arXiv subjects

Yi-Zhuang You

Publications and source records attributed to Yi-Zhuang You.

At least 19 recordsLinked to original sources

arXiv2026

A Quantitative Study of Sustained Focus in Large Language Models via Repetitive Deterministic Prediction Tasks

We investigate the performance of large language models (LLMs) on repetitive deterministic prediction tasks and study how the sequence accuracy rate (SAR) scales with output length. Each such task involves the repetition of the same operation $N$ times. Examples of such tasks include letter replacement in letter strings following a given rule, integer addition, and multiplication of string operators in many-body quantum mechanics. If the LLM performs the task by a simple repetition algorithm, the success rate would follow an exponential decay with sequence length. In contrast, our experiments on leading LLMs reveal a crossover that is sharper than exponential: $-\log\mathrm{SAR}$ grows super-linearly with $N$, and accuracy collapses around a characteristic length $N_*$, the accuracy cliff that separates reliable from unreliable generation. The hypothesis of independent per-step errors is rejected for every model and task we studied. The crossover is well described by a double-exponential accumulation law, $\mathrm{SAR}=\exp(-β_0 Nα^{N-1})$, whose crossover scale $N_*$ does not depend on the functional form chosen to fit it. To interpret this behaviour we introduce a minimal effective model in which step-correctness variables interact through dense random couplings and compete with an external field set by the prompt. Solved by direct enumeration, the model reproduces the super-linear error accumulation and the accuracy cliff qualitatively, and it assigns to each model--task pair two interpretable parameters, an intrinsic error rate and an error-accumulation factor.

cs.AI↗

arXiv2026

Quantum Process Realization of LDPC Code Dualities and Product Constructions

We realize a broad class of code transformations, including Kramers-Wannier duality, tensor product, and check product, as quantum processes consisting of ancilla initialization, local unitaries, and projective measurements. Using ZX-calculus, we formulate these code transformations diagrammatically and develop a systematic algorithm for extracting their quantum-process realizations. Central to our framework is the observation that the physical content of a classical LDPC code is captured by the operator algebra associated with its Tanner graph, and that code transformations correspond to maps between such algebras. Kramers-Wannier duality then admits a natural interpretation as gauging, while tensor and check products correspond to coupled-layer constructions in which interlayer coupling and projection implement a quotient on stacked operator algebras. Together, these results establish a unified framework connecting code transformations, quantum circuits, and mappings between distinct quantum phases of matter.

quant-ph↗

arXiv2026

Measurement-Based Quantum Diffusion Models

We introduce measurement-based quantum diffusion models that bridge classical and quantum diffusion theory through randomized weak measurements. The measurement-based approach naturally generates stochastic quantum trajectories while preserving purity at the trajectory level and inducing depolarization at the ensemble level. We address two quantum state generation problems: trajectory-level recovery of pure state ensembles and ensemble-average recovery of mixed states. For trajectory-level recovery, we establish that quantum score matching is mathematically equivalent to learning unitary generators for the reverse process. For ensemble-average recovery, we introduce local Petz recovery maps for states with finite correlation length and classical shadow reconstruction for general states, both with rigorous error bounds. Our framework establishes Petz recovery maps as quantum generalizations of reverse Fokker-Planck equations, providing a rigorous bridge between quantum recovery channels and classical stochastic reversals. This work enables new approaches to quantum state generation with potential applications in quantum information science.

quant-ph↗

arXiv2026

Symmetric Mass Generation in a Bilayer Honeycomb Lattice with $\mathrm{SU}(2)\times\mathrm{SU}(2)\times\mathrm{SU}(2)/\mathbb{Z}_2$ Symmetry

A central question beyond the Landau paradigm is the non-perturbative critical theory of the symmetric mass generation (SMG) transition, where strong interactions gap Dirac fermions in (2+1) dimensions without triggering spontaneous symmetry breaking or topological order. While previous studies have already provided evidence for direct SMG transitions in (2+1) dimensions, the fermion scaling dimension -- the key observable for distinguishing candidate critical theories -- has not been determined in a controlled unbiased way. In this Letter, using large-scale determinant quantum Monte Carlo (DQMC) simulations of a bilayer honeycomb lattice model with $\mathrm{SU}(2)\times\mathrm{SU}(2)\times\mathrm{SU}(2)/\mathbb{Z}_2$ symmetry, we establish a direct continuous transition by observing the simultaneous opening of single-particle and bosonic gaps at a critical coupling $J_c \approx 2.6$ with correlation length exponent $ν= 1.14(2)$, while an exhaustive search over all 19 symmetry-inequivalent fermion bilinear order parameters confirms the absence of any symmetry breaking. We further obtain the first controlled unbiased estimate of the fermion anomalous dimension, $η_ψ= 0.071(1)$, which deviates significantly from the large-$N$ prediction ($η_ψ\approx 0.595$) and variational Monte Carlo estimates ($η_ψ\approx 0.62$), thereby placing direct quantitative constraints on SMG criticality. By contrasting with a related $\mathrm{Spin}(5)\times\mathrm{U}(1)/\mathbb{Z}_2$ model that develops an intermediate excitonic phase, we show that pure non-Abelian symmetry plays a decisive role in stabilizing the direct SMG transition.

