arXiv subjects

Junseo Lee

Publications and source records attributed to Junseo Lee.

At least 19 recordsLinked to original sources

arXiv2026

Fast and Scalable Caputo Fractional Gradient Descent via Perturbation-Preserving Memory Compression

Fractional gradient descent (FGD) incorporates long-range memory through Caputo-type operators and has been shown to improve stability in ill-conditioned and nonconvex optimization problems. Despite these advantages, its practical use remains limited, mainly due to the high computational cost of evaluating history-dependent convolutions, which scales quadratically with the number of iterations. In this paper, we focus on making Caputo-based optimization computationally viable without sacrificing its intrinsic memory structure. We begin by expressing the fractional descent direction as a discrete convolution over past gradients, which provides a unified view of the method. Based on this formulation, we introduce two complementary mechanisms to reduce the cost of the memory term. The first uses a sum-of-exponentials (SOE) approximation of the power-law kernel, leading to efficient recursive updates. The second approach, newly proposed in this paper as dyadic hierarchical discrete convolution (DHDC), compresses the gradient history through a multiscale aggregation strategy. Rather than treating these approximations as purely numerical accelerations, we interpret them as perturbations of the ideal Caputo operator. This viewpoint allows us to analyze how the compressed memory affects the optimization dynamics. Under standard $\mu$-strong convexity and $L$-smoothness assumptions, we show that the resulting method still exhibits monotone descent and linear convergence, provided that the approximation error remains controlled.

math.OC↗

arXiv2026

Offline Reinforcement Learning with Universal Horizon Models

Model-based reinforcement learning (RL) offers a compelling approach to offline RL by enabling value learning on imagined on-policy trajectories. However, it often suffers from compounding errors due to repeated model inference on self-generated states. While geometric horizon models (GHM) alleviate this issue through direct prediction over a discounted infinite-horizon future, they remain challenged in accurately modeling distant future states. To this end, we introduce universal horizon models (UHM), a generalization of GHM that directly predicts future states under arbitrary horizons. Leveraging this flexibility, we propose a scalable value learning method that employs a winsorized horizon distribution to stabilize training by capping excessively large horizons. Experimental results on 100 challenging OGBench tasks demonstrate that the proposed method outperforms competitive baselines, particularly on tasks with highly suboptimal datasets and those requiring long-horizon reasoning. Project page: https://rllab-snu.github.io/projects/UHM/

cs.LG↗

arXiv2026

Heisenberg-limited Hamiltonian learning without short-time control

Characterizing quantum systems by learning their underlying Hamiltonians is a central task in quantum information science. While recent algorithmic advances have achieved near-optimal efficiency in this task, they critically rely on accessing arbitrarily short-time dynamics. This reliance poses severe experimental challenges due to finite control bandwidth and transient pulse errors. In this work, we demonstrate that Heisenberg-limited Hamiltonian learning can be achieved without short-time control. We introduce a framework in which every query to the unknown dynamics has duration at least a prescribed minimum time $T$, and show that this restriction does not preclude Heisenberg-limited scaling. The key ingredient is a method for emulating the continuous quantum control required by iterative learning algorithms using only such lower-bounded evolution times. This reduces the learning task to sparse pure-state tomography. Notably, for logarithmically sparse Hamiltonians, our algorithm achieves the information-theoretically optimal $1/\varepsilon$ scaling in total evolution time for any arbitrary constant minimum evolution time $T$. For many-body (polynomially sparse) systems, we uncover a rigorous quantitative tradeoff, showing that the minimum required evolution time can be significantly relaxed from the standard limit at a polynomial cost in total evolution time. Our results affirmatively resolve a prominent open problem in the field and reveal that high-bandwidth, ultra-short pulses are not fundamentally necessary for optimal quantum learning.

