant neural networks. This results in a diagrammatic approach to constructing novel neural network architectures. When applied to particles within a given local neighborhood, the resulting components, which we term "fusion blocks," serve as universal approximators of any continuous equivariant function defined in the neighborhood. We incorporate a fusion block into pre-existing equivariant architectures (Cormorant and MACE), leading to improved performance with fewer parameters on a range of challenging chemical problems. Furthermore, we apply group-equivariant neural networks to study non-adiabatic molecular dynamics of stilbene cis-trans isomerization. Our approach, which combines tensor networks with equivariant neural networks, suggests a potentially fruitful direction for designing more expressive equivariant neural networks.
System specific neural force fields (NFFs) have gained popularity in computational chemistry. One of the most popular datasets as a bencharmk to develop NFFs models is the MD17 dataset and its subsequent extension. These datasets comprise geometries from the equilibrium region of the ground electronic state potential energy surface, sampled from direct adiabatic dynamics. However, many chemical reactions involve significant molecular geometrical deformations, for example, bond breaking. Therefore, MD17 is inadequate to represent a chemical reaction. To address this limitation in MD17, we introduce a new dataset, called Extended Excited-state Molecular Dynamics (xxMD) dataset. The xxMD dataset involves geometries sampled from direct non-adiabatic dynamics, and the energies are computed at both multireference wavefunction theory and density functional theory. We show that the xxMD dataset involves diverse geometries which represent chemical reactions. Assessment of NFF models on xxMD dataset reveals significantly higher predictive errors than those reported for MD17 and its variants. This work underscores the challenges faced in crafting a generalizable NFF model with extrapolation capability.
Drug discovery is lengthy and expensive, with traditional computer-aided design facing limits. This paper examines integrating quantum computing across the drug development cycle to accelerate and enhance workflows and rigorous decision-making. It highlights quantum approaches for molecular simulation, drug-target interaction prediction, and optimizing clinical trials. Leveraging quantum capabilities could accelerate timelines and costs for bringing therapies to market, improving efficiency and ultimately benefiting public health.
Understanding the training dynamics of quantum neural networks is a fundamental task in quantum information science with wide impact in physics, chemistry and machine learning. In this work, we show that the late-time training dynamics of quantum neural networks with a quadratic loss function can be described by the generalized Lotka-Volterra equations, which lead to a transcritical bifurcation transition in the dynamics. When the targeted value of loss function crosses the minimum achievable value from above to below, the dynamics evolve from a frozen-kernel dynamics to a frozen-error dynamics, showing a duality between the quantum neural tangent kernel and the total error. In both regions, the convergence towards the fixed point is exponential, while at the critical point becomes polynomial. We provide a non-perturbative analytical theory to explain the transition via a restricted Haar ensemble at late time, when the output state approaches the steady state. Via mapping the Hessian to an effective Hamiltonian, we also identify a linearly vanishing gap at the transition point. Compared with the linear loss function, we show that a quadratic loss function within the frozen-error dynamics enables a speedup in the training convergence. The theory findings are verified experimentally on IBM quantum devices.
Energy cost is increasingly crucial in the modern computing industry with the wide deployment of large-scale machine learning models and language models. For the firms that provide computing services, low energy consumption is important both from the perspective of their own market growth and the government's regulations. In this paper, we study the energy benefits of quantum computing vis-a-vis classical computing. Deviating from the conventional notion of quantum advantage based solely on computational complexity, we redefine advantage in an energy efficiency context. Through a Cournot competition model constrained by energy usage, we demonstrate quantum computing firms can outperform classical counterparts in both profitability and energy efficiency at Nash equilibrium. Therefore quantum computing may represent a more sustainable pathway for the computing industry. Moreover, we discover that the energy benefits of quantum computing economies are contingent on large-scale computation. Based on real physical parameters, we further illustrate the scale of operation necessary for realizing this energy efficiency advantage.
