arXiv subjects

Tzu-Chieh Wei

Publications and source records attributed to Tzu-Chieh Wei.

At least 19 recordsLinked to original sources

arXiv2026

Coupled-Layer Codes: Beyond Quantum Product Constructions

Product codes are an important class of quantum error-correcting codes constructed from multiple input codes, which can give rise to asymptotically good quantum low-density parity check codes. In previous work, we showed how the product between two codes can be physically implemented by coupling layers of the first code using checks of the second code. In this work, we further unify product code constructions with coupled-layer constructions of phases of matter by introducing coupled-layer codes. The essential strategy is to condense general excitations created by Pauli operators among multiple decoupled layers of the first code. The condensation is specified by an excitation algebra, which encodes the excitations, along with an algebra-preserving map. This coupling between layers generalizes the notion of gauging in physics as well as the mapping cone in homological algebra, and can be used to produce non-CSS codes. As examples, we show how coupled-layer codes reproduce the X-cube and Chamon models. We further generalize the balanced product code by allowing a unitary transformation in addition to a group action by free permutation and describe its corresponding coupled-layer construction. In particular, we show how balancing by a ZX-duality can reproduce non-CSS codes such as the fermionic toric code and the 3-fermion Walker-Wang model in 3D.

quant-ph↗

arXiv2026

Observable Geometry for Effective Quantum Circuits

We study redundancy and effectiveness of Variational Quantum Circuits via algebraic and geometric views of Lie groups. Considering unitary transformations acting on Hermitian observables, a stabilizer group decomposition is given. Subsequently, we identify the Hermitian orbit with a quotient space of a symmetric space. Through this connection, we characterize the effective circuit degrees of freedom. Our approach of spectral decompositions and homogeneous spaces yields tractable calculation criteria, which are verified by numerical experiments.

quant-ph↗

arXiv2026

Universal energy-space localization and stable quantum phases against time-dependent perturbations

Stability against perturbations is a highly nontrivial property of quantum systems and is often a requirement to define new phases. In most systems where stability can be rigorously established, only static perturbations are considered; whether any system can remain stable against generic time-dependent perturbations is largely elusive. In this work, we identify a universal phenomenon in driving $q$-local Hamiltonians called energy-space localization and prove that it can survive under generic time-dependent perturbations, where the evolving state is exponentially localized in an energy window of the instantaneous spectrum. For spin glass models where the configuration spaces are separated by large energy barriers, the localization in energy spaces can induce a true localization in configuration spaces and robustly break ergodicity. We then demonstrate its applications in several systems with such barriers. For certain LDPC codes, we show that the system remains localized near the original codeword for an exponentially long time even under generic time-dependent perturbations. For classical optimization problems with clustered solution space, the stability becomes an obstacle for quantum Hamiltonian-based algorithms to escape local minima. Our work provides a new lens for analyzing non-equilibrium dynamics of generic quantum systems, and versatile mathematical tools for establishing stability and for designing quantum algorithms.

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arXiv2026

Speaker Identity in Non-Verbal Vocalizations: Conditional Distillation and Mixture of Experts Approach

As expressive text-to-speech (TTS) and voice conversion (VC) systems increasingly generate non-verbal vocalizations (NVVs) to enhance naturalness, reliable speaker verification (SV) becomes essential to objectively assess identity consistency across both verbal and non-verbal segments. Yet current SV systems generalize poorly to NVVs, and fine-tuning on NVV data causes catastrophic forgetting of speech performance. We present the first systematic study across 10 NVV types and propose a framework combining frozen Data2Vec self-supervised features with ECAPA-TDNN, enhanced by a Mixture of Experts (MoE) module with learned domain-aware routing. A conditional distillation loss on speech inputs via a pretrained teacher retains speech-to-speech accuracy, while a contrastive loss bridges the speech-NVV domain gap. Our method reduces speech-NVV EER from 38.93% to 22.66% over a pretrained baseline, and improves speech EER from 13.17% to 9.24% via distillation.

