论文标题
量子近似优化算法与稀疏相算子
Quantum Approximate Optimization Algorithm with Sparsified Phase Operator
论文作者
论文摘要
量子近似优化算法（QAOA）是一种有前途的候选算法，用于使用近期量子计算机在优化中证明量子优势。但是，由于需要在阶段分离运算符中编码目标函数，因此QAOA对GATE Fidelity有很高的要求，需要大量的门，这些门可能与硬件连接不符。使用MaxCut问题作为目标，我们从数值上证明，只要基态是相同的，就可以使用一种更简单的实现替代阶段运算符的方法来代替编码目标函数的相位操作员。我们观察到，如果未保留基态能，则QAOA获得的近似值可能会降低。此外，我们表明，替代操作员的低能子空间更好地对齐会导致更好的性能。利用这些观察结果，我们提出了一种稀疏策略，以减少QAOA的资源要求。我们还将我们的稀疏策略与其他一些经典图形稀疏方法进行了比较，并证明了我们方法的功效。
The Quantum Approximate Optimization Algorithm (QAOA) is a promising candidate algorithm for demonstrating quantum advantage in optimization using near-term quantum computers. However, QAOA has high requirements on gate fidelity due to the need to encode the objective function in the phase separating operator, requiring a large number of gates that potentially do not match the hardware connectivity. Using the MaxCut problem as the target, we demonstrate numerically that an easier way to implement an alternative phase operator can be used in lieu of the phase operator encoding the objective function, as long as the ground state is the same. We observe that if the ground state energy is not preserved, the approximation ratio obtained by QAOA with such phase separating operator is likely to decrease. Moreover, we show that a better alignment of the low energy subspace of the alternative operator leads to better performance. Leveraging these observations, we propose a sparsification strategy that reduces the resource requirements of QAOA. We also compare our sparsification strategy with some other classical graph sparsification methods, and demonstrate the efficacy of our approach.
