发表机构
Yau Mathematical Sciences Center, Tsinghua University（丘成桐数学科学中心，清华大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明常数空间开销的容错量子计算可实现严格对数时间开销，通过多项式子秩横向CCZ门和递归蒸馏电路，优于此前含次多对数因子的结果。
AI 中文摘要
我们证明了常数空间开销的容错量子计算可以实现严格对数时间开销，优于已知最佳结果中额外次多对数因子的方案。我们的主要构造利用良好量子局部可测试码上的多项式子秩横向逻辑CCZ门，通过将逻辑量子比特批次在密集存储与活跃逻辑子空间之间转移，同时复用相同的辅助工作空间，实现可寻址的通用计算。逻辑CCZ门直接由横向操作实现，因此仅需单独制备稳定子资源态。此外，我们给出另一种构造，基于修改Nguyen和Pattison的量子Reed-Solomon魔法态蒸馏方案，同样实现纯对数时间开销。递归应用由块长递增的qLTC保护的固定蒸馏电路，消除了次多对数时间因子。
英文摘要
We prove that constant-space-overhead fault-tolerant quantum computation can be achieved with provably strictly logarithmic time overhead, improving over the best known results with additional subpolylogarithmic factors. Our main construction uses polynomial-subrank transversal logical $\CCZ$ gates on good quantum locally testable codes to implement addressable universal computation by transferring batches of logical qubits between dense storage and active logical subspaces while reusing the same ancillary workspace. Logical $\CCZ$ gates are implemented directly by the transversal operation, so only stabilizer resource states require separate preparation. Furthermore, we give an alternative construction that also achieves purely logarithmic time overhead based on modifying the quantum Reed--Solomon magic-state distillation scheme of Nguyen and Pattison. Recursively applying a fixed distillation circuit protected by qLTCs of increasing block length eliminates the subpolylogarithmic time factor.
