arXiv subjects

Naixu Guo

Publications and source records attributed to Naixu Guo.

15 recordsLinked to original sources

arXiv2026

Near-Optimal Learning of Local Lindbladians

We study the problem of learning local Lindbladians from black-box access to the physical evolution, where the goal is to estimate all Hamiltonian and dissipative coefficients. For local Lindbladians with low-intersection dissipators and local dynamical strength at most $\Lambda$, we design an algorithm that learns the coefficients to target accuracy $\varepsilon$, whose number of channel uses and total evolution time scale as $\widetilde{O}(\Lambda^2/\varepsilon^2)$ and $\widetilde{O}(\Lambda/\varepsilon^2)$, respectively, with only logarithmic dependence on the number of qubits. The algorithm is built directly from finite-time channel probes. It runs the unknown evolution for short times, estimates the corresponding Pauli transfer matrices from classical shadows, and converts these estimates into Lindbladian coefficients by stable local Fourier inversions. The algorithm is non-adaptive, uses no ancillas, and requires only random product states as inputs followed by random Pauli measurements. The method does not require knowing the structure of the Lindbladian in advance. We prove matching lower bounds that establish the near-optimality of the algorithm in both resources. By constructing a family of single-qubit dephasing Lindbladians, we show that any algorithm, even an adaptive one with arbitrary ancillas and measurements, requires $\Omega(\Lambda^2/\varepsilon^2)$ channel uses and $\Omega(\Lambda/\varepsilon^2)$ total evolution time. In particular, the lower bounds imply that the Heisenberg-limited scaling achievable for Hamiltonian learning is information-theoretically impossible once dissipative coefficients must be estimated.

quant-ph↗

arXiv2026

Quantum enhanced rare event discovery and sampling

Financial crashes, cascading failures in infrastructure, and critical errors in AI systems are frequently triggered by events that occur with extremely small probability. Efficiently discovering and sampling events with probability below a threshold is therefore of critical interest. Yet this task is highly non-trivial using existing classical or quantum methods. Being rare, such events require an immense sampling overhead to collect sufficient data samples. Moreover, because the rare events are not known in advance, they cannot be flagged for amplification using standard techniques. Here, we introduce a quantum algorithm for rare-event discovery and sampling without first learning which events are rare. The algorithm achieves the optimal quantum scaling with the rarity threshold. We further demonstrate that this can achieve a quadratic speedup for heavy-tailed systems whose tail has nonvanishing total mass, and translates into a robust polynomial speedup for stationary stochastic processes, with the exponent determined by its entropy-rate structure.

quant-ph↗

arXiv2026

Accelerating Inference for Multilayer Neural Networks with Quantum Computers

Fault-tolerant Quantum Processing Units (QPUs) promise to deliver exponential speed-ups in select computational tasks, yet their integration into modern deep learning pipelines remains unclear. In this work, we take a step towards bridging this gap by presenting the first fully-coherent quantum implementation of a multilayer neural network with non-linear activation functions. Our constructions mirror widely used deep learning architectures based on ResNet, and consist of residual blocks with multi-filter 2D convolutions, sigmoid activations, skip-connections, and layer normalizations. We analyse the complexity of inference for networks under three quantum data access regimes. Without any assumptions, we establish a quadratic speedup over classical methods for shallow bilinear-style networks. With efficient quantum access to the weights, we obtain a quartic speedup over classical methods. With efficient quantum access to both the inputs and the network weights, we prove that a network with an $N$-dimensional vectorized input, $k$ residual block layers, and a final residual-linear-pooling layer can be implemented with an error of $ε$ with $O(\text{polylog}(N/ε)^k)$ inference cost.

