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Min-Hsiu Hsieh

Publications and source records attributed to Min-Hsiu Hsieh.

At least 37 records · Page 2Linked to original sources
arXiv2026

Optimizing Quantum Chemistry Simulations with a Hybrid Quantization Scheme

Complex quantum simulation workflows are often hindered by incompatible wavefunction representations adopted across different algorithmic frameworks. In particular, the mismatch between the first- and second-quantization formalisms prevents algorithms specialized for their respective quantizations from being integrated within a single circuit, thereby forcing practitioners to rely on suboptimal methods simply to maintain a consistent representation. To address this challenge, we propose a hybrid quantization scheme that employs a conversion circuit to switch between the two, requiring $\mathcal{O}(N\log N\log M)$ gates for a system of N electrons and M orbitals. This capability is critical for constructing complex quantum simulation workflows, allowing us to use the most efficient quantization for each individual step. We discuss its applications to bring polynomial improvements in the characterization of ground-state, ab-initio molecular dynamics, and characterization of spectroscopic properties. Quantitative estimations of such applications found up to three orders of magnitude fewer ground-state preparations when measuring the 2-reduced density matrix of molecular systems.

quant-ph↗
arXiv2026

Equivalence Checking of Quantum Circuits via Path-Sum and Weighted Model Counting

Equivalence checking of quantum circuits is a central verification task in quantum computing, ensuring the correctness of circuit optimizations, hardware mappings, and compilation pipelines. Among the primary symbolic methods for this purpose, the path-sum formalism provides a compact representation with powerful reduction rules that yield a canonical form for the classically simulable Clifford fragment, but confluence fails beyond the Clifford fragment. We introduce a new weighted model counting (WMC) encoding for path-sums and combine it with the existing path-sum reductions to obtain a verifier that is both complete and efficient. Our method applies reductions whenever possible and invokes the WMC-based decision procedure on the residual path-sum, yielding a complete semantic check up to a global phase. We implement the approach and evaluate it on standard benchmarks. Results show that the hybrid method outperforms either component in isolation and competes with state-of-the-art tools.

cs.SC↗
arXiv2026

Correlation-Converged Virtual Orbitals for Accurate and Efficient Quantum Molecular Simulations

Density functional theory with plane-wave basis sets is widely employed in computational materials science, including applications to isolated molecular systems. However, the inadequate description of electron correlation remains a fundamental limitation. Accurate correlation treatments based on many-body Hamiltonians require reliable representations of both occupied and virtual orbitals, yet virtual orbitals are often poorly described in conventional computational schemes, resulting in reduced accuracy. In this work, we introduce localized correlation-converged virtual orbitals (LCCVOs) as an efficient basis for constructing accurate many-body Hamiltonians in molecular systems. Using a substantially reduced number of orbitals, the LCCVO framework yields dissociation energies for singlet, doublet, and triplet molecules that are comparable to, and in many cases exceed, those obtained with high-level correlation-consistent basis sets such as cc-pVXZ (X = D, T, Q, 5). These results demonstrate the efficiency, scalability, and robustness of the LCCVO approach for high-accuracy quantum chemical calculations.

physics.chem-ph↗
arXiv2026

A Neural-Guided Variational Quantum Algorithm for Efficient Sign Structure Learning in Hybrid Architectures

Variational quantum algorithms hold great promise for unlocking the power of near-term quantum processors, yet high measurement costs, barren plateaus, and challenging optimization landscapes frequently hinder them. Here, we introduce sVQNHE, a neural-guided variational quantum algorithm that decouples amplitude and sign learning across classical and quantum modules, respectively. Our approach employs shallow quantum circuits composed of commuting diagonal gates to efficiently model quantum phase information, while a classical neural network learns the amplitude distribution and guides circuit optimization in a bidirectional feedback loop. This hybrid quantum-classical synergy not only reduces measurement costs but also achieves high expressivity with limited quantum resources and improves the convergence rate of the variational optimization. We demonstrate the advancements brought by sVQNHE through extensive numerical experiments. For the 6-qubit J1-J2 model, a prototypical system with a severe sign problem for Monte Carlo-based methods, it reduces the mean absolute error by 98.9% and suppresses variance by 99.6% relative to a baseline neural network, while requiring nearly 19x fewer optimization steps than a standard hardware-efficient VQE. Furthermore, for MaxCut problems on 45-vertex Erdos-Renyi graphs, sVQNHE improves solution quality by 19% and quantum resource efficiency by 85%. Importantly, this framework is designed to be scalable and robust against hardware noise and finite-sampling uncertainty, making it well-suited for both current NISQ processors and future high-quality quantum computers. Our results highlight a promising path forward for efficiently tackling complex many-body and combinatorial optimization problems by fully exploiting the synergy between classical and quantum resources in the NISQ era and beyond.

