AI 中文总结
研究逻辑纠缠门在容错量子计算中的开销问题，通过幻码机制降低成本。在二元CSS超图积码中给出答案，评估相关家族在电路级噪声下的表现，结果明确了其对码设计的约束及优势，为低开销容错提供指导。
AI 中文摘要
逻辑纠缠门是容错量子计算中物理时空开销的主要来源。幻码通过物理量子比特置换和泡利框架更新来实现每个有序的块内逻辑CNOT，从而降低成本。这种机制能否与qLDPC码的低权重稳定器结构共存是低开销容错架构的核心问题。我们在二元CSS超图积（HGP）码中给出了确定性答案。在逻辑GHZ态制备和 Trotter化多体量子模拟中，对该家族在电路级噪声下进行评估。这些码保留了低权重稳定器校验，在两个基准测试中都比旋转表面码基线有具体优势。可重构中性原子阵列为此方法提供了自然环境。这些结果明确了基于置换的逻辑纠缠如何在HGP框架内约束码设计，证明了该独特家族在电路级的优势，并指导寻找具有更好渐近参数的幻qLDPC家族，以实现中性原子硬件上的低开销容错。
英文摘要
Logical entangling gates are a major source of physical spacetime overhead in fault-tolerant quantum computation. Phantom codes reduce this cost by implementing every ordered in-block logical CNOT through physical qubit permutations and Pauli-frame updates. Whether this mechanism can coexist with the low-weight stabilizer structure of qLDPC codes is a central question for low-overhead fault-tolerant architectures. We give a deterministic answer within binary CSS hypergraph product (HGP) codes. Up to natural equivalences, the simplex-repetition family is the unique HGP family satisfying the phantom condition. We then evaluate this family under circuit-level noise in logical GHZ-state preparation and Trotterized many-body quantum simulation. The codes retain low-weight stabilizer checks and yield concrete advantages over rotated surface-code baselines in both benchmarks. Reconfigurable neutral-atom arrays offer a natural setting for this approach, supporting nonlocal qLDPC operations while enabling in-block logical CNOTs without additional physical operations. Together, these results make precise how permutation-based logical entangling constrains code design within the HGP framework, demonstrate the circuit-level benefits of the unique family, and guide the search for phantom qLDPC families with better asymptotic parameters for low-overhead fault tolerance on neutral-atom hardware.