quant-ph↗

arXiv2026

COMPOSITE-Stem

AI agents hold growing promise for accelerating scientific discovery; yet, a lack of frontier evaluations hinders adoption into real workflows. Expert-written benchmarks have proven effective at measuring AI reasoning, but most at this stage have become saturated and only measure performance on constrained outputs. To help address this gap, we introduce COMPOSITE-STEM, a benchmark of 70 expert-written tasks in physics, biology, chemistry, and mathematics, curated by doctoral-level researchers. Our benchmark combines exact-match grading and criterion-based rubrics with an LLM-as-a-jury grading protocol, allowing more flexible assessment of scientifically meaningful outputs. Using an adapted multimodal Terminus-2 agent harness within the Harbor agentic evaluation framework, we evaluate four frontier models. The top-performing model achieves 21%, demonstrating that COMPOSITE-STEM captures capabilities beyond current agent reach. All tasks are open-sourced with contributor permission to support reproducibility and to promote additional research towards AI's acceleration of scientific progress in these domains.

cs.AI↗

arXiv2026

AgentIF-OneDay: A Task-level Instruction-Following Benchmark for General AI Agents in Daily Scenarios

The capacity of AI agents to effectively handle tasks of increasing duration and complexity continues to grow, demonstrating exceptional performance in coding, deep research, and complex problem-solving evaluations. However, in daily scenarios, the perception of these advanced AI capabilities among general users remains limited. We argue that current evaluations prioritize increasing task difficulty without sufficiently addressing the diversity of agentic tasks necessary to cover the daily work, life, and learning activities of a broad demographic. To address this, we propose AgentIF-OneDay, aimed at determining whether general users can utilize natural language instructions and AI agents to complete a diverse array of daily tasks. These tasks require not only solving problems through dialogue but also understanding various attachment types and delivering tangible file-based results. The benchmark is structured around three user-centric categories: Open Workflow Execution, which assesses adherence to explicit and complex workflows; Latent Instruction, which requires agents to infer implicit instructions from attachments; and Iterative Refinement, which involves modifying or expanding upon ongoing work. We employ instance-level rubrics and a refined evaluation pipeline that aligns LLM-based verification with human judgment, achieving an 80.1% agreement rate using Gemini-3-Pro. AgentIF-OneDay comprises 104 tasks covering 767 scoring points. We benchmarked four leading general AI agents and found that agent products built based on APIs and ChatGPT agents based on agent RL remain in the first tier simultaneously. Leading LLM APIs and open-source models have internalized agentic capabilities, enabling AI application teams to develop cutting-edge Agent products.

cs.CL↗

arXiv2025

Fast-forwardable Lindbladians imply quantum phase estimation

Quantum phase estimation (QPE) and Lindbladian dynamics are both foundational in quantum information science and central to quantum algorithm design. In this work, we bridge these two concepts: certain simple Lindbladian processes can be adapted to perform QPE-type tasks. However, unlike QPE, which achieves Heisenberg-limit scaling, these Lindbladian evolutions are restricted to standard quantum limit complexity. This indicates that, different from Hamiltonian dynamics, the natural dissipative evolution speed of such Lindbladians does not saturate the fundamental quantum limit, thereby suggesting the potential for quadratic fast-forwarding. We confirm this by presenting a quantum algorithm that simulates these Lindbladians for time $t$ within an error $\varepsilon$ using $\mathcal{O}\left(\sqrt{t\log(\varepsilon^{-1})}\right)$ cost, whose mechanism is fundamentally different from the fast-forwarding examples of Hamiltonian dynamics. As a bonus, this fast-forwarded simulation naturally serves as a new Heisenberg-limit QPE algorithm. Therefore, our work explicitly bridges the standard quantum limit-Heisenberg limit transition to the fast-forwarding of dissipative dynamics. We also adopt our fast-forwarding algorithm for efficient Gibbs state preparation and demonstrate the counter-intuitive implication: the allowance of a quadratically accelerated decoherence effect under arbitrary Pauli noise.

