The Quantum Alternating Operator Ansatz (QAOA) is a hybrid classical-quantum algorithm that aims to sample the optimal solution(s) of discrete combinatorial optimization problems. We present optimized QAOA circuit constructions for sampling MAX $k$-SAT problems, specifically for $k=3$ and $k=4$. The novel $4$-SAT QAOA circuit construction we present makes use of measurement based uncomputation, followed by classical feed forward conditional operations. Parameters in the QAOA circuits are optimized via exact classical (noise-free) simulation, using HPC resources to simulate large circuits (up to 20 rounds on 10 qubits). In order to explore the limits of current NISQ devices, we execute these optimized QAOA circuits for random $3$-SAT test instances with clause-to-variable ratio $4$, on two ion-trapped quantum computers: IonQ Harmony and Quantinuum H1-1 which have 11 and 20 qubits respectively. The QAOA circuits that are executed include $n=10$ up to $20$ rounds, and $n=20$ for $1$ and $2$ rounds, the high round circuits using upwards of 8,000 gate instructions, making these some of the largest QAOA circuits executed on NISQ devices. Our main finding is that current NISQ devices perform best at low round counts (i.e., $p = 1,\ldots, 5$) and then -- as expected due to noise -- gradually start returning satisfiability truth assignments that are no better than randomly picked solutions as number of rounds are further increased.

翻译：量子交替算子Ansatz（QAOA）是一种混合经典-量子算法，旨在对离散组合优化问题的最优解进行采样。我们针对MAX $k$-SAT问题（特别是$k=3$和$k=4$）提出了优化的QAOA电路结构。我们提出的新型$4$-SAT QAOA电路结构利用了基于测量的反计算，随后进行经典前馈条件操作。QAOA电路中的参数通过精确经典（无噪声）模拟进行优化，利用高性能计算资源模拟大规模电路（在10个量子比特上运行多达20轮）。为了探索当前NISQ设备的极限，我们在两台离子阱量子计算机（分别为11和20量子比特的IonQ Harmony与Quantinuum H1-1）上，对子句-变量比为4的随机$3$-SAT测试实例执行了这些优化的QAOA电路。执行的QAOA电路包括$n=10$（多达20轮）和$n=20$（1和2轮）的实例，高轮次电路使用超过8000个门指令，使之成为NISQ设备上执行的最大规模QAOA电路之一。我们的主要发现是：当前NISQ设备在低轮次数（即$p = 1,\ldots, 5$）下表现最佳，而后——正如噪声所预期——随着轮次进一步增加，其返回的SAT真值赋值逐渐变得不优于随机选取的解。