eess.AS↗

arXiv2026

The $O(N)$ Free-Scalar and Wilson-Fisher Conformal Field Theories on the Fuzzy Sphere

The fuzzy-sphere regularization is an emerging numerical and theoretical technique for studying conformal field theories (CFTs). In this paper, we apply it to the $O(N)$ vector model, one of the most prominent theories for critical behavior in three space-time dimensions. We construct a model that realizes the $O(N)$ Wilson-Fisher and free-scalar CFTs for general $N$. For $N=2,3,4$, we present numerical evidence including the operator spectra and correlation functions in agreement with conformal symmetry and conformal bootstrap results.

cond-mat.str-el↗

arXiv2026

Higher-order topological phases protected by noninvertible and subsystem symmetries

Higher-order topological phases with invertible symmetries have been extensively studied in recent years, revealing gapless modes localized on boundaries of higher codimension. In this work, we extend the framework of higher-order symmetry-protected topological (SPT) phases to include noninvertible symmetries. We construct a concrete model of a second-order SPT phase in $2+1$ dimensions that hosts symmetry-protected corner modes protected by a noninvertible symmetry. This construction is then generalized to a $d^{th}$-order SPT phase in $d+1$ dimensions, featuring similarly protected corner modes. Additionally, we demonstrate a second-order SPT phase in $3+1$ dimensions exhibiting hinge modes protected by a noninvertible symmetry.

cond-mat.str-el↗

arXiv2026

Coupled-Layer Construction of Quantum Product Codes

Product codes are a class of quantum error correcting codes built from two or more constituent codes. They have recently gained prominence for a breakthrough yielding quantum low-density parity-check (qLDPC) codes with favorable scaling of both code distance and encoding rate. However, despite its powerful algebraic formulation, the physical mechanism for assembling a general product code from its constituents remains unclear. In this letter, we show that the tensor and balanced product codes admit an intuitive coupled-layer construction by taking a stack of one code and condensing a set of excitations in the pattern given by the checks of the other code. We also make a connection to concatenated codes by showing that the tensor product code can be obtained by gauging large-weight logicals in concatenated codes, making them qLDPC. Our framework accommodates both classical or quantum CSS input codes, unifies known physical mechanisms for constructing higher dimensional topological phases via anyon condensation, and naturally extends to non-topological codes.

quant-ph↗

arXiv2026

Hybrid quantum-classical framework for Betti number estimation with applications to topological data analysis

Topological data analysis (TDA) is a rapidly growing area that applies techniques from algebraic topology to extract robust features from large-scale data. A key task in TDA is the estimation of (normalized) Betti numbers, which capture essential topological invariants. While recent work has led to quantum algorithms for this problem, we explore an alternative direction: combining classical and quantum resources to estimate the Betti numbers of a simplicial complex more efficiently. Assuming the classical description of a simplicial complex, that is, its set of vertices and edges, we propose a hybrid quantum-classical algorithm. The classical component enumerates all simplices, and this combinatorial structure is subsequently processed by a quantum algorithm to estimate the Betti numbers. We analyze the performance of our approach and identify regimes where it potentially achieves polynomial to exponential speedups over existing quantum methods, at the trade-off of using more ancilla qubits. We further demonstrate the utility of normalized Betti numbers in concrete applications, highlighting the broader potential of hybrid quantum algorithms in topological data analysis.

quant-ph↗

arXiv2026

Do You Hear What I Mean? Quantifying the Instruction-Perception Gap in Instruction-Guided Expressive Text-To-Speech Systems