quant-ph↗
arXiv2026

Pre-training Tensor-Train Networks Facilitates Machine Learning with Variational Quantum Circuits

Data encoding remains a fundamental bottleneck in quantum machine learning, where amplitude encoding of high-dimensional classical vectors into quantum states incurs exponential cost. In this work, we propose a pre-trained tensor-train (TT) encoding network (Pre-TT-Encoder) that significantly reduces the computational complexity of amplitude encoding while preserving essential data structure. The Pre-TT-Encoder exploits low-rank TT decompositions learned from classical data, enabling polynomial-time state preparation in the number of qubits and TT-ranks. We provide a theoretical analysis of the encoding complexity and establish fidelity bounds that quantify the trade-off between TT-rank and approximation error. Empirical evaluations on classical (MNIST) and quantum-native (semiconductor quantum dot) datasets demonstrate that our approach achieves substantial gains in encoding efficiency over direct amplitude encoding and PCA-based dimensionality reduction, while maintaining competitive performance in downstream variational quantum circuit classification tasks. The proposed method highlights the role of tensor networks as scalable intermediaries between classical data and quantum processors.

quant-ph↗
arXiv2026

TensorHyper-VQC: A Tensor-Train-Guided Hypernetwork for Robust and Scalable Variational Quantum Computing

Variational Quantum Computing (VQC) faces fundamental scalability barriers, primarily due to barren plateaus and sensitivity to quantum noise. To address these challenges, we introduce TensorHyper-VQC, a novel tensor-train (TT)-guided hypernetwork framework that significantly improves the robustness and scalability of VQC. Our framework fully delegates the generation of quantum-circuit parameters to a classical TT network, thereby decoupling optimization from quantum hardware. This innovative parameterization mitigates gradient vanishing, enhances noise resilience through structured low-rank representations, and facilitates efficient gradient propagation. Grounded in Neural Tangent Kernel and statistical learning theory, our rigorous theoretical analyses establish strong guarantees on approximation capability, optimization stability, and generalization performance. Extensive empirical results across quantum dot classification, Max-Cut optimization, and molecular quantum simulation tasks demonstrate that TensorHyper-VQC consistently achieves superior performance and robust noise tolerance, including hardware-level validation on a 156-qubit IBM Heron processor. These results position TensorHyper-VQC as a scalable and noise-resilient framework for advancing practical quantum machine learning on near-term devices.

quant-ph↗
arXiv2026

Characterizing the Burst Error Correction Ability of Quantum Cyclic Codes

Quantum burst error correction codes (QBECCs) are of great importance to deal with the memory effect in quantum channels. As the most important family of QBECCs, quantum cyclic codes (QCCs) play a vital role in the correction of burst errors. In this work, we characterize the burst error correction ability of QCCs constructed from the Calderbank-Shor-Steane (CSS) and the Hermitian constructions. We determine the burst error correction limit of QCCs and quantum Reed-Solomon codes with algorithms in polynomial-time complexities. As a result, lots of QBECCs saturating the quantum Reiger bound are obtained. We show that quantum Reed-Solomon codes have better burst error correction abilities than the previous results. At last, we give the quantum error-trapping decoder (QETD) of QCCs for decoding burst errors. The decoder runs in linear time and can decode both degenerate and nondegenerate burst errors. What's more, the numerical results show that QETD can decode much more degenerate burst errors than the nondegenerate ones.