quant-ph↗

arXiv2026

Certifying and learning local quantum Hamiltonians

In this work, we study the problems of certifying and learning quantum $k$-local Hamiltonians, for a constant $k$. Our main contributions are as follows: - Certification of Hamiltonians. We show that certifying a local Hamiltonian in normalized Frobenius norm via access to its time-evolution operator can be achieved with only $O(1/\varepsilon)$ evolution time. This is optimal, as it matches the Heisenberg-scaling lower bound of $\Omega(1/\varepsilon)$. To our knowledge, this is the first optimal algorithm for testing a Hamiltonian property. A key ingredient in our analysis is the Bonami Hypercontractivity Lemma from Fourier analysis. - Learning Gibbs states. We design an algorithm for learning Gibbs states of local Hamiltonians in trace norm that is sample-efficient in all relevant parameters. In contrast, previous approaches learned the underlying Hamiltonian (which implies learning the Gibbs state), and thus inevitably suffered from exponential sample complexity scaling in the inverse temperature. - Certification of Gibbs states. We give an algorithm for certifying Gibbs states of local Hamiltonians in trace norm that is both sample and time-efficient in all relevant parameters, thereby solving a question posed by Anshu (Harvard Data Science Review, 2022).

quant-ph↗

arXiv2026

GRTX: Efficient Ray Tracing for 3D Gaussian-Based Rendering

3D Gaussian Splatting has gained widespread adoption across diverse applications due to its exceptional rendering performance and visual quality. While most existing methods rely on rasterization to render Gaussians, recent research has started investigating ray tracing approaches to overcome the fundamental limitations inherent in rasterization. However, current Gaussian ray tracing methods suffer from inefficiencies such as bloated acceleration structures and redundant node traversals, which greatly degrade ray tracing performance. In this work, we present GRTX, a set of software and hardware optimizations that enable efficient ray tracing for 3D Gaussian-based rendering. First, we introduce a novel approach for constructing streamlined acceleration structures for Gaussian primitives. Our key insight is that anisotropic Gaussians can be treated as unit spheres through ray space transformations, which substantially reduces BVH size and traversal overhead. Second, we propose dedicated hardware support for traversal checkpointing within ray tracing units. This eliminates redundant node visits during multi-round tracing by resuming traversal from checkpointed nodes rather than restarting from the root node in each subsequent round. Our evaluation shows that GRTX significantly improves ray tracing performance compared to the baseline ray tracing method with a negligible hardware cost.

cs.GR↗

arXiv2025

Optimal certification of constant-local Hamiltonians

We study the problem of certifying local Hamiltonians from real-time access to their dynamics. Given oracle access to $e^{-itH}$ for an unknown $k$-local Hamiltonian $H$ and a fully specified target Hamiltonian $H_0$, the goal is to decide whether $H$ is exactly equal to $H_0$ or differs from $H_0$ by at least $\varepsilon$ in normalized Frobenius norm, while minimizing the total evolution time. We introduce the first intolerant Hamiltonian certification protocol that achieves optimal performance for all constant-locality Hamiltonians. For general $n$-qubit, $k$-local, traceless Hamiltonians, our procedure uses $O(c^k/\varepsilon)$ total evolution time for a universal constant $c$, and succeeds with high probability. In particular, for $O(1)$-local Hamiltonians, the total evolution time becomes $\Theta(1/\varepsilon)$, matching the known $\Omega(1/\varepsilon)$ lower bounds and achieving the gold-standard Heisenberg-limit scaling. Prior certification methods either relied on implementing inverse evolution of $H$, required controlled access to $e^{-itH}$, or achieved near-optimal guarantees only in restricted settings such as the Ising case ($k=2$). In contrast, our algorithm requires neither inverse evolution nor controlled operations: it uses only forward real-time dynamics and achieves optimal intolerant certification for all constant-locality Hamiltonians.

quant-ph↗

arXiv2025

Efficient learning of bosonic Gaussian unitaries

Bosonic Gaussian unitaries are fundamental building blocks of central continuous-variable quantum technologies such as quantum-optic interferometry and bosonic error-correction schemes. In this work, we present the first time-efficient algorithm for learning bosonic Gaussian unitaries with a rigorous analysis. Our algorithm produces an estimate of the unknown unitary that is accurate to small worst-case error, measured by the physically motivated energy-constrained diamond distance. Its runtime and query complexity scale polynomially with the number of modes, the inverse target accuracy, and natural energy parameters quantifying the allowed input energy and the unitary's output-energy growth. The protocol uses only experimentally friendly photonic resources: coherent and squeezed probes, passive linear optics, and heterodyne/homodyne detection. We then employ an efficient classical post-processing routine that leverages a symplectic regularization step to project matrix estimates onto the symplectic group. In the limit of unbounded input energy, our procedure attains arbitrarily high precision using only $2m+2$ queries, where $m$ is the number of modes. To our knowledge, this is the first provably efficient learning algorithm for a multiparameter family of continuous-variable unitaries.