quant-ph↗

arXiv2025

Quantum Transformer: Accelerating model inference via quantum linear algebra

Powerful generative artificial intelligence from large language models (LLMs) harnesses extensive computational resources for inference. In this work, we investigate the transformer architecture, a key component of these models, under the lens of fault-tolerant quantum computing. We develop quantum subroutines to construct the building blocks in the transformer, including the self-attention, residual connection with layer normalization, and feed-forward network. As an important subroutine, we show how to efficiently implement the Hadamard product and element-wise functions of matrices on quantum computers. Our algorithm prepares an amplitude encoding of the transformer output, which can be measured for prediction or use in the next layer. We find that the matrix norm of the input sequence plays a dominant role in the quantum complexity. With numerical experiments on open-source LLMs, including for bio-informatics applications, we demonstrate the potential of a quantum speedup for transformer inference in practical regimes.

quant-ph↗

arXiv2025

Design nearly optimal quantum algorithm for linear differential equations via Lindbladians

Solving linear ordinary differential equations (ODE) is one of the most promising applications for quantum computers to demonstrate exponential advantages. The challenge of designing a quantum ODE algorithm is how to embed non-unitary dynamics into intrinsically unitary quantum circuits. In this work, we propose a new quantum algorithm for solving ODEs by harnessing open quantum systems. Specifically, we propose a novel technique called non-diagonal density matrix encoding, which leverages the inherent non-unitary dynamics of Lindbladians to encode general linear ODEs into the non-diagonal blocks of density matrices. This framework enables us to design quantum algorithms with both theoretical simplicity and high performance. Combined with the state-of-the-art quantum Lindbladian simulation algorithms, our algorithm can outperform all existing quantum ODE algorithms and achieve near-optimal dependence on all parameters under a plausible input model. We also give applications of our algorithm including the Gibbs state preparations and the partition function estimations.

quant-ph↗

arXiv2025

DeepMath-Creative: A Benchmark for Evaluating Mathematical Creativity of Large Language Models

To advance the mathematical proficiency of large language models (LLMs), the DeepMath team has launched an open-source initiative aimed at developing an open mathematical LLM and systematically evaluating its mathematical creativity. This paper represents the initial contribution of this initiative. While recent developments in mathematical LLMs have predominantly emphasized reasoning skills, as evidenced by benchmarks on elementary to undergraduate-level mathematical tasks, the creative capabilities of these models have received comparatively little attention, and evaluation datasets remain scarce. To address this gap, we propose an evaluation criteria for mathematical creativity and introduce DeepMath-Creative, a novel, high-quality benchmark comprising constructive problems across algebra, geometry, analysis, and other domains. We conduct a systematic evaluation of mainstream LLMs' creative problem-solving abilities using this dataset. Experimental results show that even under lenient scoring criteria -- emphasizing core solution components and disregarding minor inaccuracies, such as small logical gaps, incomplete justifications, or redundant explanations -- the best-performing model, O3 Mini, achieves merely 70% accuracy, primarily on basic undergraduate-level constructive tasks. Performance declines sharply on more complex problems, with models failing to provide substantive strategies for open problems. These findings suggest that, although current LLMs display a degree of constructive proficiency on familiar and lower-difficulty problems, such performance is likely attributable to the recombination of memorized patterns rather than authentic creative insight or novel synthesis.

cs.AI↗

arXiv2025

Quantum Machine Learning: A Hands-on Tutorial for Machine Learning Practitioners and Researchers

This tutorial intends to introduce readers with a background in AI to quantum machine learning (QML) -- a rapidly evolving field that seeks to leverage the power of quantum computers to reshape the landscape of machine learning. For self-consistency, this tutorial covers foundational principles, representative QML algorithms, their potential applications, and critical aspects such as trainability, generalization, and computational complexity. In addition, practical code demonstrations are provided in https://qml-tutorial.github.io/ to illustrate real-world implementations and facilitate hands-on learning. Together, these elements offer readers a comprehensive overview of the latest advancements in QML. By bridging the gap between classical machine learning and quantum computing, this tutorial serves as a valuable resource for those looking to engage with QML and explore the forefront of AI in the quantum era.