Quantum machine learning, which involves running machine learning algorithms on quantum devices, may be one of the most significant flagship applications for these devices. Unlike its classical counterparts, the role of data in quantum machine learning has not been fully understood. In this work, we quantify the performances of quantum machine learning in the landscape of quantum data. Provided that the encoding of quantum data is sufficiently random, the performance, we find that the training efficiency and generalization capabilities in quantum machine learning will be exponentially suppressed with the increase in the number of qubits, which we call "the curse of random quantum data". Our findings apply to both the quantum kernel method and the large-width limit of quantum neural networks. Conversely, we highlight that through meticulous design of quantum datasets, it is possible to avoid these curses, thereby achieving efficient convergence and robust generalization. Our conclusions are corroborated by extensive numerical simulations.
A quantum version of data centers might be significant in the quantum era. In this paper, we introduce Quantum Data Center (QDC), a quantum version of existing classical data centers, with a specific emphasis on combining Quantum Random Access Memory (QRAM) and quantum networks. We argue that QDC will provide significant benefits to customers in terms of efficiency, security, and precision, and will be helpful for quantum computing, communication, and sensing. We investigate potential scientific and business opportunities along this novel research direction through hardware realization and possible specific applications. We show the possible impacts of QDCs in business and science, especially the machine learning and big data industries.
With the increasing application of large language models (LLMs) in the medical domain, evaluating these models' performance using benchmark datasets has become crucial. This paper presents a comprehensive survey of various benchmark datasets employed in medical LLM tasks. These datasets span multiple modalities including text, image, and multimodal benchmarks, focusing on different aspects of medical knowledge such as electronic health records (EHRs), doctor-patient dialogues, medical question-answering, and medical image captioning. The survey categorizes the datasets by modality, discussing their significance, data structure, and impact on the development of LLMs for clinical tasks such as diagnosis, report generation, and predictive decision support. Key benchmarks include MIMIC-III, MIMIC-IV, BioASQ, PubMedQA, and CheXpert, which have facilitated advancements in tasks like medical report generation, clinical summarization, and synthetic data generation. The paper summarizes the challenges and opportunities in leveraging these benchmarks for advancing multimodal medical intelligence, emphasizing the need for datasets with a greater degree of language diversity, structured omics data, and innovative approaches to synthesis. This work also provides a foundation for future research in the application of LLMs in medicine, contributing to the evolving field of medical artificial intelligence.
Word embeddings and language models have transformed natural language processing (NLP) by facilitating the representation of linguistic elements in continuous vector spaces. This review visits foundational concepts such as the distributional hypothesis and contextual similarity, tracing the evolution from sparse representations like one-hot encoding to dense embeddings including Word2Vec, GloVe, and fastText. We examine both static and contextualized embeddings, underscoring advancements in models such as ELMo, BERT, and GPT and their adaptations for cross-lingual and personalized applications. The discussion extends to sentence and document embeddings, covering aggregation methods and generative topic models, along with the application of embeddings in multimodal domains, including vision, robotics, and cognitive science. Advanced topics such as model compression, interpretability, numerical encoding, and bias mitigation are analyzed, addressing both technical challenges and ethical implications. Additionally, we identify future research directions, emphasizing the need for scalable training techniques, enhanced interpretability, and robust grounding in non-textual modalities. By synthesizing current methodologies and emerging trends, this survey offers researchers and practitioners an in-depth resource to push the boundaries of embedding-based language models.
Pei Zeng, Debayan Bandyopadhyay, José A. Méndez Méndez et al.
Quantum resistance is vital for emerging cryptographic systems as quantum technologies continue to advance towards large-scale, fault-tolerant quantum computers. Resistance may be offered by quantum key distribution (QKD), which provides information-theoretic security using quantum states of photons, but may be limited by transmission loss at long distances. An alternative approach uses classical means and is conjectured to be resistant to quantum attacks, so-called post-quantum cryptography (PQC), but it is yet to be rigorously proven, and its current implementations are computationally expensive. To overcome the security and performance challenges present in each, here we develop hybrid protocols by which QKD and PQC inter-operate within a joint quantum-classical network. In particular, we consider different hybrid designs that may offer enhanced speed and/or security over the individual performance of either approach. Furthermore, we present a method for analyzing the security of hybrid protocols in key distribution networks. Our hybrid approach paves the way for joint quantum-classical communication networks, which leverage the advantages of both QKD and PQC and can be tailored to the requirements of various practical networks.
