发表机构
North Carolina State University（北卡罗来纳州立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究提出基于Monoid的AOD算子分解架构，将全局算子映射为局部算子以降低量子电路深度，补充量子纠错方法，给出其数学基础与模拟结果。
AI 中文摘要
我们提出一种算子分解架构，其可将全局算子通过数学方式映射为可独立执行的局部算子，以经典重构与采样开销为代价降低最大量子电路深度。通过将复杂量子电路置于可代数预分解的算子向量空间中，AOD（代数算子分解）在量子执行前进行代数分解，以补充量子纠错与误差缓解方法。我们的方法基于计算机科学中的幺半群（Monoid）定义：一种设计模式与数学概念，由数据类型、满足结合律的组合函数，以及组合时不改变其他值的安全恒等（中性）元素构成。在模拟方面，我们定义了一种MapReduce编程模型，其中加法（+）作为归约器，从而利用天然稳定的交换幺半群，其无“负概率损耗”或相位冲突。此外，我们定义了加法阿贝尔群上的线性算子向量空间，可受益于该范式，包括内积、级数展开、迹与卷积。最后，我们给出该范式的数学基础与模拟结果。
英文摘要
We present an operator-decomposition architecture that mathematically maps a global operator into independently executable local operators, reducing the maximum quantum circuit depth at the cost of classical reconstruction and sampling overhead. By framing complex Quantum Circuits around an operator in a vector space that can be algebraically pre-decomposed, AOD complements quantum error correction and error-mitigation approaches by performing algebraic decomposition before quantum execution. Our approach leans in the computer science definition of a Monoid: a design pattern and mathematical concept consisting of a data type, a combining function that is associative, and a safe identity (neutral) element that does not change other values when combined. Simulation wise we define a MapReduce programming model where the addition (+) is the reducer, thus leveraging a naturally stable commutative monoid which carries zero "negative-probability tax" or phase conflicts. Furthermore, we define a Vector Space of Linear Operators over Additive Abelian Groups that benefit from this paradigm, including: Inner Products, Series expansions, Traces and Convolutions. Finally, we present the mathematical foundations and simulation results for this paradigm.
Comments11 pages, 7 figures