Instruction-guided text-to-speech (ITTS) enables users to control speech generation through natural language prompts, offering a more intuitive interface than traditional TTS. However, the alignment between user style instructions and listener perception remains largely unexplored. This work first presents a perceptual analysis of ITTS controllability across two expressive dimensions (adverbs of degree and graded emotion intensity) and collects human ratings on speaker age and word-level emphasis attributes. To comprehensively reveal the instruction-perception gap, we provide a data collection with large-scale human evaluations, named Expressive VOice Control (E-VOC) corpus. Furthermore, we reveal that (1) gpt-4o-mini-tts is the most reliable ITTS model with great alignment between instruction and generated utterances across acoustic dimensions. (2) The 5 analyzed ITTS systems tend to generate Adult voices even when the instructions ask to use child or Elderly voices. (3) Fine-grained control remains a major challenge, indicating that most ITTS systems have substantial room for improvement in interpreting slightly different attribute instructions.

eess.AS↗

arXiv2026

An Exploration of Mamba for Speech Self-Supervised Models

While Mamba has demonstrated strong performance in language modeling, its potential as a speech self-supervised learning (SSL) model remains underexplored, with prior studies limited to isolated tasks. To address this, we explore Mamba-based HuBERT models as alternatives to Transformer-based SSL architectures. Leveraging the linear-time Selective State Space, these models enable fine-tuning on long-context ASR with significantly lower compute. Moreover, they show superior performance when fine-tuned for streaming ASR. Beyond fine-tuning, these models show competitive performance on SUPERB probing benchmarks, particularly in causal settings. Our analysis shows that they yield higher-quality quantized representations and capture speaker-related features more distinctly than Transformer-based models. These findings highlight Mamba-based SSL as a promising and complementary direction for long-sequence modeling, real-time speech modeling, and speech unit extraction. The codebase is available at https://github.com/hckuo145/Mamba-based-HuBERT.

cs.CL↗

arXiv2026

Hybrid Quantum-Classical Algorithm for Hamiltonian Simulation

We introduce a hybrid classical-quantum algorithm for simulating a Hamiltonian of the form $H= \sum_{i=1}^K H_i = \sum_{i=1}^K H_{i_1} \otimes H_{i_2} \otimes \cdots \otimes H_{i_M}$. Given that the entries of all $\{ H_{i_1}, H_{i_2} , \cdots , H_{i_M}\}$ (for all $i$) are classically known, we present a procedure (with three variants) in which these operators are classically diagonalized, and then this information is fed into three possible quantum procedures to obtain the block-encoding of $H$. The evolution operator $\exp(-iHt)$ is then obtained using the standard block-encoding/quantum singular value transformation framework. In the case where $\{H_i\}_{i=1}^K$ commute pairwise, our method can be trivially extended to the case with time-dependent coefficients. We provide a detailed discussion of the efficient regime of our hybrid framework and compare it with existing quantum simulation algorithms. Our algorithm can serve as a useful complement to existing quantum simulation algorithms, thereby expanding the reach of quantum computers for practically simulating physical systems. As a side contribution, we will show how the recent technique called \textit{randomized truncation to a quantum state} developed by Harrow, Lowe, and Witteveen [arXiv preprint arXiv:2510.08518, 2025] can be applied to the context of quantum simulation and particularly quantum state preparation, for which the latter can be of independent interest.

quant-ph↗

arXiv2026

Mixed-state Phases from Higher-order SSPTs with Kramers-Wannier Symmetry

Mixed-state phases have recently attracted significant attention as a generalization beyond their pure-state counterparts. Prominent examples include mixed-state symmetry-protected topological (mSPT) phases and the strong-to-weak symmetry breaking (SWSSB) phases. It has been shown recently that mSPT phases admit a holographic dual description in terms of higher-order subsystem SPT phases. In this work, we investigate the mixed-state phases obtained by tracing out the bulk degrees of freedom of higher-order subsystem SPT phases protected by non-invertible symmetries. We find that the resulting mixed states exhibit the coexistence of the symmetry-protected topological order and SWSSB. We also use the interface as a probe to characterize the mixed state phases, and specifically, when there is no local modification to preserve the symmetries across the interface, the two sides of the interface are in distinct phases.

