arXiv subjects

Changhun Oh

Publications and source records attributed to Changhun Oh.

At least 37 records · Page 2Linked to original sources

arXiv2026

Bound Entanglement Is Insufficient for an Exponential Quantum Learning Advantage

While entanglement is known to enable exponential improvements in the sample complexity of quantum learning, it remains unclear which properties of entangled resources are responsible for such improvements. We address this question through the reduction criterion, a condition obeyed by all bound-entangled states. In $n$-qubit Pauli-channel learning, we show that restricting either the input states or the measurement effects to satisfy this criterion rules out an exponential advantage for incoherent adaptive protocols. An exponential lower bound persists for the one-sided coherent adaptive protocols considered here, even when the unrestricted side retains quantum correlations across channel uses. Using conditional min-entropy, we further quantify how the sample-complexity lower bounds weaken as larger violations of the reduction criterion are allowed. Finally, we show that the same obstruction appears in conjugate-state learning: restricted joint measurements cannot reproduce the logarithmic-sample advantage of unrestricted joint measurements on $ρ\otimesρ^*$. These results identify violation of the reduction criterion as a necessary condition for an exponential advantage in the learning tasks considered here.

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arXiv2026

Disentangling Haldane Phase by Generalized Clifford Circuits

Disentangling transformations play a central role in the classical simulation of quantum many-body systems, yet their analytic structure and underlying mechanism remain largely unexplored. Here, we study the structure of the disentangler in the Haldane phase of spin-1 systems using generalized Clifford circuits. To this end, we extend the Clifford-circuit-augmented matrix product states (CAMPS)-based density-matrix renormalization group (DMRG) method to spin-1 systems. Within this framework, we find that the local disentanglers optimized for the Haldane phase implement the generalized Kramers--Wannier (KW) transformation, and we analytically verify its optimality for the Affleck--Kennedy--Lieb--Tasaki (AKLT) state. Beyond reducing entanglement, the KW transformation maps the Haldane phase to a phase with spontaneously broken $\mathbb{Z}_{2}$ symmetry. This mapping is distinct from the Kennedy--Tasaki transformation and provides a new unitary route from symmetry-protected topological order to symmetry breaking.

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arXiv2026

When to Skip Syndrome Extraction in Surface-GKP Codes

Fault-tolerant quantum error correction requires repeated syndrome extraction to address errors induced by the syndrome-extraction circuit itself. However, repeated syndrome extraction incurs significant overhead in terms of gate count and ancilla consumption (e.g., Gottesman-Kitaev-Preskill (GKP) states). Moreover, noisy syndrome extraction can itself inject additional errors into the data qubits. To address these issues, we propose a concrete adaptive skipping scheme for the surface-GKP code, a representative GKP-concatenated architecture, that uses analog information naturally generated during inner GKP correction. At each round, the scheme selects one of four actions: measuring both Z-type and X-type surface-code stabilizers, measuring only one type, or skipping both types and reusing previous syndromes. The decision is based on a reliability comparison between reusing the previous syndrome value and performing a new noisy syndrome extraction. Using circuit-level simulations, we show that the adaptive skipping scheme can reduce the number of surface-code stabilizer measurements while maintaining logical error rates comparable to or lower than those of the full-measurement baseline. The improvement is most pronounced when gate and measurement noise are larger than idle noise, so that avoiding unnecessary syndrome extraction reduces the noise injected into the code. These results indicate that analog information from inner GKP correction can be used not only to improve decoding but also to reduce the measurement overhead of outer-code syndrome extraction.

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arXiv2026

Representing Time Series as Structured Programs for LLM Reasoning

Large language models (LLMs) have demonstrated strong reasoning and instruction-following capabilities, making them potentially powerful tools for time-series analysis. However, time series lie outside their native textual modality, raising a fundamental question: how should time series be represented so that LLMs can reason about them effectively? Existing work typically serializes raw numerical sequences or fine-tunes pre-trained LLMs on time-series data. These approaches place the burden of extracting temporal structure directly on the LLM, creating a modality mismatch that often degrades performance on long sequences and introduces substantial computational overhead. In this work, we introduce Time-Series-to-Structured-Program representation (T2SP), a deterministic, training-free method that represents a time series as a structured symbolic program. T2SP decomposes time series into trends, periods, and salient events, expressing them in a program-friendly format aligned with the textual and code-like modalities on which LLMs are natively trained. By shifting temporal-structure extraction from the model to the representation itself, T2SP enables off-the-shelf LLMs to leverage their existing reasoning capabilities for time-series understanding. We evaluate T2SP on three reasoning tasks -- editing, captioning, and question answering -- where it consistently improves performance, reduces reasoning time, and lowers failure rates compared with raw-string representations. Our results demonstrate that T2SP provides an effective interface between time series and LLMs.