Yue Tu, Mark Dubynskyi, Mohammadhossein Mohammadisiahroudi et al.
Quantum computing, a prominent non-Von Neumann paradigm beyond Moore's law, can offer superpolynomial speedups for certain problems. Yet its advantages in efficiency for tasks like machine learning remain under investigation, and quantum noise complicates resource estimations and classical comparisons. We provide a detailed estimation of space, time, and energy resources for fault-tolerant superconducting devices running the Harrow-Hassidim-Lloyd (HHL) algorithm, a quantum linear system solver relevant to linear algebra and machine learning. Excluding memory and data transfer, possible quantum advantages over the classical conjugate gradient method could emerge at $N \approx 2^{33} \sim 2^{48}$ or even lower, requiring ${O}(10^5)$ physical qubits, ${O}(10^{12}\sim10^{13})$ Joules, and ${O}(10^6)$ seconds under surface code fault-tolerance with three types of magic state distillation (15-1, 116-12, 225-1). Key parameters include condition number, sparsity, and precision $κ, s\approx{O}(10\sim100)$, $ε\sim0.01$, and physical error $10^{-5}$. Our resource estimator adjusts $N, κ, s, ε$, providing a map of quantum-classical boundaries and revealing where a practical quantum advantage may arise. Our work quantitatively determine how advanced a fault-tolerant quantum computer should be to achieve possible, significant benefits on problems related to real-world.
A diffusion probabilistic model (DPM) is a generative model renowned for its ability to produce high-quality outputs in tasks such as image and audio generation. However, training DPMs on large, high-dimensional datasets such as high-resolution images or audio incurs significant computational, energy, and hardware costs. In this work, we introduce efficient quantum algorithms for implementing DPMs through various quantum ODE solvers. These algorithms highlight the potential of quantum Carleman linearization for diverse mathematical structures, leveraging state-of-the-art quantum linear system solvers (QLSS) or linear combination of Hamiltonian simulations (LCHS). Specifically, we focus on two approaches: DPM-solver-$k$ which employs exact $k$-th order derivatives to compute a polynomial approximation of $ε_θ(x_λ,λ)$; and UniPC which uses finite difference of $ε_θ(x_λ,λ)$ at different points $(x_{s_m}, λ_{s_m})$ to approximate higher-order derivatives. As such, this work represents one of the most direct and pragmatic applications of quantum algorithms to large-scale machine learning models, presumably taking substantial steps towards demonstrating the practical utility of quantum computing.
Quantum computing is an exciting non-Von Neumann paradigm, offering provable speedups over classical computing for specific problems. However, the practical limits of classical simulatability for quantum circuits remain unclear, especially with current noisy quantum devices. In this work, we explore the potential of leveraging Large Language Models (LLMs) to simulate the output of a quantum Turing machine using Grover's quantum circuits, known to provide quadratic speedups over classical counterparts. To this end, we developed GroverGPT, a specialized model based on LLaMA's 8-billion-parameter architecture, trained on over 15 trillion tokens. Unlike brute-force state-vector simulations, which demand substantial computational resources, GroverGPT employs pattern recognition to approximate quantum search algorithms without explicitly representing quantum states. Analyzing 97K quantum search instances, GroverGPT consistently outperformed OpenAI's GPT-4o (45\% accuracy), achieving nearly 100\% accuracy on 6- and 10-qubit datasets when trained on 4-qubit or larger datasets. It also demonstrated strong generalization, surpassing 95\% accuracy for systems with over 20 qubits when trained on 3- to 6-qubit data. Analysis indicates GroverGPT captures quantum features of Grover's search rather than classical patterns, supported by novel prompting strategies to enhance performance. Although accuracy declines with increasing system size, these findings offer insights into the practical boundaries of classical simulatability. This work suggests task-specific LLMs can surpass general-purpose models like GPT-4o in quantum algorithm learning and serve as powerful tools for advancing quantum research.
