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 uses measurement based uncomputation, followed by classical feed forward conditional operations. The QAOA circuit parameters for $3$-SAT are optimized via exact classical (noise-free) simulation, using HPC resources to simulate 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 four trapped ion quantum computers: Quantinuum H1-1 (20 qubits), IonQ Harmony (11 qubits), IonQ Aria 1 (25 qubits), and IonQ Forte (30 qubits). The QAOA circuits that are executed include $n=10$ up to $p=20$, and $n=22$ for $p=1$ and $p=2$. The high round circuits use upwards of 9,000 individual 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 the number of QAOA 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（具体为$k=3$和$k=4$）提出了优化的QAOA电路结构。所提出的新型$4$-SAT QAOA电路结构采用了基于测量的反计算，随后结合经典前馈条件操作。$3$-SAT的QAOA电路参数通过精确经典（无噪声）模拟进行优化，利用HPC资源在10量子比特上模拟多达20轮。为探索当前NISQ设备的极限，我们在四台离子阱量子计算机上执行了这些优化后的QAOA电路，针对子句-变量比为4的随机$3$-SAT测试实例：Quantinuum H1-1（20量子比特）、IonQ Harmony（11量子比特）、IonQ Aria 1（25量子比特）和IonQ Forte（30量子比特）。执行的QAOA电路包括$n=10$至$p=20$，以及$n=22$对应的$p=1$和$p=2$。高轮次电路使用了超过9000个单独的量子门指令，使其成为NISQ设备上执行的最大QAOA电路之一。我们的主要发现是：当前NISQ设备在低轮次（即$p = 1,\ldots, 5$）时表现最佳，随后——因噪声预期——随着QAOA轮次进一步增加，返回的可满足性真值赋值逐渐不再优于随机选取的解。