Preparing Tetra-Digit Long-Range Entangled States via Unified Sequential Quantum Circuit

• URL: http://arxiv.org/abs/2503.05374v1
• Date: Fri, 07 Mar 2025 12:32:13 GMT
• Title: Preparing Tetra-Digit Long-Range Entangled States via Unified Sequential Quantum Circuit
• Authors: Yu-Tao Hu, Meng-Yuan Li, Peng Ye,
• Abstract summary: This work introduces a framework to prepare ground states of Tetra-Digit (TD) quantum spin models.<n> TD models host spatially extended excitations with constrained mobility and deformability.<n>With experimental feasibility via synthetic dimensions in quantum simulators, this framework bridges a great variety of gapped long-range entangled states cross dimensions through quantum circuits.
• Score: 10.829837447593139
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The quest to systematically prepare long-range entangled phases has gained momentum with advances in quantum circuit design, particularly through sequential quantum circuits (SQCs) that constrain entanglement growth via locality and depth constraints. This work introduces a \textit{unified} SQC framework to prepare ground states of Tetra-Digit (TD) quantum spin models -- a class of long-range entangled stabilizer codes labeled by a four-digit index $[d_n,d_s,d_l,D]$ -- which encompass Toric Codes across dimensions and the X-cube fracton phase as special cases. Featuring a hierarchical structure of entanglement renormalization group, TD 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. We demonstrate the unified SQC through low-dimension examples first, graphically and algebraically, and then extend to general cases, with a detailed proof for the effectiveness of general SQC given in the appendix. With experimental feasibility via synthetic dimensions in quantum simulators, this framework bridges a great variety of gapped long-range entangled states cross dimensions through quantum circuits and shows plentiful mathematical and physical structures in TD models. Through unifying previously disparate preparation strategies, it offers a pathway toward engineered topological phases and fault-tolerant technologies.

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