MarQSim：调和量子模拟编译器优化中的确定性与随机性
MarQSim: Reconciling Determinism and Randomness in Compiler Optimization for Quantum Simulation
AI总结：
MarQSim提出基于马尔可夫链和哈密顿量项转移图的编译框架，通过最小费用流模型调和确定性与随机性编译，在保证正确性的同时生成更高效的量子哈密顿量模拟电路。
摘要：
量子模拟是量子算法设计的基础，其影响远超其根基本身，驱动着多样化的量子计算应用。然而，优化量子哈密顿量模拟的编译面临重大挑战。现有方法在调和确定性与随机性编译方面存在不足，缺乏合适的中间表示，并且难以保证正确性。针对这些挑战，我们提出了MarQSim，一个新颖的编译框架。MarQSim采用基于马尔可夫链的方法，封装在哈密顿量项转移图中，巧妙地调和了确定性与随机性编译的优势。我们严格证明了其算法效率和正确性准则。此外，我们构建了一个最小费用流模型，可以调整转移矩阵以强制正确性，同时适应各种优化目标。实验结果表明，MarQSim在为模拟各种量子哈密顿量生成更高效的量子电路方面具有优越性，同时保持精度。
英文摘要：
Quantum simulation, fundamental in quantum algorithm design, extends far beyond its foundational roots, powering diverse quantum computing applications. However, optimizing the compilation of quantum Hamiltonian simulation poses significant challenges. Existing approaches fall short in reconciling deterministic and randomized compilation, lack appropriate intermediate representations, and struggle to guarantee correctness. Addressing these challenges, we present MarQSim, a novel compilation framework. MarQSim leverages a Markov chain-based approach, encapsulated in the Hamiltonian Term Transition Graph, adeptly reconciling deterministic and randomized compilation benefits. We rigorously prove its algorithmic efficiency and correctness criteria. Furthermore, we formulate a Min-Cost Flow model that can tune transition matrices to enforce correctness while accommodating various optimization objectives. Experimental results demonstrate MarQSim's superiority in generating more efficient quantum circuits for simulating various quantum Hamiltonians while maintaining precision.
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