arXiv subjects

Yabo Li

Publications and source records attributed to Yabo Li.

18 recordsLinked to original sources

arXiv2026

State preparation via measurement and feedback: pushing relations, state structures, and non-invertible symmetries

Quantum circuits with measurements and unitary feedback (MF) can prepare long-range entangled states in constant depth, but a systematic construction of the MF preparation circuit for a given target state remains underexplored. We develop such a scheme for one-dimensional states, based on the notion of pushable defects: virtual-bond operators of a matrix product state that can be pushed through the tensor at the price of a physical feedback unitary. We show that the set of pushable defects, together with their pushing relations classifies finite-depth MF-preparable states and dictates their preparation circuits. To each class of the target state $|A\rangle$, we associate a state $|B\rangle$ from which $|A\rangle$ can be prepared using a 1-round MF circuit; in particular, $|A\rangle$ is preparable from a product state using a circuit with 1 round of MF whenever $|B\rangle$ is preparable by a finite-depth local unitary (FDLU) circuit. For a general target state, the scheme is obtained by iterating this procedure until the associated state is FDLU-preparable. For open-boundary matrix product states, the scheme is complete: it constructs a preparation circuit whenever finite-depth MF preparation with left-conditioned feedback corrections is possible. Pushable defects and pushing relations thus emerge as a unifying principle for quantum state preparation via measurements and feedback. This characterization further reveals an intrinsic connection between MF circuits and non-invertible symmetries: states with certain classes of pushing relations are related to a product state by Tambara-Yamagami duality operators, or by continuous cosine symmetry operators with fusion rules $L_{\alpha} L_{\alpha'} = L_{\alpha+\alpha'} + L_{\alpha-\alpha'}$, together with their generalizations up to (not necessarily transversal) gates.

quant-ph↗

arXiv2026

Anyon Permutations in Quantum Double Models through Constant-depth Circuits

We provide explicit constant-depth local unitary circuits that realize general anyon permutations in Kitaev's quantum double models. This construction can be naturally understood through a correspondence between anyon permutation symmetries of two-dimensional topological orders and self-dualities in one-dimensional systems, where local gates implement self-duality transformations on the boundaries of microscopic regions. From this holographic perspective, general anyon permutations in the $D(G)$ quantum double correspond to compositions of three classes of one-dimensional self-dualities, including gauging of certain subgroups of $G$, stacking with $G$ symmetry-protected topological phases, and outer automorphisms of the group $G$. We construct circuits realizing the first class by employing self-dual unitary gauging maps, and present transversal circuits for the latter two classes.

quant-ph↗

arXiv2026

Average Categorical Symmetries in One-Dimensional Disordered Systems

We study one-dimensional disordered systems with average non-invertible symmetries, where quenched disorder may locally break part of the symmetry while preserving it upon disorder averaging. A canonical example is the random transverse-field Ising model, which at criticality exhibits an average Kramers-Wannier duality. We consider the general setting in which the full symmetry is described by a $G$-graded fusion category $\mathcal{B}$, whose identity component $\mathcal{A}$ remains exact, while the components with nontrivial $G$-grading are realized either exactly or only on average. We develop a topological holographic framework that encodes the symmetry data of the 1D system in a 2D topological order $\mathcal{Z}[\mathcal{A}]$ (the Drinfeld center of $\mathcal{A}$), enriched by an exact or, respectively, average $G$ symmetry. Within this framework, we obtain a complete classification of anomalies and average symmetry-protected topological (SPT) phases: when the components with nontrivial $G$-grading are realized only on average, the symmetry is anomaly-free if and only if $\mathcal{Z}[\mathcal{A}]$ admits a magnetic Lagrangian algebra that is invariant under the permutation action of $G$ on anyons. When an anomaly is present, we show that the ground state of a single disorder realization is long-range entangled with probability one in the thermodynamic limit, and is expected to exhibit power-law Griffiths singularities in the low-energy spectrum. Finally, we present an explicit, exactly solvable lattice model based on a symmetry-enriched string-net construction. It yields trivial ground state ensemble in the anomaly-free case, and exhibits exotic low-energy behavior in the presence of an average anomaly.