cs.LG↗

arXiv2026

Virtual purification complements quantum error correction in quantum metrology

Quantum resources enable one to achieve quantum-enhanced estimation sensitivity beyond its classical counterpart. Many studies mainly focus on reducing statistical error, under the assumption that one can always set an unbiased estimator. However, setting an unbiased estimator is not always feasible, especially when one cannot fully characterize noise. Such incomplete noise characterization induces a bias and eventually makes it impossible to attain the enhanced-estimation. In this work, we explore two systematic approaches; quantum error correction (QEC) and the virtual purification (VP) to reduce the bias, and compare their performance. First, we show that when the noise is indistinguishable from the signal, QEC cannot reduce the bias since it is impossible to construct a QEC code that corrects the noise while preserving the signal. We then show that VP can mitigate indistinguishable error that eventually enable a more accurate estimation compared to QEC. Our findings reveal that VP offers a robust alternative to QEC in scenarios where indistinguishable errors pose significant challenges. We then demonstrate that VP with a stabilizer state probe can efficiently suppress the bias under local depolarizing noise, thereby yielding a significant improvement in estimation performance compared to the QEC-based approach.

quant-ph↗

arXiv2026

Classical simulation of free-fermionic dynamics and quantum chemistry with magic input

Establishing the precise computational boundary between classically tractable fermionic systems and those capable of genuine quantum advantage is a central challenge in quantum simulation. While injecting non-Gaussian ``magic" inputs into free-fermion circuits is widely expected to generate intractable complexity, we identify a physically motivated intermediate regime. We prove that for block-product paired non-Gaussian fermionic states, essential quantum simulation primitives -- transition amplitudes, overlaps, and arbitrary-weight number correlators -- can be efficiently approximated to additive error under free-fermionic dynamics. This tractability stems from an algebraic reduction that compresses exponentially large multiparticle interference into a single coefficient of a multivariate Pfaffian polynomial. Because these classical estimators match the intrinsic $O(1/\sqrt{K})$ statistical uncertainty of quantum hardware utilizing $K$ measurement shots, they constitute a practical benchmark. Building on this foundation, we construct an additive-error estimator for high-weight Wilson observables in the noninteracting quench of recent trapped-ion experiments, providing a rigorous classical benchmark. Extending this to quantum chemistry, we demonstrate that core overlap-based subroutines for antisymmetrized products of strongly orthogonal geminals admit efficient additive-error Pfaffian-kernel estimators. Ultimately, these results sharpen the boundary of quantum advantage, establishing that the paired-electron scaffold is dequantized and clarifying where quantum resources are indispensable.

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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

Complexity phase transition for continuous-variable cluster state

Continuous-variable (CV) cluster states offer a promising platform for large-scale measurement-based quantum computations (MBQC). However, finite squeezing inevitably introduces Gaussian noise during MBQC. While fault-tolerant MBQC schemes exist in principle, they require the scalable incorporation of non-Gaussian resources, such as GKP states, which remain experimentally challenging. Consequently, a central question at this stage is how finite squeezing fundamentally constrains the intrinsic computational power of CV cluster states themselves. In this work, we address this question by analyzing the classical complexity of measurement-based linear optics (MBLO) implemented with such states, motivated by its near-term feasibility and recent experimental progress. We develop an explicit MBLO framework and examine how the squeezing level governs the complexity of the classical simulation of the resulting output states. Specifically, we identify squeezing-level thresholds that delineate classically tractable and intractable regimes, thereby revealing a squeezing-driven complexity phase transition. These findings advance our understanding of the squeezing resources necessary for meaningful quantum computation in current experimental regimes. Furthermore, they underscore the critical need to either scale the squeezing level or integrate error-correction schemes to achieve reliable, large-scale quantum computation with CV cluster states.

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arXiv2026

Generative modeling with Gaussian Boson Sampling: classically trainable Bosonic Born Machines

Quantum generative modeling has emerged as a promising application of quantum computers, aiming to model complex probability distributions beyond the reach of classical methods. In practice, however, training such models often requires costly gradient estimation performed directly on the quantum hardware. Crucially, for certain structured quantum circuits, expectation values of local observables can be efficiently evaluated on a classical computer, enabling classical training without calls to the quantum hardware in the optimization loop. In these models, sampling from the resulting circuits can still be classically hard, so inference must be performed on a quantum device, yielding a potential computational advantage. In this work, we introduce a photonic quantum generative model built on parametrized Gaussian Boson Sampling circuits. The training is based on the efficient classical evaluation of expectation values enabled by the Gaussian structure of the state, allowing scalable optimization of the model parameters through the maximum mean discrepancy loss function. We demonstrate the effectiveness of the approach through numerical experiments on photonic systems with up to 805 modes and over a million trainable parameters, highlighting its scalability and suitability for near-term photonic quantum devices.