cond-mat.str-el↗

arXiv2026

Continuous symmetry analysis and systematic identification of candidate order parameters for interacting fermion models

Symmetry plays a central role in modern physics, from classifying quantum states to characterizing phases of matter through spontaneous symmetry breaking. In interacting fermionic systems with multiple internal degrees of freedom, however, determining the full continuous symmetry group and classifying possible order parameters remain challenging. In this work, we present a systematic framework for analyzing continuous symmetries and identifying candidate order parameters in such systems. By mapping the Hamiltonian to a Majorana representation, we obtain the generators of continuous symmetries from the Lie algebra of operators that commute with the Hamiltonian. We then identify the structure of this Lie algebra using the theory of semisimple Lie algebras. Building on representation theory, we further develop a systematic method for exhaustively enumerating candidate order parameters. By decomposing the exterior-power representations induced by the symmetry algebra on the Majorana space and incorporating discrete lattice symmetries, we classify these order parameters according to the symmetries they break. (Abridged. Please see the PDF manuscript for the complete abstract and specific model applications.)

cond-mat.str-el↗

arXiv2026

Superconductivity in doped symmetric mass generation insulator: a quantum Monte-Carlo study

Understanding unconventional superconductivity (SC) driven by strong electronic correlations is a central challenge in condensed matter physics. In this work, we employ sign-problem-free quantum Monte Carlo (QMC) simulations to systematically investigate a bilayer fermionic model featuring strong interlayer antiferromagnetic (AFM) exchange and on-site repulsive Hubbard interactions. This system serves as a prototypical model for realizing a symmetric mass generation (SMG) insulator. Our numerically exact results unambiguously demonstrate that robust superconducting pairing emerges upon doping the SMG phase. Remarkably, we find that the SC order is significantly enhanced by the repulsive Hubbard interaction. Given its potential relevance to the essential features of the high-$T_c$ superconductor $\mathrm{La}_{3}\mathrm{Ni}_{2}\mathrm{O}_{7}$ under pressure, our study establishes a new paradigm for superconductivity arising from a doped SMG parent state and provides key theoretical guidance for future experimental investigations.

cond-mat.str-el↗

arXiv2026

Machine Learning Symmetry Discovery for Integrable Hamiltonian Dynamics

We propose a data-driven Machine-Learning Symmetry Discovery (MLSD) framework for identifying continuous symmetry generators and their Lie-algebraic structure directly from phase-space trajectory data expressed in canonical coordinates. MLSD parameterizes candidate conserved quantities with neural networks and learns antisymmetric structure coefficients by enforcing Poisson-bracket closure, supplemented by a weak independence regularizer. We validate MLSD on two integrable benchmark systems -- the three-dimensional Kepler problem and the three-dimensional isotropic harmonic oscillator -- recovering the expected non-Abelian algebras (respectively $\mathfrak{so}(4)$ and $\mathfrak{su}(3)$) up to basis transformations. This work focuses on integrable benchmark dynamics, where global conserved quantities are well-defined and admit compact representations learnable from canonical-coordinate trajectories. Extending symmetry discovery to mixed or chaotic phase-space regimes is an important direction for future work.

cond-mat.dis-nn↗

arXiv2025

Sequential learning on a Tensor Network Born machine with Trainable Token Embedding