cond-mat.str-el↗

arXiv2026

Measurement-Based Preparation of Higher-Dimensional AKLT States and Their Quantum Computational Power

We investigate a constant-time, fusion measurement-based scheme to create AKLT states beyond one dimension. We show that it is possible to prepare such states on a given graph up to random spin-1 `decorations', each corresponding to a probabilistic insertion of a vertex along an edge. In investigating their utility in measurement-based quantum computation, we demonstrate that any such randomly decorated AKLT state possesses at least the same computational power as non-random ones, such as those on trivalent planar lattices. For AKLT states on Bethe lattices and their decorated versions we show that there exists a deterministic, constant-time scheme for their preparation. In addition to randomly decorated AKLT states, we also consider random-bond AKLT states, whose construction involves any of the canonical Bell states in the bond degrees of freedom instead of just the singlet in the original construction. Such states naturally emerge upon measuring all the decorative spin-1 sites in the randomly decorated AKLT states. We show that those random-bond AKLT states on trivalent lattices can be converted to encoded random graph states after acting with the same POVM on all sites. We also argue that these random-bond AKLT states possess similar quantum computational power as the original singlet-bond AKLT states via the percolation perspective.

quant-ph↗

arXiv2025

Quantum Algorithm for Estimating Betti Numbers Using Cohomology Approach

Topological data analysis has emerged as a powerful tool for analyzing large-scale data. An abstract simplicial complex, in principle, can be built from data points, and by using tools from homology, topological features could be identified. Given a simplex, an important feature is called the Betti numbers, which roughly count the number of `holes' in different dimensions. Calculating Betti numbers exactly can be $\#$P-hard, and approximating them can be NP-hard, which rules out the possibility of any generic efficient algorithms and unconditional exponential quantum speedup. Here, we explore the specific setting of a triangulated manifold. In contrast to most known methods to estimate Betti numbers, which rely on homology, we exploit the `dual' approach, namely, cohomology, combining the insight of the Hodge theory and de Rham cohomology. Our proposed algorithm can calculate its $r$-th normalized Betti number $β_r/|S_r|$ up to some additive error $ε$ with running time $\mathcal{O}\Big(\frac{\log(|S_r^K| |S_{r+1}^K|)}{ε^2} \log (\log |S_r^K|) \big( r\log |S_r^K| \big) \Big)$, where $|S_r|$ is the number of $r$-simplexes in the given complex. For the estimation of $r$-th Betti number $β_r$ to a chosen multiplicative accuracy $ε'$, our algorithm has complexity $ \mathcal{O}\Big(\frac{\log(|S_r^K| |S_{r+1}^K|)}{ε'^2} \big( \frac{ Γ}{β_r}\big)^2 (\log |S_r^K|) \log \big( r\log |S_r^K| \big) \Big)$, where $Γ\leq |S_r^K|$ can be chosen. A detailed analysis is provided, showing that our cohomology framework can even perform exponentially faster than previous homology methods in several regimes. In particular, our method is most effective when $β_r \ll |S_r^K|$, which can offer more flexibility and practicability than existing quantum algorithms that achieve the best performance in the regime $β_r \approx |S_r^K|$.

quant-ph↗

arXiv2025

Quantum Algorithm for Estimating Ollivier-Ricci Curvature

We introduce a quantum algorithm for computing the Ollivier Ricci curvature, a discrete analogue of the Ricci curvature defined via optimal transport on graphs and general metric spaces. This curvature has seen applications ranging from signaling fragility in financial networks to serving as basic quantities in combinatorial quantum gravity. For inputs given as a point cloud with pairwise distances, we show that our algorithm can achieve an exponential speedup over the best-known classical methods for two particular classes of problem. Our work is another step toward quantum algorithms for geometrical problems that are capable of delivering practical value while also informing fundamental theory.