quant-ph↗
arXiv2026

AQER: a scalable and efficient data loader for digital quantum computers

Digital quantum computing promises to offer computational capabilities beyond the reach of classical systems, yet its capabilities are often challenged by scarce quantum resources. A critical bottleneck in this context is how to load classical or quantum data into quantum circuits efficiently. Approximate quantum loaders (AQLs) provide a viable solution to this problem by balancing fidelity and circuit complexity. However, most existing AQL methods are either heuristic or provide guarantees only for specific input types, and a general theoretical framework is still lacking. To address this gap, here we reformulate most AQL methods into a unified framework and establish information-theoretic bounds on their approximation error. Our analysis reveals that the achievable infidelity between the prepared state and target state scales linearly with the total entanglement entropy across subsystems when the loading circuit is applied to the target state. In light of this, we develop AQER, a scalable AQL method that constructs the loading circuit by systematically reducing entanglement in target states. We conduct systematic experiments to evaluate the effectiveness of AQER, using synthetic datasets, classical image and language datasets, and a quantum many-body state datasets with up to 50 qubits. The results show that AQER consistently outperforms existing methods in both accuracy and gate efficiency. Our work paves the way for scalable quantum data processing and real-world quantum computing applications.

quant-ph↗
arXiv2026

Quantum LEGO Learning: A Modular Design Principle for Hybrid Artificial Intelligence

Hybrid quantum-classical learning models increasingly integrate neural networks with variational quantum circuits (VQCs) to exploit complementary inductive biases. However, many existing approaches rely on tightly coupled architectures or task-specific encoders, limiting conceptual clarity, generality, and transferability across learning settings. In this work, we introduce Quantum LEGO Learning, a modular and architecture-agnostic learning framework that treats classical and quantum components as reusable, composable learning blocks with well-defined roles. Within this framework, a pre-trained classical neural network serves as a frozen feature block, while a VQC acts as a trainable adaptive module that operates on structured representations rather than raw inputs. This separation enables efficient learning under constrained quantum resources and provides a principled abstraction for analyzing hybrid models. We develop a block-wise generalization theory that decomposes learning error into approximation and estimation components, explicitly characterizing how the complexity and training status of each block influence overall performance. Our analysis generalizes prior tensor-network-specific results and identifies conditions under which quantum modules provide representational advantages over comparably sized classical heads. Empirically, we validate the framework through systematic block-swap experiments across frozen feature extractors and both quantum and classical adaptive heads. Experiments on quantum dot classification demonstrate stable optimization, reduced sensitivity to qubit count, and robustness to realistic noise.

cs.LG↗
arXiv2026

Continual Quantum Architecture Search with Tensor-Train Encoding: Theory and Applications to Signal Processing

We introduce CL-QAS, a continual quantum architecture search framework that mitigates the challenges of costly amplitude encoding and catastrophic forgetting in variational quantum circuits. The method uses Tensor-Train encoding to efficiently compress high-dimensional stochastic signals into low-rank quantum feature representations. A bi-loop learning strategy separates circuit parameter optimization from architecture exploration, while an Elastic Weight Consolidation regularization ensures stability across sequential tasks. We derive theoretical upper bounds on approximation, generalization, and robustness under quantum noise, demonstrating that CL-QAS achieves controllable expressivity, sample-efficient generalization, and smooth convergence without barren plateaus. Empirical evaluations on electrocardiogram (ECG)-based signal classification and financial time-series forecasting confirm substantial improvements in accuracy, balanced accuracy, F1 score, and reward. CL-QAS maintains strong forward and backward transfer and exhibits bounded degradation under depolarizing and readout noise, highlighting its potential for adaptive, noise-resilient quantum learning on near-term devices.

quant-ph↗
arXiv2026

Random-Matrix-Induced Simplicity Bias in Over-parameterized Variational Quantum Circuits