Generative models aim to learn the probability distributions underlying data, enabling the generation of new, realistic samples. Quantum inspired generative models, such as Born machines based on the matrix product state framework, have demonstrated remarkable capabilities in unsupervised learning tasks. This study advances the Born machine paradigm by introducing trainable token embeddings through positive operator valued measurements, replacing the traditional approach of static tensor indices. Key technical innovations include encoding tokens as quantum measurement operators with trainable parameters and leveraging QR decomposition to adjust the physical dimensions of the MPS. This approach maximizes the utilization of operator space and enhances the model's expressiveness. Empirical results on RNA data demonstrate that the proposed method significantly reduces negative log likelihood compared to one hot embeddings, with higher physical dimensions further enhancing single site probabilities and multi site correlations. The model also outperforms GPT2 in single site estimation and achieves competitive correlation modeling, showcasing the potential of trainable POVM embeddings for complex data correlations in quantum inspired sequence modeling.

cs.LG↗

arXiv2025

Application of deep neural networks for computing the renormalization group flow of the two-dimensional phi^4 field theory

We introduce RGFlow, a deep neural network-based real-space renormalization group (RG) framework tailored for continuum scalar field theories. Leveraging generative capabilities of flow-based neural networks, RGFlow autonomously learns real-space RG transformations from data without prior knowledge of the underlying model. In contrast to conventional approaches, RGFlow is bijective (information-preserving) and is optimized based on the principle of minimal mutual information. We demonstrate the method on two examples. The first one is a one-dimensional Gaussian model, where RGFlow is shown to learn the classical decimation rule. The second is the two-dimensional phi^4 theory, where the network successfully identifies a Wilson-Fisher-like critical point and provides an estimate of the correlation-length critical exponent.

cond-mat.dis-nn↗

arXiv2025

Designing Shadow Tomography Protocols by Natural Language Processing

Quantum circuits form a foundational framework in quantum science, enabling the description, analysis, and implementation of quantum computations. However, designing efficient circuits, typically constructed from single- and two-qubit gates, remains a major challenge for specific computational tasks. In this work, we introduce a novel artificial intelligence-driven protocol for quantum circuit design, benchmarked using shadow tomography for efficient quantum state readout. Inspired by techniques from natural language processing (NLP), our approach first selects a compact gate dictionary by optimizing the entangling power of two-qubit gates. We identify the iSWAP gate as a key element that significantly enhances sample efficiency, resulting in a minimal gate set of {I, SWAP, iSWAP}. Building on this, we implement a recurrent neural network trained via reinforcement learning to generate high-performing quantum circuits. The trained model demonstrates strong generalization ability, discovering efficient circuit architectures with low sample complexity beyond the training set. Our NLP-inspired framework offers broad potential for quantum computation, including extracting properties of logical qubits in quantum error correction.

quant-ph↗

arXiv2025

Quantum Many-Body Lattice C-R-T Symmetry: Fractionalization, Anomaly, and Symmetric Mass Generation

Charge conjugation (C), mirror reflection (R), and time reversal (T) symmetries, along with internal symmetries, are essential for massless Majorana and Dirac fermions. These symmetries are sufficient to rule out potential fermion bilinear mass terms, thereby establishing a gapless free fermion fixed point phase, pivotal for symmetric mass generation (SMG) transition. In this work, we systematically study the anomaly of C-R-T-internal symmetry in all spacetime dimensions by analyzing the projective representation (i.e. the fractionalization) of the C-R-T-internal symmetry group in the quantum many-body Hilbert space on the lattice. By discovering the fermion-flavor-number-dependent C-R-T-internal symmetry's anomaly structure, we demonstrate an alternative way to derive the minimal flavor number for SMG, which shows consistency with known results from Kähler-Dirac fermion or cobordism classification. Our findings reveal that, in general spatial dimensions, either 8 copies of staggered Majorana fermions or 4 copies of staggered Dirac fermions admit SMG. By directly searching for 4-fermion interactions that form commuting stabilizers respecting all symmetry constraints, we can prove the explicit SMG gapping retained a unique ground state in the codespace. Furthermore, we establish the correspondence between the symmetry operators of staggered fermions and free fermions, which is instrumental in facilitating the analysis of symmetry fractionalization at the field theory level.

cond-mat.str-el↗

arXiv2025

Machine learning the effects of many quantum measurements

Measurements are essential for the processing and protection of information in quantum computers. They can also induce long-range entanglement between unmeasured qubits. However, when post-measurement states depend on many non-deterministic measurement outcomes, there is a barrier to observing and using the entanglement induced by prior measurements. Here we demonstrate a new approach for detecting such measurement-induced entanglement. We create short-range entangled states of one- and two-dimensional arrays of qubits in a superconducting quantum processor, and aim to characterize the long-range entanglement induced between distant pairs of qubits when we measure all of the others. To do this we use unsupervised training of neural networks on observations to create computational models for post-measurement states and, by correlating these models with experimental data, we reveal measurement-induced entanglement. Our results additionally demonstrate a transition in the ability of a classical agent to accurately model the experimental data; this is closely related to a measurement-induced phase transition. We anticipate that our work can act as a basis for future experiments on quantum error correction and more general problems in quantum control.

