Conventional approaches to fault-tolerant quantum computing realize logical circuits gate-by-gate, synthesizing each gate independently on one or more code blocks. This incurs excess overhead and doesn't leverage common structures in quantum algorithms. In contrast, we propose a framework that enables the execution of entire logical circuit blocks at once, preserving their global structure. This whole-block approach allows for the direct implementation of logical Trotter circuits - of arbitrary rotation angles - on any stabilizer code, providing a powerful new method for fault tolerant Hamiltonian simulation within a single code block. At the heart of our approach lies a deep structural correspondence between symplectic transvections and Trotter circuits. This connection enables both logical and physical circuits to share the Trotter structure while preserving stabilizer centralization and circuit symmetry even in the presence of non-Clifford rotations. We discuss potential approaches to fault tolerance via biased noise and code concatenation. While we illustrate the key principles using a $[[8,3,3]]$ code, our simulations show that the framework applies to Hamiltonian simulation on even good quantum LDPC codes. These results open the door to new algorithm-tailored, block-level strategies for fault tolerant circuit design, especially in quantum simulation.

翻译：传统的容错量子计算方法通过逐门实现逻辑电路，在每个或多个编码块上独立合成各个门。这种方法会产生额外的开销，且未能充分利用量子算法中的常见结构。相比之下，我们提出一个框架，能够一次性执行整个逻辑电路块，保持其全局结构。这种整体块方法允许在任何稳定子码上直接实现逻辑Trotter电路（具有任意旋转角度），为在单个编码块内进行容错哈密顿量模拟提供了一种强大的新方法。我们方法的核心在于辛平推与Trotter电路之间的深层结构对应关系。这种联系使得逻辑电路和物理电路能够共享Trotter结构，同时即使在存在非Clifford旋转的情况下也能保持稳定子中心化和电路对称性。我们讨论了通过偏置噪声和码级联实现容错的潜在途径。虽然我们使用$[[8,3,3]]$码来说明关键原理，但我们的模拟表明该框架也适用于在良好量子LDPC码上进行哈密顿量模拟。这些结果为容错电路设计，特别是在量子模拟领域，开启了新的算法定制化、块级策略的大门。