We present a quantum-inspired algorithm that utilizes Quantum Hamiltonian Descent (QHD) for efficient community detection. Our approach reformulates the community detection task as a Quadratic Unconstrained Binary Optimization (QUBO) problem, and QHD is deployed to identify optimal community structures. We implement a multi-level algorithm that iteratively refines community assignments by alternating between QUBO problem setup and QHD-based optimization. Benchmarking shows our method achieves up to 5.49\% better modularity scores while requiring less computational time compared to classical optimization approaches. This work demonstrates the potential of hybrid quantum-inspired solutions for advancing community detection in large-scale graph data.
Remote sensing has evolved from simple image acquisition to complex systems capable of integrating and processing visual and textual data. This review examines the development and application of multi-modal language models (MLLMs) in remote sensing, focusing on their ability to interpret and describe satellite imagery using natural language. We cover the technical underpinnings of MLLMs, including dual-encoder architectures, Transformer models, self-supervised and contrastive learning, and cross-modal integration. The unique challenges of remote sensing data--varying spatial resolutions, spectral richness, and temporal changes--are analyzed for their impact on MLLM performance. Key applications such as scene description, object detection, change detection, text-to-image retrieval, image-to-text generation, and visual question answering are discussed to demonstrate their relevance in environmental monitoring, urban planning, and disaster response. We review significant datasets and resources supporting the training and evaluation of these models. Challenges related to computational demands, scalability, data quality, and domain adaptation are highlighted. We conclude by proposing future research directions and technological advancements to further enhance MLLM utility in remote sensing.
Optimization techniques in deep learning are predominantly led by first-order gradient methodologies, such as SGD. However, neural network training can greatly benefit from the rapid convergence characteristics of second-order optimization. Newton's GD stands out in this category, by rescaling the gradient using the inverse Hessian. Nevertheless, one of its major bottlenecks is matrix inversion, which is notably time-consuming in $O(N^3)$ time with weak scalability. Matrix inversion can be translated into solving a series of linear equations. Given that quantum linear solver algorithms (QLSAs), leveraging the principles of quantum superposition and entanglement, can operate within a $\text{polylog}(N)$ time frame, they present a promising approach with exponential acceleration. Specifically, one of the most recent QLSAs demonstrates a complexity scaling of $O(d\cdotκ\log(N\cdotκ/ε))$, depending on: {size~$N$, condition number~$κ$, error tolerance~$ε$, quantum oracle sparsity~$d$} of the matrix. However, this also implies that their potential exponential advantage may be hindered by certain properties (i.e. $κ$ and $d$). We propose Q-Newton, a hybrid quantum-classical scheduler for accelerating neural network training with Newton's GD. Q-Newton utilizes a streamlined scheduling module that coordinates between quantum and classical linear solvers, by estimating & reducing $κ$ and constructing $d$ for the quantum solver. Our evaluation showcases the potential for Q-Newton to significantly reduce the total training time compared to commonly used optimizers like SGD. We hypothesize a future scenario where the gate time of quantum machines is reduced, possibly realized by attoseconds physics. Our evaluation establishes an ambitious and promising target for the evolution of quantum computing.
Quantum machine learning is considered one of the flagship applications of quantum computers, where variational quantum circuits could be the leading paradigm both in the near-term quantum devices and the early fault-tolerant quantum computers. However, it is not clear how to identify the regime of quantum advantages from these circuits, and there is no explicit theory to guide the practical design of variational ansatze to achieve better performance. We address these challenges with the stabilizer bootstrap, a method that uses stabilizer-based techniques to optimize quantum neural networks before their quantum execution, together with theoretical proofs and high-performance computing with 10000 qubits or random datasets up to 1000 data. We find that, in a general setup of variational ansatze, the possibility of improvements from the stabilizer bootstrap depends on the structure of the observables and the size of the datasets. The results reveal that configurations exhibit two distinct behaviors: some maintain a constant probability of circuit improvement, while others show an exponential decay in improvement probability as qubit numbers increase. These patterns are termed strong stabilizer enhancement and weak stabilizer enhancement, respectively, with most situations falling in between. Our work seamlessly bridges techniques from fault-tolerant quantum computing with applications of variational quantum algorithms. Not only does it offer practical insights for designing variational circuits tailored to large-scale machine learning challenges, but it also maps out a clear trajectory for defining the boundaries of feasible and practical quantum advantages.