quant-ph↗

arXiv2025

C-R-T Fractionalization in the First Quantized Hamiltonian Theory

Recent research has revealed that the CRT symmetry for fermions exhibits a fractionalization distinct from the $\mathbb{Z}_2^{\mathcal{C}}\times\mathbb{Z}_2^{\mathcal{R}}\times\mathbb{Z}_2^{\mathcal{T}}$ for scalar bosons. In fact, the CRT symmetry for fermions can be extended by internal symmetries such as fermion parity, thereby forming a group extension of the $\mathbb{Z}_2$ direct product. Conventionally, a Majorana fermion is defined by one Dirac fermion with trivial charge conjugation. However, when the spacetime dimension $d+1=5,6,7\bmod8$, the real dimension of Majorana fermion (dim$_{\mathbb{R}}χ_{\mathcal{C}\ell(d,0)}$) aligns with the real dimension of Dirac fermion (dim$_{\mathbb{R}}ψ_{\mathcal{C}\ell(d)}$), rather than being half, which necessitates the introduction of a symplectic Majorana fermion, defined by two Dirac fermions with trivial charge conjugation. To include these two types of Majorana fermions, we embed the theory in $n_{\mathbb{R}}$ and define the Majorana fermion field as a representation of the real Clifford algebra with 8-fold periodicity. Within the Hamiltonian formalism, we identify the 8-fold CRT-internal symmetry groups across general dimensions. Similarly, Dirac fermion field is defined as a representation of the complex Clifford algebra with 2-fold periodicity. Interestingly, we discover that the CRT-internal symmetry groups exhibit an 8-fold periodicity that is distinct from that of the complex Clifford algebra. In certain dimensions where distinct mass terms can span a mass manifold, the CRT-internal symmetries can act non-trivially upon this mass manifold. Employing domain wall reduction method, we are able to elucidate the relationships between symmetries across different dimensions.

cond-mat.str-el↗

arXiv2025

Dual-unitary shadow tomography

We introduce ``dual-unitary shadow tomography'' (DUST), a classical shadow tomography protocol based on dual-unitary brick-wall circuits. To quantify the performance of DUST, we study operator spreading and Pauli weight dynamics in one-dimensional qubit systems, evolved by random two-local dual-unitary gates arranged in a brick-wall structure, ending with a measurement layer. We do this by deriving general constraints on the Pauli weight transfer matrix and specializing to the case of dual-unitarity. Remarkably, we find that operator spreading in these circuits have a rich structure resembling that of relativistic quantum field theories, with massless chiral excitations that can decay or fuse into each other, which we call left- or right-movers. We develop a mean-field description of the Pauli weight in terms of $ρ(x,t)$, which represents the probability of having nontrivial support at site $x$ and depth $t$ starting from a fixed weight distribution. We develop an equation of state for $ρ(x,t)$ and simulate it numerically using Monte Carlo simulations. For the task of predicting operators with (nearly) full support, we show that DUST outperforms brick-wall Clifford shadows of equal depth. This advantage is further pronounced for small system sizes and our results are generally robust to finite-size effects.

quant-ph↗

arXiv2025

Strange correlator and string order parameter for non-invertible symmetry protected topological phases in 1+1d

In this paper, we construct strange correlators and string order parameters for non-invertible symmetry protected topological phases (NISPTs) in 1+1d quantum lattice spin models. The strange correlator exhibits long-range order when evaluated between two distinct NISPTs and decays exponentially otherwise. We show that strange charged operators inserted into the strange correlator are linked to the interface algebra (boundary tube algebra) and are non-trivial when all its irreducible representations have dimensions greater than one. We discuss the generalization to higher dimensions. The string order parameter is obtained by contracting the truncated symmetry operator with charge decoration operators, which are determined by the NISPT action tensors. We illustrate the above construction using the three NISPTs of $\text{Rep}(D_8)$ and demonstrate the extraction of categorical data via tensor networks, particularly through the ZX calculus. Finally, we show that the entanglement spectrum degeneracy is determined by the irreducible representations of the interface algebra when assuming non-invertible symmetry on-site condition.

