论文标题
解决SAT问题的解决方案具有自适应偏置量子近似优化算法
Solution of SAT Problems with the Adaptive-Bias Quantum Approximate Optimization Algorithm
论文作者
论文摘要
量子近似优化算法（QAOA）是在近期量子设备上解决某些经典组合优化问题的有前途方法。当使用QAOA到3-SAT和MAX-3-SAT问题时，随着子句密度的变化，量子成本分别表现出易于硬的或易于硬的模式。对于当前的NISQ设备而言，硬区域问题中所需的量子资源遥不可及。我们通过数值模拟显示，最多有14个变量和分析论点表明，自适应偏置QAOA（AB-QAOA）极大地改善了3-SAT问题和最大3-SAT问题的硬区域的硬性区域的性能。为了类似的准确性，平均而言，AB-QAOA需要3个水平，即10个可验证的3-SAT问题，而QAOA则需要22个水平。对于10变量的Max-3-SAT问题，数字为7个级别和62个级别。改进来自进化过程中更具针对性，更有限制的纠缠。我们证明，在AB-QAOA中，经典优化并不是必需的，因为使用本地领域来指导进化。这使我们提出了一个无优化的AB-QAOA，与原始的AB-QAOA相比，可以有效地解决硬区域3-SAT和MAX-3-SAT问题，而量子门也明显较少。我们的工作为实现NISQ设备优化问题的量子优势铺平了道路。
The quantum approximate optimization algorithm (QAOA) is a promising method for solving certain classical combinatorial optimization problems on near-term quantum devices. When employing the QAOA to 3-SAT and Max-3-SAT problems, the quantum cost exhibits an easy-hard-easy or easy-hard pattern respectively as the clause density is changed. The quantum resources needed in the hard-region problems are out of reach for current NISQ devices. We show by numerical simulations with up to 14 variables and analytical arguments that the adaptive-bias QAOA (ab-QAOA) greatly improves performance in the hard region of the 3-SAT problems and hard region of the Max-3-SAT problems. For similar accuracy, on average, ab-QAOA needs 3 levels for 10-variable 3-SAT problems as compared to 22 for QAOA. For 10-variable Max-3-SAT problems, the numbers are 7 levels and 62 levels. The improvement comes from a more targeted and more limited generation of entanglement during the evolution. We demonstrate that classical optimization is not strictly necessary in the ab-QAOA since local fields are used to guide the evolution. This leads us to propose an optimization-free ab-QAOA that can solve the hard-region 3-SAT and Max-3-SAT problems effectively with significantly fewer quantum gates as compared to the original ab-QAOA. Our work paves the way for realizing quantum advantages for optimization problems on NISQ devices.