quant-ph↗

arXiv2026

On computational complexity and average-case hardness of shallow-depth boson sampling

Boson sampling, a computational task believed to be classically hard to simulate, is expected to hold promise for demonstrating quantum computational advantage using near-term quantum devices. However, noise in experimental implementations poses a significant challenge, potentially rendering boson sampling classically simulable and compromising its classical intractability. Numerous studies have proposed classical algorithms under various noise models that can efficiently simulate boson sampling as noise rates increase with circuit depth. To address this issue particularly related to circuit depth, we explore the viability of achieving quantum computational advantage through boson sampling with shallow-depth linear optical circuits. Specifically, as the average-case hardness of estimating output probabilities of boson sampling is a crucial ingredient in demonstrating its classical intractability, we make progress on establishing the average-case hardness confined to logarithmic-depth regimes. We also obtain the average-case hardness for logarithmic-depth Fock-state boson sampling subject to lossy environments and for the logarithmic-depth Gaussian boson sampling. By providing complexity-theoretical backgrounds for the classical simulation hardness of logarithmic-depth boson sampling, we expect that our findings will mark a crucial step towards a more noise-tolerant demonstration of quantum advantage with shallow-depth boson sampling.

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arXiv2026

On the Fundamental Resource for Exponential Advantage in Quantum Channel Learning

Quantum resources enable us to achieve an exponential advantage in learning the properties of unknown physical systems by employing quantum memory. While entanglement with quantum memory is recognized as a necessary qualitative resource, its quantitative role remains less understood. In this work, we distinguish between two fundamental resources provided by quantum memory -- entanglement and ancilla qubits -- and analyze their separate contributions to the sampling complexity of quantum learning. Focusing on the task of Pauli channel learning, a prototypical example of quantum channel learning, remarkably, we prove that vanishingly small entanglement in the input state already suffices to accomplish the learning task with only a polynomial number of channel queries in the number of qubits. In contrast, we show that without a sufficient number of ancilla qubits, even learning partial information about the channel demands an exponentially large sample complexity. Thus, our findings reveal that while a large amount of entanglement is not necessary, the dimension of the quantum memory is a crucial resource. Hence, by identifying how the two resources contribute differently, our work offers deeper insight into the nature of the quantum learning advantage.

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arXiv2026

Classical simulation of a quantum circuit with noisy magic inputs

Magic states are essential for universal quantum computation and are widely viewed as a key source of quantum advantage, yet in realistic devices they are inevitably noisy. In this work, we characterize how noise on injected magic resources changes the classical simulability of quantum circuits and when it induces a transition from classically intractable behavior to efficient classical simulation. We adopt a resource-centric noise model in which only the injected magic components are noisy, while the baseline states, operations, and measurements belong to an efficiently simulable family. Within this setting, we develop an approximate classical sampling algorithm with controlled error and prove explicit noise-dependent conditions under which the algorithm runs in polynomial time. Our framework applies to both qubit circuits with Clifford baselines and fermionic circuits with matchgate baselines, covering representative noise channels such as dephasing and particle loss. We complement the analysis with numerical estimates of the simulation cost, providing concrete thresholds and runtime scaling across practically relevant parameter regimes.

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arXiv2025

Exponential advantage in continuous-variable quantum state learning

We consider the task of learning quantum states in bosonic continuous-variable (CV) systems. We present an experimentally feasible protocol that uses entangled measurements and reflected states to efficiently learn, up to sign, the characteristic function of CV quantum states, with sample complexity independent of the number of modes $n$. We prove that any adaptive scheme without entangled measurements requires exponentially many samples in $n$ for this learning task, thereby demonstrating an exponential advantage from entangled measurements. Remarkably, we also prove that any entanglement-assisted scheme that does not have access to reflected states requires exponentially many samples in $n$. Together, these results establish a rigorous exponential advantage that jointly relies on entangled measurements and reflected states. Finally, we relate the sample-complexity bounds to the input state's classicality, revealing a classicality-complexity tradeoff: entanglement-free schemes suffice for highly classical states, whereas in the genuinely nonclassical regime the sample cost can be reduced only by providing both entanglement and reflected states.

quant-ph↗

arXiv2025

Classical algorithms for measurement-adaptive Gaussian circuits

Gaussian building blocks are essential for photonic quantum information processing, and universality can be practically achieved by equipping Gaussian circuits with adaptive measurement and feedforward. The number of adaptive steps then provides a natural parameter for computational power. Rather than assessing power only through sampling problems -- the usual benchmark -- we follow the ongoing shift toward tasks of practical relevance and study the quantum mean-value problem, i.e., estimating observable expectation values that underpin simulation and variational algorithms. More specifically, we analyze bosonic circuits with adaptivity and prove that when the number of adaptive measurements is small, the mean-value problem admits efficient classical algorithms even if a large amount of non-Gaussian resources are present in the input state, whereas less constrained regimes are computationally hard. This yields a task-level contrast with sampling, where non-Gaussian ingredients alone often induce hardness, and provides a clean complexity boundary parameterized by the number of adaptive measurement-and-feedforward steps between classical simulability and quantum advantage. Beyond the main result, we introduce classical techniques -- including a generalization of Gurvits' second algorithm to arbitrary product inputs and Gaussian circuits -- for computing the marginal quantities needed by our estimators, which may be of independent interest.

