论文标题
量子近似优化中的近似Boltzmann分布
Approximate Boltzmann Distributions in Quantum Approximate Optimization
论文作者
论文摘要
需要从量子近似优化算法（QAOA）计算或估计输出概率分布的方法来评估它将获得量子计算优势的可能性。我们分析了QAOA电路求解7,200个随机最大实例的输出，其中$ n = 14-23 $ Qubits和Depth参数$ P \ LEQ 12 $，并发现平均基础概率遵循近似Boltzmann分布：平均概率与最佳解决方案的平均概率高度缩放，并在最佳解决方案下进行峰值。我们用领先的订单项$ t \ sim c_ \ mathrm {min}/n \ sqrt {p} $描述了指数缩放率或“有效温度”的速率，带有$ c_ \ mathrm {min {min} $。使用此尺度，我们生成近似的输出分布，最多38个Qubits，并在我们可以精确模拟的情况下找到了重要的重要性能指标的准确说明。
Approaches to compute or estimate the output probability distributions from the quantum approximate optimization algorithm (QAOA) are needed to assess the likelihood it will obtain a quantum computational advantage. We analyze output from QAOA circuits solving 7,200 random MaxCut instances, with $n=14-23$ qubits and depth parameter $p \leq 12$, and find that the average basis state probabilities follow approximate Boltzmann distributions: The average probabilities scale exponentially with their energy (cut value), with a peak at the optimal solution. We describe the rate of exponential scaling or "effective temperature" in terms of a series with a leading order term $T \sim C_\mathrm{min}/n\sqrt{p}$, with $C_\mathrm{min}$ the optimal solution energy. Using this scaling we generate approximate output distributions with up to 38 qubits and find these give accurate accounts of important performance metrics in cases we can simulate exactly.