quant-ph↗

arXiv2025

Bounding quantum uncommon information with quantum neural estimators

In classical information theory, uncommon information refers to the amount of information that is not shared between two messages, and it admits an operational interpretation as the minimum communication cost required to exchange the messages. Extending this notion to the quantum setting, quantum uncommon information is defined as the amount of quantum information necessary to exchange two quantum states. While the value of uncommon information can be computed exactly in the classical case, no direct method is currently known for calculating its quantum analogue. Prior work has primarily focused on deriving upper and lower bounds for quantum uncommon information. In this work, we propose a new approach for estimating these bounds by utilizing the quantum Donsker-Varadhan representation and implementing a gradient-based optimization method. Our results suggest a pathway toward efficient approximation of quantum uncommon information using variational techniques grounded in quantum neural architectures.

quant-ph↗

arXiv2025

Collapses in quantum-classical probabilistically checkable proofs and the quantum polynomial hierarchy

We investigate the structure of quantum proof systems by establishing collapse results that reveal simplifications in their complexity landscape. By extending classical theorems such as the Karp-Lipton theorem to quantum settings and analyzing uniqueness in quantum-classical PCPs, we clarify how various constraints influence computational power. Our main contributions are: (1) We show that restricting quantum-classical PCPs to unique proofs does not reduce their power: $\mathsf{UniqueQCPCP} = \mathsf{QCPCP}$ under $\mathsf{BQ}$-operator and randomized reductions. This parallels the known $\mathsf{UniqueQCMA} = \mathsf{QCMA}$ result, indicating robustness of uniqueness even in quantum PCP-type systems. (2) We prove a non-uniform quantum analogue of the Karp-Lipton theorem: if $\mathsf{QMA} \subseteq \mathsf{BQP}/\mathsf{qpoly}$, then $\mathsf{QPH} \subseteq \mathsf{Q\Sigma}_2/\mathsf{qpoly}$. This conditional collapse suggests limits on quantum advice for $\mathsf{QMA}$-complete problems. (3) We define a bounded-entanglement version of the quantum polynomial hierarchy, $\mathsf{BEQPH}$, and prove that it collapses above the fourth level. We also introduce the separable hierarchy $\mathsf{SepQPH}$ (zero entanglement), for which the same collapse result holds. These collapses stem not from entanglement, as in prior work, but from the convex structure of the protocols, which renders higher levels tractable. Collectively, these results offer new insights into the structure of quantum proof systems and the role of entanglement, uniqueness, and advice in defining their complexity.

quant-ph↗

arXiv2025

VR-Pipe: Streamlining Hardware Graphics Pipeline for Volume Rendering

Graphics rendering that builds on machine learning and radiance fields is gaining significant attention due to its outstanding quality and speed in generating photorealistic images from novel viewpoints. However, prior work has primarily focused on evaluating its performance through software-based rendering on programmable shader cores, leaving its performance when exploiting fixed-function graphics units largely unexplored. In this paper, we investigate the performance implications of performing radiance field rendering on the hardware graphics pipeline. In doing so, we implement the state-of-the-art radiance field method, 3D Gaussian splatting, using graphics APIs and evaluate it across synthetic and real-world scenes on today's graphics hardware. Based on our analysis, we present VR-Pipe, which seamlessly integrates two innovations into graphics hardware to streamline the hardware pipeline for volume rendering, such as radiance field methods. First, we introduce native hardware support for early termination by repurposing existing special-purpose hardware in modern GPUs. Second, we propose multi-granular tile binning with quad merging, which opportunistically blends fragments in shader cores before passing them to fixed-function blending units. Our evaluation shows that VR-Pipe greatly improves rendering performance, achieving up to a 2.78x speedup over the conventional graphics pipeline with negligible hardware overhead.

