Yu-Tao Hu | Searcharxiv

arXiv2026

Fracton Topological Holography

Topological holography (TH), or SymTFT, realizes symmetries and dualities of a quantum system as boundary data of a topological bulk in one higher dimension. We formulate fracton topological holography (FTH), extending this mechanism from liquid topological orders to fracton stabilizer codes. The construction is organized as a general four-stage framework: prepare the bulk model and compute its excitations, determine boundary data and admissible gapped top boundaries, identify the low-energy preserving operator algebra together with its symmetry, relation, and twist data, and then switch among top boundaries to compare the induced boundary descriptions. As a type-I example, we develop FTH for the X-cube model with smooth and rough top boundaries; for a minimal effective Hamiltonian, both yield transverse-field plaquette Ising models, with exchanged subsystem symmetry and twist data, and the boundary switch is implemented by a linear-depth local unitary sequential quantum circuit (SQC). As a type-II example, we formulate FTH for Haah's cubic code in the Laurent-polynomial stabilizer formalism and analyze the natural $(Z)$ and $(X)$ top boundaries, which induce two two-dimensional qubit systems related locally by exchanging generalized plaquette Ising and transverse-field terms and nonlocally by a symmetry--relation duality. These results show that FTH is a genuine extension of TH to both type-I and type-II fracton orders. FTH therefore provides a concrete framework for organizing and understanding duality, with the prospect of offering a systematic route to new dualities.

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arXiv2025

Preparing Code States via Seed-Entangler-Enriched Sequential Quantum Circuits: Application to Tetra-Digit Topological Error-Correcting Codes

Demonstrating how long-range entangled states are born from product states has gained much attention, which is not only important for quantum technology but also provides an unconventional tool in characterizing and classifying exotic phases of matter. In this paper, we introduce a unified and efficient framework of quantum circuits (i.e., a series of local unitary transformations), termed the \emph{Seed-Entangler-Enriched Sequential Quantum Circuit} (SEESQC) to construct long-range entangled states (i.e., code states) in code space of topological error-correcting codes. Specifically, we apply SEESQC to construct code states of Tetra-Digit models -- a broad class of long-range entangled stabilizer codes indexed by a four-digit parameter. These models are not rare but encompass Toric Codes across arbitrary dimensions and subsume the X-cube fracton code as special cases. Featuring a hierarchical structure of generalized entanglement renormalization group, many Tetra-Digit models host spatially extended excitations (e.g., loops, membranes, and exotic non-manifold objects) with constrained mobility and deformability, and exhibit system-size-dependent ground state degeneracies that scale exponentially with a polynomial in linear sizes. In this work, we begin with graphical and algebraic demonstration of quantum circuits for computational basis states, before generalizing to broader cases. Central to this framework is a key ingredient termed the \emph{seed-entangler} acting on a small number of qubits termed \textit{seeds}, enabling a systematic scheme to achieve arbitrary code states. Remarkably, the number of available seeds equals the number of logical qubits for the constructed examples, which leaves plenty of room for future investigation in theoretical physics, mathematics and quantum information science. Beyond the critical limitation of prior state-engineering methodologies, ...

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