quant-ph↗

arXiv2025

Online Learning of Pure States is as Hard as Mixed States

Quantum state tomography, the task of learning an unknown quantum state, is a fundamental problem in quantum information. In standard settings, the complexity of this problem depends significantly on the type of quantum state that one is trying to learn, with pure states being substantially easier to learn than general mixed states. A natural question is whether this separation holds for any quantum state learning setting. In this work, we consider the online learning framework and prove the surprising result that learning pure states in this setting is as hard as learning mixed states. More specifically, we show that both classes share almost the same sequential fat-shattering dimension, leading to identical regret scaling. We also generalize previous results on full quantum state tomography in the online setting to (i) the $\epsilon$-realizable setting and (ii) learning the density matrix only partially, using smoothed analysis.

quant-ph↗

arXiv2024

Nonlinear transformation of complex amplitudes via quantum singular value transformation

Due to the linearity of quantum operations, it is not straightforward to implement nonlinear transformations on a quantum computer, making some practical tasks like a neural network hard to be achieved. In this work, we define a task called nonlinear transformation of complex amplitudes and provide an algorithm to achieve this task. Specifically, we construct a block-encoding of complex amplitudes from a state preparation unitary. This allows us to transform the complex amplitudes by using quantum singular value transformation. We evaluate the required overhead in terms of input dimension and precision, which reveals that the algorithm depends on the roughly square root of input dimension and achieves an exponential speedup on precision compared with previous work. We also discuss its possible applications to quantum machine learning, where complex amplitudes encoding classical or quantum data are processed by the proposed method. This paper provides a promising way to introduce highly complex nonlinearity of the quantum states, which is essentially missing in quantum mechanics.

quant-ph↗

arXiv2024

Estimating properties of a quantum state by importance-sampled operator shadows

Measuring properties of quantum systems is a fundamental problem in quantum mechanics. We provide a simple method for estimating the expectation value of observables with an unknown quantum state. The idea is to use a data structure to sample the terms of observables based on the Pauli decomposition proportionally to their importance. We call this technique operator shadow as a shorthand for the procedure of preparing a sketch of an operator to estimate properties. Only when the numbers of observables are small for multiple local observables, the sample complexity of this method is better than the classical shadow technique. However, if we want to estimate the expectation value of a linear combination of local observables, for example the energy of a local Hamiltonian, the sample complexity is better on all parameters. The time complexity to construct the data structure is $2^{O(k)}$ for $k$-local observables, similar to the post-processing time of classical shadows.

quant-ph↗

arXiv2023

Quantum Alphatron: quantum advantage for learning with kernels and noise

At the interface of machine learning and quantum computing, an important question is what distributions can be learned provably with optimal sample complexities and with quantum-accelerated time complexities. In the classical case, Klivans and Goel discussed the \textit{Alphatron}, an algorithm to learn distributions related to kernelized regression, which they also applied to the learning of two-layer neural networks. In this work, we provide quantum versions of the Alphatron in the fault-tolerant setting. In a well-defined learning model, this quantum algorithm is able to provide a polynomial speedup for a large range of parameters of the underlying concept class. We discuss two types of speedups, one for evaluating the kernel matrix and one for evaluating the gradient in the stochastic gradient descent procedure. We also discuss the quantum advantage in the context of learning of two-layer neural networks. Our work contributes to the study of quantum learning with kernels and from samples.

quant-ph↗

arXiv2023

Provable learning of quantum states with graphical models

The complete learning of an $n$-qubit quantum state requires samples exponentially in $n$. Several works consider subclasses of quantum states that can be learned in polynomial sample complexity such as stabilizer states or high-temperature Gibbs states. Other works consider a weaker sense of learning, such as PAC learning and shadow tomography. In this work, we consider learning states that are close to neural network quantum states, which can efficiently be represented by a graphical model called restricted Boltzmann machines (RBMs). To this end, we exhibit robustness results for efficient provable two-hop neighborhood learning algorithms for ferromagnetic and locally consistent RBMs. We consider the $L_p$-norm as a measure of closeness, including both total variation distance and max-norm distance in the limit. Our results allow certain quantum states to be learned with a sample complexity \textit{exponentially} better than naive tomography. We hence provide new classes of efficiently learnable quantum states and apply new strategies to learn them.

quant-ph↗