cs.GR↗

arXiv2024

Adversarial Environment Design via Regret-Guided Diffusion Models

Training agents that are robust to environmental changes remains a significant challenge in deep reinforcement learning (RL). Unsupervised environment design (UED) has recently emerged to address this issue by generating a set of training environments tailored to the agent's capabilities. While prior works demonstrate that UED has the potential to learn a robust policy, their performance is constrained by the capabilities of the environment generation. To this end, we propose a novel UED algorithm, adversarial environment design via regret-guided diffusion models (ADD). The proposed method guides the diffusion-based environment generator with the regret of the agent to produce environments that the agent finds challenging but conducive to further improvement. By exploiting the representation power of diffusion models, ADD can directly generate adversarial environments while maintaining the diversity of training environments, enabling the agent to effectively learn a robust policy. Our experimental results demonstrate that the proposed method successfully generates an instructive curriculum of environments, outperforming UED baselines in zero-shot generalization across novel, out-of-distribution environments. Project page: https://rllab-snu.github.io/projects/ADD

cs.LG↗

arXiv2024

Resource-efficient algorithm for estimating the trace of quantum state powers

Estimating the trace of quantum state powers, $\text{Tr}(\rho^k)$, for $k$ identical quantum states is a fundamental task with numerous applications in quantum information processing, including nonlinear function estimation of quantum states and entanglement detection. On near-term quantum devices, reducing the required quantum circuit depth, the number of multi-qubit quantum operations, and the copies of the quantum state needed for such computations is crucial. In this work, inspired by the Newton-Girard method, we significantly improve upon existing results by introducing an algorithm that requires only $\mathcal{O}(\widetilde{r})$ qubits and $\mathcal{O}(\widetilde{r})$ multi-qubit gates, where $\widetilde{r} = \min\left\{\text{rank}(\rho), \left\lceil\ln\left({2k}/{\epsilon}\right)\right\rceil\right\}$. This approach is efficient, as it employs the $\tilde{r}$-entangled copy measurement instead of the conventional $k$-entangled copy measurement, while asymptotically preserving the known sample complexity upper bound. Furthermore, we prove that estimating $\{\text{Tr}(\rho^i)\}_{i=1}^{\tilde{r}}$ is sufficient to approximate $\text{Tr}(\rho^k)$ even for large integers $k > \widetilde{r}$. This leads to a rank-dependent complexity for solving the problem, providing an efficient algorithm for low-rank quantum states while also improving existing methods when the rank is unknown or when the state is not low-rank. Building upon these advantages, we extend our algorithm to the estimation of $\text{Tr}(M\rho^k)$ for arbitrary observables and $\text{Tr}(\rho^k \sigma^l)$ for multiple quantum states.

quant-ph↗

arXiv2024

Safe CoR: A Dual-Expert Approach to Integrating Imitation Learning and Safe Reinforcement Learning Using Constraint Rewards

In the realm of autonomous agents, ensuring safety and reliability in complex and dynamic environments remains a paramount challenge. Safe reinforcement learning addresses these concerns by introducing safety constraints, but still faces challenges in navigating intricate environments such as complex driving situations. To overcome these challenges, we present the safe constraint reward (Safe CoR) framework, a novel method that utilizes two types of expert demonstrations$\unicode{x2013}$reward expert demonstrations focusing on performance optimization and safe expert demonstrations prioritizing safety. By exploiting a constraint reward (CoR), our framework guides the agent to balance performance goals of reward sum with safety constraints. We test the proposed framework in diverse environments, including the safety gym, metadrive, and the real$\unicode{x2013}$world Jackal platform. Our proposed framework enhances the performance of algorithms by $39\%$ and reduces constraint violations by $88\%$ on the real-world Jackal platform, demonstrating the framework's efficacy. Through this innovative approach, we expect significant advancements in real-world performance, leading to transformative effects in the realm of safe and reliable autonomous agents.

cs.RO↗

arXiv2024

Disentangling quantum neural networks for unified estimation of quantum entropies and distance measures