Pei Zeng, Debayan Bandyopadhyay, José A. Méndez Méndez et al.
The rapid advancement of quantum technologies calls for the design and deployment of quantum-safe cryptographic protocols and communication networks. There are two primary approaches to achieving quantum-resistant security: quantum key distribution (QKD) and post-quantum cryptography (PQC). While each offers unique advantages, both have drawbacks in practical implementation. In this work, we introduce the pros and cons of these protocols and explore how they can be combined to achieve a higher level of security and/or improved performance in key distribution. We hope our discussion inspires further research into the design of hybrid cryptographic protocols for quantum-classical communication networks.
The efficient simulation of complex quantum systems remains a central challenge due to the exponential growth of Hilbert space with system size. Tensor network methods have long been established as powerful approximation schemes, and their efficiency can be further enhanced by incorporating physics-informed priors. A prominent example is symmetry: recent progress on $U(1)$-symmetric tensor networks, accelerated on GPUs and scaled to supercomputers, shows how conserved charges induce block-sparse structures that reduce computational cost and enable larger simulations. The same principle extends to general symmetries, inspiring equivariant neural networks in machine learning and guiding symmetry-preserving ansatze in variational quantum algorithms. Beyond symmetry, physics-informed design also includes strategies such as hybrid tensor networks and parallel sequential circuits, which pursue efficiency from complementary principles. This Perspective argues that physics-informed tensor networks, grounded in both symmetry and beyond-symmetry insights, provide unifying strategies for scalable approaches in quantum simulation, computation, and machine learning.
Interfacing quantum and classical processors is an important subroutine in full-stack quantum algorithms. The so-called "classical shadow" method efficiently extracts essential classical information from quantum states, enabling the prediction of many properties of a quantum system from only a few measurements. However, for a small number of highly non-local observables, or when classical post-processing power is limited, the classical shadow method is not always the most efficient choice. Here, we address this issue quantitatively by performing a full-stack resource analysis that compares classical shadows with "quantum footage," which refers to direct quantum measurement. Under certain assumptions, our analysis illustrates a boundary of download efficiency between classical shadows and quantum footage. For observables expressed as linear combinations of Pauli matrices, the classical shadow method outperforms direct measurement when the number of observables is large and the Pauli weight is small. For observables in the form of large Hermitian sparse matrices, the classical shadow method shows an advantage when the number of observables, the sparsity of the matrix, and the number of qubits fall within a certain range. The key parameters influencing this behavior include the number of qubits $n$, observables $M$, sparsity $k$, Pauli weight $w$, accuracy requirement $ε$, and failure tolerance $δ$. We also compare the resource consumption of the two methods on different types of quantum computers and identify break-even points where the classical shadow method becomes more efficient, which vary depending on the hardware. This paper opens a new avenue for quantitatively designing optimal strategies for hybrid quantum-classical tomography and provides practical insights for selecting the most suitable quantum measurement approach in real-world applications.
As quantum information science advances and the need for pre-college engagement grows, a critical question remains: How can young learners be prepared to participate in a field so radically different from what they have encountered before? This paper argues that meeting this challenge will require strong interdisciplinary collaboration with the Learning Sciences (LS), a field dedicated to understanding how people learn and designing theory-guided environments to support learning. Drawing on lessons from previous STEM education efforts, we discuss two key contributions of the learning sciences to quantum information science (QIS) education. The first is design-based research, the signature methodology of learning sciences, which can inform the development, refinement, and scaling of effective QIS learning experiences. The second is a framework for reshaping how learners reason about, learn and participate in QIS practices through shifts in knowledge representations that provide new forms of engagement and associated learning. We call for a two-way partnership between quantum information science and the learning sciences, one that not only supports learning in quantum concepts and practices but also improves our understanding of how to teach and support learning in highly complex domains. We also consider potential questions involved in bridging these disciplinary communities and argue that the theoretical and practical benefits justify the effort.