quant-ph↗

arXiv2025

Quantum Algorithm for Estimating Intrinsic Geometry

High-dimensional datasets typically cluster around lower-dimensional manifolds but are also often marred by severe noise, obscuring the intrinsic geometry essential for downstream learning tasks. We present a quantum algorithm for estimating the intrinsic geometry of a point cloud -- specifically its local intrinsic dimension and local scalar curvature. These quantities are crucial for dimensionality reduction, feature extraction, and anomaly detection -- tasks that are central to a wide range of data-driven and data-assisted applications. In this work, we propose a quantum algorithm which takes a dataset with pairwise geometric distance, output the estimation of local dimension and curvature at a given point. We demonstrate that this quantum algorithm achieves an exponential speedup over its classical counterpart, and, as a corollary, further extend our main technique to diffusion maps, yielding exponential improvements even over existing quantum algorithms. Our work marks another step toward efficient quantum applications in geometrical data analysis, moving beyond topological summaries toward precise geometric inference and opening a novel, scalable path to quantum-enhanced manifold learning.

quant-ph↗

arXiv2025

Dynamic-SUPERB Phase-2: A Collaboratively Expanding Benchmark for Measuring the Capabilities of Spoken Language Models with 180 Tasks

Multimodal foundation models, such as Gemini and ChatGPT, have revolutionized human-machine interactions by seamlessly integrating various forms of data. Developing a universal spoken language model that comprehends a wide range of natural language instructions is critical for bridging communication gaps and facilitating more intuitive interactions. However, the absence of a comprehensive evaluation benchmark poses a significant challenge. We present Dynamic-SUPERB Phase-2, an open and evolving benchmark for the comprehensive evaluation of instruction-based universal speech models. Building upon the first generation, this second version incorporates 125 new tasks contributed collaboratively by the global research community, expanding the benchmark to a total of 180 tasks, making it the largest benchmark for speech and audio evaluation. While the first generation of Dynamic-SUPERB was limited to classification tasks, Dynamic-SUPERB Phase-2 broadens its evaluation capabilities by introducing a wide array of novel and diverse tasks, including regression and sequence generation, across speech, music, and environmental audio. Evaluation results show that no model performed well universally. SALMONN-13B excelled in English ASR and Qwen2-Audio-7B-Instruct showed high accuracy in emotion recognition, but current models still require further innovations to handle a broader range of tasks. We open-source all task data and the evaluation pipeline at https://github.com/dynamic-superb/dynamic-superb.

cs.CL↗

arXiv2025

The robustness condition for general disordered discrete time crystals, and subspace-thermal DTCs from phase transitions between different n-tuple DTCs

We propose a new Floquet time crystal model that responds in arbitrary multiples of the driving period. Such an $n$-tuple discrete time crystal is theoretically constructed by permuting spins in a disordered chain and is well suited for experimental implementations. Transitions between these time crystals with different periods give rise to a novel phase of matter that we call subspace-thermal discrete time crystals, where states within subspaces of definite charges are fully thermalized at an early time. However, the whole system still robustly responds to the periodic driving subharmonically, with a period being the greatest common divisor of the original two periods. Existing theoretical analysis from many-body localization cannot be used to understand the rigidity of such subspace-thermal time crystal phases. To resolve this, we develop a new theoretical framework for the robustness of DTCs from the perspective of the robust $2π/n$ quasi-energy gap. Its robustness is rigorously proved if the system satisfies a certain condition where the mixing length, defined by the Hamming distance of the symmetry charges, does not exceed a global threshold. The proof applies beyond the models considered here to other existing DTCs realized by kicking disordered systems, where conventional MBL-DTCs can be regarded as a special case of the subspace-thermal DTC with the subspace dimension being one, thus offering a systematic way to construct new discrete time crystal models. We also introduce the notion of DTC-charges that allow us to probe the observables that spontaneously break the time-translation symmetry in both the regular discrete time crystals and subspace-thermal discrete time crystals. Moreover, our discrete time crystal models can be generalized to systems with higher spin magnitudes or qudits, as well as to higher spatial dimensions.

quant-ph↗