Over-parameterization is commonly used to increase the expressivity of variational quantum circuits (VQCs), yet deeper and more highly parameterized circuits often exhibit poor trainability and limited generalization. In this work, we provide a theoretical explanation for this phenomenon from a function-class perspective. We show that sufficiently expressive, unstructured variational ansatze enter a Haar-like universality class in which both observable expectation values and parameter gradients concentrate exponentially with system size. As a consequence, the hypothesis class induced by such circuits collapses with high probability to a narrow family of near-constant functions, a phenomenon we term simplicity bias, with barren plateaus arising as a consequence rather than the root cause. Using tools from random matrix theory and concentration of measure, we rigorously characterize this universality class and establish uniform hypothesis-class collapse over finite datasets. We further show that this collapse is not unavoidable: tensor-structured VQCs, including tensor-network-based and tensor-hypernetwork parameterizations, lie outside the Haar-like universality class. By restricting the accessible unitary ensemble through bounded tensor rank or bond dimension, these architectures prevent concentration of measure, preserve output variability for local observables, and retain non-degenerate gradient signals even in over-parameterized regimes. Together, our results unify barren plateaus, expressivity limits, and generalization collapse under a single structural mechanism rooted in random-matrix universality, highlighting the central role of architectural inductive bias in variational quantum algorithms.

quant-ph↗
arXiv2025

One-Shot Distributed Source Simulation: As Quantum as it Can Get

Distributed source simulation is the task where two (or more) parties share some correlated randomness and use local operations and no communication to convert this into some target correlation. Wyner's seminal result showed that asymptotically the rate of uniform shared randomness needed for this task is given by a mutual information induced measure, now referred to as Wyner's common information. This asymptotic result was extended by Hayashi in the quantum setting to separable states, the largest class of states for which this task can be performed to vanishing error. In this work we characterize this task in a near-tight manner in the one-shot setting using the smooth entropy framework. We do this by introducing one-shot operational quantities and correlation measures that characterize them. We establish asymptotic equipartition properties for our correlation measures thereby recovering the previous vanishing-error asymptotic results. In doing so, we consider technical points in one-shot network information theory and provide methods for cardinality bounds in the smooth entropy calculus. We also introduce entangled state versions of the distributed source simulation task and determine bounds in this setting via quantum embezzling. This provides a strong characterization of this network task in the one-shot, quantum regime.

quant-ph↗
arXiv2025

VQC-MLPNet: An Unconventional Hybrid Quantum-Classical Architecture for Scalable and Robust Quantum Machine Learning

Variational quantum circuits (VQCs) hold promise for quantum machine learning but face challenges in expressivity, trainability, and noise resilience. We propose VQC-MLPNet, a hybrid architecture where a VQC generates the first-layer weights of a classical multilayer perceptron during training, while inference is performed entirely classically. This design preserves scalability, reduces quantum resource demands, and enables practical deployment. We provide a theoretical analysis based on statistical learning and neural tangent kernel theory, establishing explicit risk bounds and demonstrating improved expressivity and trainability compared to purely quantum or existing hybrid approaches. These theoretical insights demonstrate exponential improvements in representation capacity relative to quantum circuit depth and the number of qubits, providing clear computational advantages over standalone quantum circuits and existing hybrid quantum architectures. Empirical results on diverse datasets, including quantum-dot classification and genomic sequence analysis, show that VQC-MLPNet achieves high accuracy and robustness under realistic noise models, outperforming classical and quantum baselines while using significantly fewer trainable parameters.

quant-ph↗
arXiv2025

Characterizing Space-Constrained Implementability of Quantum Instruments via Signaling Conditions

Scaling up the number of qubits available on quantum processors remains technically demanding even in the long term; it is therefore crucial to clarify the number of qubits required to implement a given quantum operation. For the most general class of quantum operations, known as quantum instruments, the qubit requirements are not well understood, especially when mid-circuit measurements and delayed input preparation are permitted. In this work, we characterize lower and upper bounds on the number of qubits required to implement a given quantum instrument in terms of the causal structure of the instrument. We further apply our results to entanglement distillation protocols based on stabilizer codes and show that, in these cases, the lower and upper bounds coincide, so the optimal qubit requirement is determined. In particular, we compute that the optimal number of qubits is 3 for the $[[9,1,3]]$-code-based protocol and 4 for the $[[5,1,3]]$-code-based protocol.

