发表机构
Joint Center for Quantum Information and Computer Science, University of Maryland and NIST; DIENS, École Normale Supérieure, PSL University, CNRS, INRIA; QuEra Computing Inc.; QuEra Computing UK Ltd.; Binghamton University; Cornell University（马里兰大学与国家标准技术研究院量子信息与计算机科学联合中心; 巴黎高等师范学院、PSL大学、法国国家科学研究中心、法国国家信息与自动化研究所; QuEra计算公司; QuERA计算英国有限公司; 宾厄姆顿大学; 康奈尔大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对容错量子模拟中标准编译破坏对称性的问题，提出一种精确保持SU(2)对称性的编译框架，通过测量与前馈绕过数论障碍，将误差限制在对称代数内，并在海森堡模型输运模拟中显著降低T计数，同时扩展到规范及费米子对称性。
AI 中文摘要
容错量子模拟要求将保持对称性的时间演化编译为离散门集。即使目标演化保持对称性，标准Clifford+T综合也可能破坏连续对称性，导致编译后的模拟丢失原始系统的基本特征。我们开发了一个精确保持SU(2)对称性的容错编译框架。我们刻画了阻止保持对称性的酉Clifford+T电路逼近任意SU(2)对称演化的数论障碍，并利用测量和前馈绕开该障碍。由此产生的综合将编译误差限制在保持对称性的算子代数内，而不是引入破坏对称性的微扰。我们通过模拟一维海森堡模型中的输运来演示该算法。在较低的匹配T计数下，例如每个双位点Trotter步54个T门，标准综合产生错误的输运指数，而我们的对称保持编译在相同的预期T计数下再现了预期的指数。如果相反，每种方法被分配必要的资源以相同精度估计该指数，我们的构造将T计数减少约五倍。我们进一步将该框架扩展到格点规范理论中的规范对称性，以及量子化学和Fermi-Hubbard模型相关的费米子模型中的粒子数和自旋对称性。这些结果表明，保持对称性的容错编译可以定性改变综合误差的影响，同时大幅减少量子模拟所需的资源。
英文摘要
Fault-tolerant quantum simulation requires compiling symmetry-preserving time evolutions into discrete gate sets. Standard Clifford+T synthesis can break continuous symmetries even when the target evolution preserves them, causing compiled simulations to lose essential features of the original system. We develop a fault-tolerant compilation framework that preserves SU(2) symmetry exactly. We characterize the number-theoretic obstruction preventing symmetry-preserving unitary Clifford+T circuits from approximating arbitrary SU(2)-symmetric evolutions and circumvent it using measurement and feed-forward. The resulting synthesis confines compilation errors to the symmetry-preserving operator algebra rather than introducing symmetry-breaking perturbations. We demonstrate the algorithm by simulating transport in the one-dimensional Heisenberg model. At a lower matched T-count, for instance, 54 T gates per two-site Trotter step, standard synthesis yields an incorrect transport exponent, whereas our symmetry-preserving compilation reproduces the expected exponent for the same expected T-count. If instead each approach is allocated whatever resources are necessary to estimate this exponent to the same accuracy, our construction reduces the T-count by approximately a factor of five. We further extend the framework to gauge symmetries in lattice gauge theories and to particle-number and spin symmetries in fermionic models relevant to quantum chemistry and the Fermi-Hubbard model. These results show that symmetry-preserving fault-tolerant compilation can qualitatively change the effects of synthesis error while substantially reducing the resources required for quantum simulation.
Comments24 pages, 11 figures