The estimation of quantum entropies and distance measures, such as von Neumann entropy, R\'{e}nyi entropy, Tsallis entropy, trace distance, and fidelity-induced distances such as the Bures distance, has been a key area of research in quantum information science. In our study, we introduce the disentangling quantum neural network (DEQNN), designed to efficiently estimate various physical quantities in quantum information. Estimation algorithms for these quantities are generally tied to the size of the Hilbert space of the quantum state to be estimated. Our proposed DEQNN offers a unified dimensionality reduction methodology that can significantly reduce the size of the Hilbert space while preserving the values of diverse physical quantities. We provide an in-depth discussion of the physical scenarios and limitations in which our algorithm is applicable, as well as the learnability of the proposed quantum neural network.

quant-ph↗

arXiv2023

Weighted $p$-R\'{e}nyi Entropy Power Inequality: Information Theory to Quantum Shannon Theory

We study the $p$-R\'{e}nyi entropy power inequality with a weight factor $t$ on two independent continuous random variables $X$ and $Y$. The extension essentially relies on a modulation on the sharp Young's inequality due to Bobkov and Marsiglietti. Our research provides a key result that can be used as a fundamental research finding in quantum Shannon theory, as it offers a R\'{e}nyi version of the entropy power inequality for quantum systems.

quant-ph↗

arXiv2023

Mutual information maximizing quantum generative adversarial networks

One of the most promising applications in the era of Noisy Intermediate-Scale Quantum (NISQ) computing is quantum generative adversarial networks (QGANs), which offer significant quantum advantages over classical machine learning in various domains. However, QGANs suffer from mode collapse and lack explicit control over the features of generated outputs. To overcome these limitations, we propose InfoQGAN, a novel quantum-classical hybrid generative adversarial network that integrates the principles of InfoGAN with a QGAN architecture. Our approach employs a variational quantum circuit for data generation, a classical discriminator, and a Mutual Information Neural Estimator (MINE) to explicitly optimize the mutual information between latent codes and generated samples. Numerical simulations on synthetic 2D distributions and Iris dataset augmentation demonstrate that InfoQGAN effectively mitigates mode collapse while achieving robust feature disentanglement in the quantum generator. By leveraging these advantages, InfoQGAN not only enhances training stability but also improves data augmentation performance through controlled feature generation. These results highlight the potential of InfoQGAN as a foundational approach for advancing quantum generative modeling in the NISQ era.

quant-ph↗

arXiv2023

Estimating Quantum Mutual Information Through a Quantum Neural Network

We propose a method of quantum machine learning called quantum mutual information neural estimation (QMINE) for estimating von Neumann entropy and quantum mutual information, which are fundamental properties in quantum information theory. The QMINE proposed here basically utilizes a technique of quantum neural networks (QNNs), to minimize a loss function that determines the von Neumann entropy, and thus quantum mutual information, which is believed more powerful to process quantum datasets than conventional neural networks due to quantum superposition and entanglement. To create a precise loss function, we propose a quantum Donsker-Varadhan representation (QDVR), which is a quantum analog of the classical Donsker-Varadhan representation. By exploiting a parameter shift rule on parameterized quantum circuits, we can efficiently implement and optimize the QNN and estimate the quantum entropies using the QMINE technique. Furthermore, numerical observations support our predictions of QDVR and demonstrate the good performance of QMINE.

quant-ph↗

arXiv2023

Enhanced Scalability in Assessing Quantum Integer Factorization Performance

With the advancement of quantum technologies, there is a potential threat to traditional encryption systems based on integer factorization. Therefore, developing techniques for accurately measuring the performance of associated quantum algorithms is crucial, as it can provide insights into the practical feasibility from the current perspective. In this chapter, we aim to analyze the time required for integer factorization tasks using Shor's algorithm within a gate-based quantum circuit simulator of the matrix product state type. Additionally, we observe the impact of parameter pre-selection in Shor's algorithm. Specifically, this pre-selection is expected to increase the success rate of integer factorization by reducing the number of iterations and facilitating performance measurement under fixed conditions, thus enabling scalable performance evaluation even on real quantum hardware.

quant-ph↗