quant-ph↗
arXiv2025

Single-Shot Universality in Quantum LDPC Codes via Code-Switching

Code-switching is a powerful technique in quantum error correction that allows one to leverage the complementary strengths of different codes to achieve fault-tolerant universal quantum computation. However, existing code-switching protocols that encapsulate recent generalized lattice surgery approaches often either require many rounds of measurements to ensure fault-tolerance or suffer from low code rates. We present a single-shot, universal protocol that uses code-switching between high-rate quantum codes to perform fault-tolerant quantum computation. To our best knowledge, our work contains the first universal fault-tolerant quantum computation protocol that achieves what we term single-shot universality on high-rate codes that is characterized by (i) single-shot error correction, (ii) single-shot state preparation, as well as (iii) universal logical gates and logical measurements with constant depth circuits. We achieve this feat with single-shot code-switching between constant-rate 2D hypergraph product (HGP) codes and high-rate 3D HGP codes that can be viewed as a generalization of Bombin's dimensional jump for color codes and Hillmann et al.'s single-shot lattice surgery for higher-dimensional topological codes. In addition, we prove the fault-tolerance of our code-switching protocol under both the adversarial and local-stochastic noise models. We introduce a vastly simpler recipe to construct high-rate 3D HGP codes with transversal CCZ gates that grants immense flexibility in the choice of expander graphs and local codes, allowing us to expand the search space for codes with good parameters and interesting logical gates. Our work opens an alternative path towards universal fault-tolerant quantum computation with low space-time overhead by circumventing the need for magic state distillation.

quant-ph↗
arXiv2025

Universal classical-quantum channel resolvability and private channel coding

We address the problem of constructing fully universal private channel coding protocols for classical-quantum (c-q) channels. Previous work constructed universal decoding strategies, but the encoder relied on random coding, which prevents fully universal code construction. In this work, we resolve this gap by identifying an explicit structural property of codebooks -- namely, the spectral expansion of an associated Schreier graph -- that guarantees universal channel resolvability. Our analysis reveals how this property can be related to channel resolvability through the theory of induced representation. Our main technical result shows that when the transition matrix of a graph associated with a codebook has a large spectral gap, the channel output induced by uniformly sampled codewords is asymptotically indistinguishable from the target output distribution, independently of the channel. This establishes the first deterministic, channel-independent construction of resolvability codebooks. Building on this, we construct a fully universal private channel coding protocol by combining it with universal c-q channel coding based on the Schur-Weyl duality. With appropriate modifications to the requirements on codebooks of universal c-q channel coding, we show that our fully universal private channel coding achieves the known optimal rate. This work thus sheds new light on the expander property of a graph in the context of secure communication.

quant-ph↗
arXiv2025

Optimal Particle-Conserved Linear Encoding for Practical Fermionic Simulation

Number-conserved subspace encoding reduces resources needed for quantum simulations, but scalable complexity trade-off bounds for $M$ modes and $N$ particles with $\mathcal{O}(N\log M)$ qubits have remained unknown. We study qubit-gate-measurement trade-offs through the lens of classical/quantum error correction complexity, and develop a framework of fermionic gate and measurement complexity based on encoder and decoder complexities appeared in error correction framework. We demonstrate optimal encoding with random classical parity check code and propose the Fermionic Expectation Decoder for scalable probability decoding in $\mathcal{O}(M^4)$ bases. The protocol is tested with variational quantum eigensolver on LiH in the STO-3G and 6-31G basis, and $\text{H}_2$ potential energy curve in the 6-311G* basis.

quant-ph↗
arXiv2025

Efficient Learning for Linear Properties of Bounded-Gate Quantum Circuits

The vast and complicated large-qubit state space forbids us to comprehensively capture the dynamics of modern quantum computers via classical simulations or quantum tomography. Recent progress in quantum learning theory prompts a crucial question: can linear properties of a large-qubit circuit with d tunable RZ gates and G-d Clifford gates be efficiently learned from measurement data generated by varying classical inputs? In this work, we prove that the sample complexity scaling linearly in $d$ is required to achieve a small prediction error, while the corresponding computational complexity may scale exponentially in d. To address this challenge, we propose a kernel-based method leveraging classical shadows and truncated trigonometric expansions, enabling a controllable trade-off between prediction accuracy and computational overhead. Our results advance two crucial realms in quantum computation: the exploration of quantum algorithms with practical utilities and learning-based quantum system certification. We conduct numerical simulations to validate our proposals across diverse scenarios, encompassing quantum information processing protocols, Hamiltonian simulation, and variational quantum algorithms up to 60 qubits.

quant-ph↗