cond-mat.dis-nn↗

arXiv2025

Classification of Thouless pumps with non-invertible symmetries and implications for Floquet phases

We study symmetry preserving adiabatic and Floquet dynamics of one-dimensional systems. Using quasiadiabatic evolution, we establish a correspondence between adiabatic cycles and invertible defects generated by spatially truncated Thouless pump operators. Employing the classification of gapped phases by module categories, we show that the Thouless pumps are classified by the group of autoequivalences of the module category. We then explicitly construct Thouless pump operators for minimal lattice models with $\text{Vec}_G$, Rep($G$), and Rep($H$) symmetries, and show how the Thouless pump operators have the group structure of autoequivalences. The Thouless pump operators, together with Hamiltonians with gapped ground states, are then used to construct Floquet drives. An analytic solution for the Floquet phase diagram characterized by winding numbers is constructed when the Floquet drives obey an Onsager algebra. Our approach points the way to a general connection between distinct Thouless pumps and distinct families of Floquet phases.

cond-mat.str-el↗

arXiv2025

Non-invertible symmetries out of equilibrium: Eigenstate order and Floquet physics

Through the study of the Rep($D_8$) non-invertible symmetry, we show how non-invertible symmetries manifest in dynamics. Results are presented for dynamics generated by Hamiltonians as well as Floquet unitaries. For both examples, the role of the non-invertible symmetry is studied through the appearance of non-invertible symmetry protected edge modes. In addition, the role of the non-invertible symmetry for the Hamiltonian is studied through eigenstate order. In particular, by considering the effect of symmetry preserving disorder, the non-invertible symmetry is shown to give rise to degeneracies in the spectra of the Hamiltonian that can only be completely lifted at orders of perturbation that scale with system size. The eigenstates of disordered Hamiltonians, whose ground states correspond to non-trivial symmetry protected topological (SPT) states, are shown to have either trivial or non-trivial SPT order that are detected as non-zero expectation value of string order-parameters. In contrast, non-trivial SPT order is absent in the eigenstates of trivial SPT Hamiltonians with disorder. The interface between two different SPT phases host edge modes whose dynamics is studied numerically and analytically. The edge mode is shown to oscillate at frequencies related to different effective chain lengths that are weighted by the temperature, becoming an exact zero mode in the limit of zero temperature. A Floquet model with the non-invertible symmetry is constructed whose edge mode is shown to exhibit period-doubled dynamics at low effective-temperatures. The zero and period-doubled edge modes differ from those in conventional SPTs by being symmetric under the invertible symmetry, while being charged under the non-invertible symmetry.

cond-mat.str-el↗

arXiv2025

Non-Clifford gates between stabilizer codes via non-Abelian topological order

We propose protocols to implement non-Clifford logical gates between stabilizer codes by entangling into a non-Abelian topological order as an intermediate step. Generalizing previous approaches, we provide a framework that generates a large class of non-Clifford and non-diagonal logical gates between qudit surface codes by gauging the topological symmetry of symmetry-enriched topological orders. As our main example, we concretely detail a protocol that utilizes the quantum double of $S_3$ to generate a controlled-charge conjugation ($C\mathcal{C}$) gate between a qubit and qutrit surface code. Both the preparation of non-Abelian states and logical state injection between the Abelian and non-Abelian codes are executed via finite-depth quantum circuits with measurement and feedforward. We discuss aspects of the fault-tolerance of our protocol, presenting insights on how to construct a heralded decoder for the quantum double of $S_3.$ We also outline how analogous protocols can be used to obtain logical gates between qudit surface codes by entangling into $\mathcal{D}(G),$ where $G$ is a semidirect product of Abelian groups. This work serves as a step towards classifying the computational power of non-Abelian quantum phases beyond the paradigm of anyon braiding on near-term quantum devices.