cond-mat.str-el↗

arXiv2025

Deconfined criticality as intrinsically gapless topological state in one dimension

Deconfined criticality and gapless topological states have recently attracted growing attention, as both phenomena go beyond the traditional Landau paradigm. However, the deep connection between these two critical states, particularly in lattice realization, remains insufficiently explored. In this Letter, we reveal that certain deconfined criticality can be regarded as an intrinsically gapless topological state without gapped counterparts in a one dimensional lattice model. Using a combination of field-theoretic arguments and large-scale numerical simulations, we establish the global phase diagram of the model, which features deconfined critical lines separating two distinct spontaneous symmetry breaking ordered phases. More importantly, we unambiguously demonstrate that the mixed anomaly inherent to deconfined criticality enforces topologically robust edge modes near the boundary, providing a general mechanism by which deconfined criticality manifests as a gapless topological state. Our findings not only offer a new perspective on deconfined criticality but also deepen our understanding of gapless topological phases of matter.

cond-mat.str-el↗

arXiv2025

Topological Responses of the Standard Model Gauge Group

The local Lie algebra of the Standard Model (SM) is $su(3)\times su(2) \times u(1)$, yet its global gauge group, $G_{{\rm SM}_{\rm q}}=$SU(3)$\times$SU(2)$\times$U(1)/$\mathbb{Z}_{\rm q}$, q$=1,2,3,6$ remains undetermined. Building on previous work on 4d anomalies and 5d cobordism invariants, we classify lower-dimensional invertible field theories (iFTs) or symmetry-protected topological states (SPTs) in 4d, 3d, 2d, and 1d. While the integer SPTs are hard to detect, the fractional SPTs produce measurable topological responses. In particular, the symmetry fractionalization labeled by $k\in\mathbb{Z}_{6/{\rm q}}$ in [arXiv:2411.18160] introduces the symmetry-enriched SM variants, denoted as SM$_{({\rm q},k)}$. We further introduce a new integer $n$ series of baryon-minus-lepton $({\bf B}-{\bf L})$-like U(1) symmetries, $X_n \equiv n (\mathbf{B}-\mathbf{L}) + (1-\frac{n}{N_c})\tilde{Y}$ with electroweak hypercharge $\tilde{Y}$, $n\ge1$, $N_c=3$, where the charge $q_{X_n} = q_{\tilde{Y}} \mod n$. Analyzing the symmetry-enriched SM with 0-form and 1-form symmetries $(G_{[0]}, G_{[1]})$, symmetry-twist group homomorphism $ρ$, and symmetry frationalization obstruction $[β]$, their spacetime-internal gauge bundle constraints, and their mixed anomalies, we derive the fractional topological response $σ_n({\rm q},k)=\frac{{\rm q}(1-n)\gcd(2,n)}{2n}+\frac{k{\rm q}}{6}\mod1.$ Our $σ_n$ response requires more general Spin$^c$ manifolds for odd $n$ and Spin manifolds for even $n$. For a given $n$ (with $n\ge 7$ and $n\ne 10,12,15,30$), $σ_n$ uniquely fixes the gauge group parameter q and fractionalization label $k$. Moreover, using pairs such as $(n_1,n_2)=(2,3),(2,5),(3,4),(3,5),(4,5)$, etc. uniquely distinguishes SM$_{({\rm q},k)}$. Our results illuminate the global structure of the SM gauge group via measurable topological responses.

hep-th↗

arXiv2025

Monte Carlo Simulation of Operator Dynamics and Entanglement in Dual-Unitary Circuits

We investigate operator dynamics and entanglement growth in dual-unitary circuits, a class of locally scrambled quantum systems that enables efficient simulation beyond the exponential complexity of the Hilbert space. By mapping the operator evolution to a classical Markov process,we perform Monte Carlo simulations to access the time evolution of local operator density and entanglement with polynomial computational cost. Our results reveal that the operator density converges exponentially to a steady-state value, with analytical bounds that match our simulations. Additionally, we observe a volume-law scaling of operator entanglement across different subregions,and identify a critical transition from maximal to sub-maximal entanglement growth, governed by the circuit's gate parameter. This transition, confirmed by both mean-field theory and Monte Carlo simulations, provides new insights into operator entanglement dynamics in quantum many-body systems. Our work offers a scalable computational framework for studying long-time operator evolution and entanglement, paving the way for deeper exploration of quantum information dynamics.

quant-ph↗