Clinical trials are an indispensable part of the drug development process, bridging the gap between basic research and clinical application. During the development of new drugs, clinical trials are used not only to evaluate the safety and efficacy of the drug but also to explore its dosage, treatment regimens, and potential side effects. This review discusses the various stages of clinical trials, including Phase I (safety assessment), Phase II (preliminary efficacy evaluation), Phase III (large-scale validation), and Phase IV (post-marketing surveillance), highlighting the characteristics of each phase and their interrelationships. Additionally, the paper addresses the major challenges encountered in clinical trials, such as ethical issues, subject recruitment difficulties, diversity and representativeness concerns, and proposes strategies for overcoming these challenges. With the advancement of technology, innovative technologies such as artificial intelligence, big data, and digitalization are gradually transforming clinical trial design and implementation, improving trial efficiency and data quality. The article also looks forward to the future of clinical trials, particularly the impact of emerging therapies such as gene therapy and immunotherapy on trial design, as well as the importance of regulatory reforms and global collaboration. In conclusion, the core role of clinical trials in drug development will continue to drive the progress of innovative drug development and clinical treatment.
Quantum machine learning, which involves running machine learning algorithms on quantum devices, has garnered significant attention in both academic and business circles. In this paper, we offer a comprehensive and unbiased review of the various concepts that have emerged in the field of quantum machine learning. This includes techniques used in Noisy Intermediate-Scale Quantum (NISQ) technologies and approaches for algorithms compatible with fault-tolerant quantum computing hardware. Our review covers fundamental concepts, algorithms, and the statistical learning theory pertinent to quantum machine learning.
Parameterized quantum circuits can be used as quantum neural networks and have the potential to outperform their classical counterparts when trained for addressing learning problems. To date, much of the results on their performance on practical problems are heuristic in nature. In particular, the convergence rate for the training of quantum neural networks is not fully understood. Here, we analyze the dynamics of gradient descent for the training error of a class of variational quantum machine learning models. We define wide quantum neural networks as parameterized quantum circuits in the limit of a large number of qubits and variational parameters. We then find a simple analytic formula that captures the average behavior of their loss function and discuss the consequences of our findings. For example, for random quantum circuits, we predict and characterize an exponential decay of the residual training error as a function of the parameters of the system. We finally validate our analytic results with numerical experiments.
The emerging trends of Internet-of-Vehicles (IoV) demand centralized servers to collect/process sensitive data with limited computational resources on a single vehicle. Such centralizations of sensitive data demand practical privacy protections. One widely-applied paradigm, Differential Privacy, can provide strong guarantees over sensitive data by adding noises. However, directly applying DP for IoV incurs significant challenges for data utility and effective protection. We observe that the key issue about DP-enabled protection in IoV lies in how to synergistically combine DP with special characteristics of IoV, whose query sequences are usually formed as unbalanced batches due to frequent interactions between centralized servers and edge vehicles. To this end, we propose HUT, a new algorithm to enable High UTility for DP-enabled protection in IoV. Our key insight is to leverage the inherent characteristics in IoV: the unbalanced batches. Our key idea is to aggregate local batches and apply Order Constraints, so that information loss from DP protection can be mitigated. We evaluate the effectiveness of HUT against the state-of-the-art DP protection mechanisms. The results show that HUT can provide much lower information loss by 95.69\% and simultaneously enable strong mathematically-guaranteed protection over sensitive data.
Emerging Autonomous Vehicles (AV) breed great potentials to exploit data-driven techniques for adaptive and personalized Human-Vehicle Interactions. However, the lack of high-quality and rich data supports limits the opportunities to explore the design space of data-driven techniques, and validate the effectiveness of concrete mechanisms. Our goal is to initialize the efforts to deliver the building block for exploring data-driven Human-Vehicle Interaction designs. To this end, we present BROOK dataset, a multi-modal dataset with facial video records. We first brief our rationales to build BROOK dataset. Then, we elaborate how to build the current version of BROOK dataset via a year-long study, and give an overview of the dataset. Next, we present three example studies using BROOK to justify the applicability of BROOK dataset. We also identify key learning lessons from building BROOK dataset, and discuss about how BROOK dataset can foster an extensive amount of follow-up studies.