quant-ph↗

arXiv2025

Advancing quantum imaging through learning theory

We study quantum imaging by applying the resolvable expressive capacity (REC) formalism developed for physical neural networks (PNNs). In this paradigm of quantum learning, the imaging system functions as a physical learning device that maps input parameters to measurable features, while complex practical tasks are handled by training only the output weights, enabled by the systematic identification of well-estimated features (eigentasks) and their corresponding sample thresholds. Using this framework, we analyze both direct imaging and superresolution strategies for compact sources, defined as sources with sizes bounded below the Rayleigh limit. In particular, we introduce the orthogonalized SPADE method-a nontrivial generalization of existing superresolution techniques-that achieves superior performance when multiple compact sources are closely spaced. This method relaxes the earlier superresolution studies' strong assumption that the entire source must lie within the Rayleigh limit, marking an important step toward developing more general and practically applicable approaches. Using the example of face recognition, which involve complex structured sources, we demonstrate the superior performance of our orthogonalized SPADE method and highlight key advantages of the quantum learning approach-its ability to tackle complex imaging tasks and enhance performance by selectively extracting well-estimated features.

quant-ph↗

arXiv2025

Neo: Real-Time On-Device 3D Gaussian Splatting with Reuse-and-Update Sorting Acceleration

3D Gaussian Splatting (3DGS) rendering in real-time on resource-constrained devices is essential for delivering immersive augmented and virtual reality (AR/VR) experiences. However, existing solutions struggle to achieve high frame rates, especially for high-resolution rendering. Our analysis identifies the sorting stage in the 3DGS rendering pipeline as the major bottleneck due to its high memory bandwidth demand. This paper presents Neo, which introduces a reuse-and-update sorting algorithm that exploits temporal redundancy in Gaussian ordering across consecutive frames, and devises a hardware accelerator optimized for this algorithm. By efficiently tracking and updating Gaussian depth ordering instead of re-sorting from scratch, Neo significantly reduces redundant computations and memory bandwidth pressure. Experimental results show that Neo achieves up to 10.0x and 5.6x higher throughput than state-of-the-art edge GPU and ASIC solution, respectively, while reducing DRAM traffic by 94.5% and 81.3%. These improvements make high-quality and low-latency on-device 3D rendering more practical.

cs.AR↗

arXiv2025

Classical algorithms for estimating expectation values in linear-optical circuits

We present a classical algorithm for approximating the expectation values of observables in linear-optical circuits with arbitrary product input states, achieving additive-error accuracy. This result indicates that current applications of photonic systems aimed at demonstrating practical quantum supremacy through expectation value estimation, such as photonic variational algorithms, may face challenges in attaining the computational advantage. It also implies the output probabilities of boson sampling with arbitrary product input states can be efficiently approximated by our method, resulting that boson sampling becomes efficiently simulable when its output probability distribution is polynomially sparse. We also develop an efficient classical algorithm for estimating transition amplitudes of arbitrary product states in linear-optical circuits. This provides additive-error approximation algorithms for matrix functions associated with linear-optical circuits, such as the (loop-)hafnian, which are of independent interest. As an application, it solves the generalized molecular vibronic spectra problem (Oh et al., 2024), previously suggested as a candidate for practical quantum advantage. Finally, we extend our framework to near-Clifford circuits, enabling classical approximation of their expectation values.

quant-ph↗

arXiv2025

Sufficient conditions for hardness of lossy Gaussian boson sampling

Gaussian boson sampling (GBS) is a prominent candidate for the experimental demonstration of quantum advantage. However, while the current implementations of GBS are unavoidably subject to noise, the robustness of the classical intractability of GBS against noise remains largely unexplored. In this work, we establish the complexity-theoretic foundations for the classical intractability of noisy GBS under photon loss, which is a dominant source of imperfection in current implementations. We identify the loss threshold below which lossy GBS maintains the same complexity-theoretic level as ideal GBS, and show that this holds when at most a logarithmic fraction of photons is lost. We additionally derive an intractability criterion for the loss rate through a direct quantification of the statistical distance between ideal and lossy GBS. This work presents the first rigorous characterization of classically intractable regimes of lossy GBS, thereby serving as a crucial step toward demonstrating quantum advantage with near-term implementations.

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