Quantum annealing (QA) and Quantum Alternating Operator Ansatz (QAOA) are both heuristic quantum algorithms intended for sampling optimal solutions of combinatorial optimization problems. In this article we implement a rigorous direct comparison between QA on D-Wave hardware and QAOA on IBMQ hardware. These two quantum algorithms are also compared against classical simulated annealing. The studied problems are instances of a class of Ising models, with variable assignments of $+1$ or $-1$, that contain cubic $ZZZ$ interactions (higher order terms) and match both the native connectivity of the Pegasus topology D-Wave chips and the heavy hexagonal lattice of the IBMQ chips. The novel QAOA implementation on the heavy hexagonal lattice has a CNOT depth of $6$ per round and allows for usage of an entire heavy hexagonal lattice. Experimentally, QAOA is executed on an ensemble of randomly generated Ising instances with a grid search over $1$ and $2$ round angles using all 127 programmable superconducting transmon qubits of ibm_washington. The error suppression technique digital dynamical decoupling is also tested on all QAOA circuits. QA is executed on the same Ising instances with the programmable superconducting flux qubit devices D-Wave Advantage_system4.1 and Advantage_system6.1 using modified annealing schedules with pauses. We find that QA outperforms QAOA on all problem instances. We also find that dynamical decoupling enables 2-round QAOA to marginally outperform 1-round QAOA, which is not the case without dynamical decoupling.

翻译：量子退火（QA）与量子交替算子拟设（QAOA）均为启发式量子算法，旨在对组合优化问题的最优解进行采样。本文在D-Wave硬件与IBMQ硬件上分别实现了QA与QAOA的严格直接比较，并将这两种量子算法与经典模拟退火算法进行了对比。所研究的问题属于一类包含立方ZZZ相互作用（高阶项）的伊辛模型实例，变量赋值为+1或-1，且同时匹配Pegasus拓扑D-Wave芯片的原生连接性与IBMQ芯片的重六角晶格结构。基于重六角晶格的新型QAOA实现每轮CNOT深度为6，并允许利用整个重六角晶格。实验中，QAOA在一组随机生成的伊辛实例上执行，采用网格搜索对ibm_washington所有127个可编程超导传输子量子比特进行1轮和2轮角度优化，并测试了所有QAOA电路中的误差抑制技术——数字动态解耦。QA则在同一伊辛实例上，利用可编程超导磁通量子比特设备D-Wave Advantage_system4.1和Advantage_system6.1，采用带暂停的修正退火调度方案执行。研究发现，在所有问题实例上QA均优于QAOA。同时，动态解耦使2轮QAOA的性能略优于1轮QAOA，而若无动态解耦则这一优势不复存在。