Recent developments of advanced Human-Vehicle Interactions rely on the concept Internet-of-Vehicles (IoV), to achieve large-scale communications and synchronizations of data in practice. The concept of IoV is highly similar to a distributed system, where each vehicle is considered as a node and all nodes are grouped with a centralized server. In this manner, the concerns of data privacy are significant since all vehicles collect, process and share personal statistics (e.g. multi-modal, driving statuses and etc.). Therefore, it's important to understand how modern privacy-preserving techniques suit for IoV. We present the most comprehensive study to characterize modern privacy-preserving techniques for IoV to date. We focus on Differential Privacy (DP), a representative set of mathematically-guaranteed mechanisms for both privacy-preserving processing and sharing on sensitive data. The purpose of our study is to demystify the tradeoffs of deploying DP techniques, in terms of service quality. We first characterize representative privacy-preserving processing mechanisms, enabled by advanced DP approaches. Then we perform a detailed study of an emerging in-vehicle, Deep-Neural-Network-driven application, and study the upsides and downsides of DP for diverse types of data streams. Our study obtains 11 key findings and we highlight FIVE most significant observations from our detailed characterizations. We conclude that there are a large volume of challenges and opportunities for future studies, by enabling privacy-preserving IoV with low overheads for service quality.
We develop a theoretical framework for $S_n$-equivariant convolutional quantum circuits with SU$(d)$-symmetry, building on and significantly generalizing Jordan's Permutational Quantum Computing (PQC) formalism based on Schur-Weyl duality connecting both SU$(d)$ and $S_n$ actions on qudits. In particular, we utilize the Okounkov-Vershik approach to prove Harrow's statement (Ph.D. Thesis 2005 p.160) on the equivalence between $\operatorname{SU}(d)$ and $S_n$ irrep bases and to establish the $S_n$-equivariant Convolutional Quantum Alternating Ansätze ($S_n$-CQA) using Young-Jucys-Murphy (YJM) elements. We prove that $S_n$-CQA is able to generate any unitary in any given $S_n$ irrep sector, which may serve as a universal model for a wide array of quantum machine learning problems with the presence of SU($d$) symmetry. Our method provides another way to prove the universality of Quantum Approximate Optimization Algorithm (QAOA) and verifies that 4-local SU($d$) symmetric unitaries are sufficient to build generic SU($d$) symmetric quantum circuits up to relative phase factors. We present numerical simulations to showcase the effectiveness of the ansätze to find the ground state energy of the $J_1$--$J_2$ antiferromagnetic Heisenberg model on the rectangular and Kagome lattices. Our work provides the first application of the celebrated Okounkov-Vershik's $S_n$ representation theory to quantum physics and machine learning, from which to propose quantum variational ansätze that strongly suggests to be classically intractable tailored towards a specific optimization problem.
The challenges of polyphonic sound event detection (PSED) stem from the detection of multiple overlapping events in a time series. Recent efforts exploit Deep Neural Networks (DNNs) on Time-Frequency Representations (TFRs) of audio clips as model inputs to mitigate such issues. However, existing solutions often rely on a single type of TFR, which causes under-utilization of input features. To this end, we propose a novel PSED framework, which incorporates Multi-Type-Multi-Scale TFRs. Our key insight is that: TFRs, which are of different types or in different scales, can reveal acoustics patterns in a complementary manner, so that the overlapped events can be best extracted by combining different TFRs. Moreover, our framework design applies a novel approach, to adaptively fuse different models and TFRs symbiotically. Hence, the overall performance can be significantly improved. We quantitatively examine the benefits of our framework by using Capsule Neural Networks, a state-of-the-art approach for PSED. The experimental results show that our method achieves a reduction of 7\% in error rate compared with the state-of-the-art solutions on the TUT-SED 2016 dataset.
Junyu Liu, Francesco Tacchino, Jennifer R. Glick et al.