quant-ph↗

arXiv2025

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↗

arXiv2025

Robustness via Referencing: Defending against Prompt Injection Attacks by Referencing the Executed Instruction

Large language models (LLMs) have demonstrated impressive performance and have come to dominate the field of natural language processing (NLP) across various tasks. However, due to their strong instruction-following capabilities and inability to distinguish between instructions and data content, LLMs are vulnerable to prompt injection attacks. These attacks manipulate LLMs into deviating from the original input instructions and executing maliciously injected instructions within data content, such as web documents retrieved from search engines. Existing defense methods, including prompt-engineering and fine-tuning approaches, typically instruct models to follow the original input instructions while suppressing their tendencies to execute injected instructions. However, our experiments reveal that suppressing instruction-following tendencies is challenging. Through analyzing failure cases, we observe that although LLMs tend to respond to any recognized instructions, they are aware of which specific instructions they are executing and can correctly reference them within the original prompt. Motivated by these findings, we propose a novel defense method that leverages, rather than suppresses, the instruction-following abilities of LLMs. Our approach prompts LLMs to generate responses that include both answers and their corresponding instruction references. Based on these references, we filter out answers not associated with the original input instructions. Comprehensive experiments demonstrate that our method outperforms prompt-engineering baselines and achieves performance comparable to fine-tuning methods, reducing the attack success rate (ASR) to 0 percent in some scenarios. Moreover, our approach has minimal impact on overall utility.

cs.CR↗

arXiv2024

Quantum Cellular Automata on Symmetric Subalgebras

We investigate quantum cellular automata (QCA) on one-dimensional spin systems defined over a subalgebra of the full local operator algebra - the symmetric subalgebra under a finite Abelian group symmetry $G$. For systems where each site carries a regular representation of $G$, we establish a complete classification of such subalgebra QCAs based on two topological invariants: (1) a surjective homomorphism from the group of subalgebra QCAs to the group of anyon permutation symmetries in a $(2+1)d$ $G$ gauge theory; and (2) a generalization of the Gross-Nesme-Vogts-Werner (GNVW) index that characterizes the flow of the symmetric subalgebra. Specifically, two subalgebra QCAs correspond to the same anyon permutation and share the same index if and only if they differ by a finite-depth unitary circuit composed of $G$-symmetric local gates. We also identify a set of operations that generate all subalgebra QCAs through finite compositions. As an example, we examine the Kramers-Wannier duality on a $\mathbb{Z}_2$ symmetric subalgebra, demonstrating that it maps to the $e$-$m$ permutation in the two-dimensional toric code and has an irrational index of $\sqrt{2}$. Therefore, it cannot be extended to a QCA over the full local operator algebra and mixes nontrivially with lattice translations.

quant-ph↗

arXiv2024

Domain walls from SPT-sewing

We introduce a systematic method for constructing gapped domain walls of topologically ordered systems by gauging a lower-dimensional symmetry-protected topological (SPT) order. Based on our construction, we propose a correspondence between 1d SPT phases with a non-invertible $G\times \text{Rep}(G)\times G$ symmetry and invertible domain walls in the quantum double associated with the group $G$. We prove this correspondence when $G$ is Abelian and provide evidence for the general case by studying the quantum double model for $G=S_3$. We also use our method to construct \emph{anchoring domain walls}, which are novel exotic domain walls in the 3d toric code that transform point-like excitations to semi-loop-like excitations anchored on these domain walls.

quant-ph↗

arXiv2024

Non-onsite symmetry breaking: topological phase coexistence and criticality

We explore the states of matter arising from the spontaneous symmetry breaking (SSB) of $\mathbb{Z}_2$ non-onsite symmetries. In one spatial dimension, we construct a frustration-free lattice model exhibiting SSB of a non-onsite symmetry, which features the coexistence of two ground states with distinct symmetry-protected topological (SPT) orders. We analytically prove the two-fold ground-state degeneracy and the existence of a finite energy gap. Fixing the symmetry sector yields a long-range entangled ground state that features long-range correlations among non-invertible charged operators. We also present a constant-depth measurement-feedback protocol to prepare such a state with a constant success probability in the thermodynamic limit, which may be of independent interest. Under a symmetric deformation, the SSB persists up to a critical point, beyond which a gapless phase characterized by a conformal field theory emerges. In two spatial dimensions, the SSB of 1-form non-onsite symmetries leads to a long-range entangled state (SPT soup) - a condensate of 1d SPT along any closed loops. On a torus, there are four such locally indistinguishable states that exhibit algebraic correlations between local operators, which we derived via a mapping to the critical $O(2)$ loop model. This constitutes an intriguing example of `topological quantum criticality'.

cond-mat.str-el↗

arXiv2024

SNN-PAR: Energy Efficient Pedestrian Attribute Recognition via Spiking Neural Networks

Artificial neural network based Pedestrian Attribute Recognition (PAR) has been widely studied in recent years, despite many progresses, however, the energy consumption is still high. To address this issue, in this paper, we propose a Spiking Neural Network (SNN) based framework for energy-efficient attribute recognition. Specifically, we first adopt a spiking tokenizer module to transform the given pedestrian image into spiking feature representations. Then, the output will be fed into the spiking Transformer backbone networks for energy-efficient feature extraction. We feed the enhanced spiking features into a set of feed-forward networks for pedestrian attribute recognition. In addition to the widely used binary cross-entropy loss function, we also exploit knowledge distillation from the artificial neural network to the spiking Transformer network for more accurate attribute recognition. Extensive experiments on three widely used PAR benchmark datasets fully validated the effectiveness of our proposed SNN-PAR framework. The source code of this paper is released on \url{https://github.com/Event-AHU/OpenPAR}.

cs.CV↗

arXiv2024

Non-invertible SPT, gauging and symmetry fractionalization

We explicitly realize the Rep($Q_8$) non-invertible symmetry-protected topological (SPT) state as a 1+1d cluster state on a tensor product Hilbert space of qubits. Using the Kramers-Wannier operator, we construct the lattice models for the phases of all the symmetries in the Rep($Q_8$) duality web. We further show that we can construct a class of lattice models with Rep($G$) symmetry including non-invertible SPT phases if they have a dual anomalous abelian symmetry. Upon dualizing, there is a rich interplay between onsite symmetries, non-onsite symmetries, non-abelian symmetries, and non-invertible symmetries. We show that these interplay can be explained using the symmetry fractionalization in the 2+1d bulk SET.

cond-mat.str-el↗

arXiv2024

Kennedy-Tasaki transformation and non-invertible symmetry in lattice models beyond one dimension

We give an explicit operator representation (via a sequential circuit and projection to symmetry subspaces) of Kramers-Wannier duality transformation in higher-dimensional subsystem symmetric models generalizing the construction in the 1D transverse-field Ising model. Using the Kramers-Wannier duality operator, we also construct the Kennedy-Tasaki transformation that maps subsystem symmetry-protected topological phases to spontaneous subsystem symmetry breaking phases, where the symmetry group for the former is either $\mathbb{Z}_2\times\mathbb{Z}_2$ or $\mathbb{Z}_2$. This generalizes the recently proposed picture of one-dimensional Kennedy-Tasaki transformation as a composition of manipulations involving gauging and stacking symmetry-protected topological phases to higher dimensions.

cond-mat.str-el↗

arXiv2023

Measuring Topological Field Theories: Lattice Models and Field-Theoretic Description

Recent years have witnessed a surge of interest in performing measurements within topological phases of matter, e.g., symmetry-protected topological (SPT) phases and topological orders. Notably, measurements of certain SPT states have been known to be related to Kramers-Wannier duality and Jordan-Wigner transformations, giving rise to long-range entangled states and invertible phases, such as the Kitaev chain. Moreover, measurements of topologically ordered states correspond to charge condensations. In this work, we present a field-theoretic framework for describing measurements within topological field theories. We employ various lattice models as examples to illustrate the outcomes of measuring local symmetry operators within topological phases, demonstrating their agreement with the predictions from field-theoretic descriptions. We demonstrate that these measurements can lead to SPT, spontaneous symmetry-breaking, and topologically ordered phases. Specifically, when there is emergent symmetry after measurement, the remaining symmetry and emergent symmetry will have a mixed anomaly, which leads to long-ranged entanglement.