Variational quantum circuits are used in quantum machine learning and variational quantum simulation tasks. Designing good variational circuits or predicting how well they perform for given learning or optimization tasks is still unclear. Here we discuss these problems, analyzing variational quantum circuits using the theory of neural tangent kernels. We define quantum neural tangent kernels, and derive dynamical equations for their associated loss function in optimization and learning tasks. We analytically solve the dynamics in the frozen limit, or lazy training regime, where variational angles change slowly and a linear perturbation is good enough. We extend the analysis to a dynamical setting, including quadratic corrections in the variational angles. We then consider hybrid quantum-classical architecture and define a large-width limit for hybrid kernels, showing that a hybrid quantum-classical neural network can be approximately Gaussian. The results presented here show limits for which analytical understandings of the training dynamics for variational quantum circuits, used for quantum machine learning and optimization problems, are possible. These analytical results are supported by numerical simulations of quantum machine learning experiments.
Rapid developments of quantum information technology show promising opportunities for simulating quantum field theory in near-term quantum devices. In this work, we formulate the theory of (time-dependent) variational quantum simulation of the 1+1 dimensional $λφ^4$ quantum field theory including encoding, state preparation, and time evolution, with several numerical simulation results. These algorithms could be understood as near-term variational quantum circuit (quantum neural network) analogs of the Jordan-Lee-Preskill algorithm, the basic algorithm for simulating quantum field theory using universal quantum devices. Besides, we highlight the advantages of encoding with harmonic oscillator basis based on the LSZ reduction formula and several computational efficiency such as when implementing a bosonic version of the unitary coupled cluster ansatz to prepare initial states. We also discuss how to circumvent the "spectral crowding" problem in the quantum field theory simulation and appraise our algorithm by both state and subspace fidelities.
Random ordinary differential equations (RODEs), i.e. ODEs with random parameters, are often used to model complex dynamics. Most existing methods to identify unknown governing RODEs from observed data often rely on strong prior knowledge. Extracting the governing equations from data with less prior knowledge remains a great challenge. In this paper, we propose a deep neural network, called RODE-Net, to tackle such challenge by fitting a symbolic expression of the differential equation and the distribution of parameters simultaneously. To train the RODE-Net, we first estimate the parameters of the unknown RODE using the symbolic networks \cite{long2019pde} by solving a set of deterministic inverse problems based on the measured data, and use a generative adversarial network (GAN) to estimate the true distribution of the RODE's parameters. Then, we use the trained GAN as a regularization to further improve the estimation of the ODE's parameters. The two steps are operated alternatively. Numerical results show that the proposed RODE-Net can well estimate the distribution of model parameters using simulated data and can make reliable predictions. It is worth noting that, GAN serves as a data driven regularization in RODE-Net and is more effective than the $\ell_1$ based regularization that is often used in system identifications.
Objective: We propose an end-to-end CNN-based locating model for pulmonary tuberculosis (TB) diagnosis in radiographs. This model makes full use of chest radiograph (X-ray) for its improved accessibility, reduced cost and high accuracy for TB disease. Methods: Several specialized improvements are proposed for detection task in medical field. A false positive (FP) restrictor head is introduced for FP reduction. Anchor-oriented network heads is proposed in the position regression section. An optimization of loss function is designed for hard example mining. Results: The experimental results show that when the threshold of intersection over union (IoU) is set to 0.3, the average precision (AP) of two test data sets provided by different hospitals reaches 0.9023 and 0.9332. Ablation experiments shows that hard example mining and change of regressor heads contribute most in this work, but FP restriction is necessary in a CAD diagnose system. Conclusion: The results prove the high precision and good generalization ability of our proposed model comparing to previous works. Significance: We first make full use of the feature extraction ability of CNNs in TB diagnostic field and make exploration in localization of TB, when the previous works focus on the weaker task of healthy-sick subject classification.
In this paper we propose that artificial neural network, the basis of machine learning, is useful to generate the inflationary landscape from a cosmological point of view. Traditional numerical simulations of a global cosmic landscape typically need an exponential complexity when the number of fields is large. However, a basic application of artificial neural network could solve the problem based on the universal approximation theorem of the multilayer perceptron. A toy model in inflation with multiple light fields is investigated numerically as an example of such an application.