cond-mat.str-el↗

arXiv2023

Symmetry-enriched topological order from partially gauging symmetry-protected topologically ordered states assisted by measurements

Symmetry protected topological phases exhibit nontrivial short-ranged entanglement protected by symmetry and cannot be adiabatically connected to trivial product states while preserving the symmetry. In contrast, intrinsic topological phases do not need ordinary symmetry to stabilize them and their ground states exhibit long-range entanglement. It is known that for a given symmetry group $G$, the 2D SPT phase protected by $G$ is dual to the 2D topological phase exemplified by the twisted quantum double model $D^{\omega}(G)$ via gauging the global symmetry $G$. Recently it was realized that such a general gauging map can be implemented by some local unitaries and local measurements when $G$ is a finite, solvable group. Here, we review the general approach to gauging a $G$-SPT starting from a fixed-point ground-state wave function and applying a $N$-step gauging procedure. We provide an in-depth analysis of the intermediate states emerging during the N-step gauging and provide tools to measure and identify the emerging symmetry-enriched topological order of these states. We construct the generic lattice parent Hamiltonians for these intermediate states, and show that they form an entangled superposition of a twisted quantum double with an SPT ordered state. Notably, we show that they can be connected to the TQD through a finite-depth, local quantum circuit which does not respect the global symmetry of the SET order. We introduce the so-called symmetry branch line operators and show that they can be used to extract the symmetry fractionalization classes and symmetry defectification classes of the SET phases with the input data $G$ and $[\omega]\in H^3(G,U(1))$ of the pre-gauged SPT ordered state. We illustrate the procedure of preparing and characterizing the emerging SET ordered states for some Abelian and non-Abelian examples such as dihedral groups $D_n$ and the quaternion group $Q_8$.

quant-ph↗

arXiv2022

Two-particle States in One-dimensional Coupled Bose-Hubbard Models

We study dynamically coupled one-dimensional Bose-Hubbard models and solve for the wave functions and energies of two-particle eigenstates. Even though the wave functions do not directly follow the form of a Bethe Ansatz, we describe an intuitive construction to express them as combinations of Choy-Haldane states for models with intra- and inter-species interaction. We find that the two-particle spectrum of the system with generic interactions comprises in general four different continua and three doublon dispersions. The existence of doublons depends on the coupling strength $Ω$ between two species of bosons, and their energies vary with $Ω$ and interaction strengths. We give details on one specific limit, i.e., with infinite interaction, and derive the spectrum for all types of two-particle states and their spatial and entanglement properties. We demonstrate the difference in time evolution under different coupling strengths, and examine the relation between the long-time behavior of the system and the doublon dispersion. These dynamics can in principle be observed in cold atoms and might also be simulated by digital quantum computers.

quant-ph↗

arXiv2017

Coulomb Branch for A-type Balanced Quivers in 3d $\mathcal{N}=4$ gauge theories

We study Coulomb branch moduli spaces of a class of three dimensional $\mathcal{N}=4$ gauge theories whose quiver satisfies the balance condition. The Coulomb branch is described by dressed monopole operators which can be counted using the Monopole formula. We mainly focus on A-type quivers in this paper, using Hilbert Series to study their moduli spaces, and present the interesting pattern which emerges. All of these balanced A-type quiver gauge theories can be realized on brane intervals in Type IIB string theory, where mirror symmetry acts by exchanging the five branes and induces an equivalence between Coulomb branch and Higgs branch of mirror pairs. For each theory, we explicitly discuss the gauge invariant generators on the Higgs branch and the relations they satisfy. Finally, some analysis on $D_4$ balanced quivers also presents an interesting structure of their moduli spaces.

hep-th↗