[论文解读] An adaptive quantum approximate optimization algorithm for solving combinatorial problems on a quantum computer

Li Zhu, Ho Lun Tang+5 more|arXiv (Cornell University)|May 20, 2020

Quantum Computing Algorithms and Architecture被引用 31

一句话总结

本文提出 ADAPT-QAOA，一种迭代式、面向问题定制的 QAOA 版本，通过从混合器池中依据梯度准则选择混合器来扩展 Ansatz，在 Max-Cut 基准测试中展示了更快的收敛和更少的资源。

ABSTRACT

The quantum approximate optimization algorithm (QAOA) is a hybrid variational quantum-classical algorithm that solves combinatorial optimization problems. While there is evidence suggesting that the fixed form of the standard QAOA ansatz is not optimal, there is no systematic approach for finding better ansätze. We address this problem by developing an iterative version of QAOA that is problem-tailored, and which can also be adapted to specific hardware constraints. We simulate the algorithm on a class of Max-Cut graph problems and show that it converges much faster than the standard QAOA, while simultaneously reducing the required number of CNOT gates and optimization parameters. We provide evidence that this speedup is connected to the concept of shortcuts to adiabaticity.

研究动机与目标

• Motivate and address limitations of fixed-form QAOA ansätze for combinatorial optimization.
• Develop an adaptive, problem-tailored ansatz that grows layer-by-layer using a mixer-pool with a gradient-based selector.
• Demonstrate performance improvements on Max-Cut benchmarks and analyze resource implications.

提出的方法

• Replace the fixed QAOA mixer with a problem-tailored mixer pool and construct the ansatz iteratively layer-by-layer.
• Measure the energy gradient with respect to pool operators to select the next mixer based on the largest gradient component.
• Add the selected mixer to the ansatz and optimize all current parameters to minimize the cost function.
• Compare three pools: standard QAOA mixer, single-qubit mixer pool, and multi-qubit entangling mixer pool.
• Benchmark on Max-Cut problems on regular graphs with n=6, D=3 and D=5, using Nelder-Mead for parameter optimization.

实验结果

研究问题

• RQ1 Can an adaptive, problem-tailored mixer pool improve QAOA performance over fixed-form ansätze for Max-Cut?
• RQ2 To what extent do entangling mixers reduce resources (parameters, CNOTs) while accelerating convergence?
• RQ3 How does ADAPT-QAOA relate to shortcuts to adiabaticity (STA) in explaining observed speedups?

主要发现

• ADAPT-QAOA with a multi-qubit mixer pool converges dramatically faster than standard QAOA, typically within ~3 layers on tested graphs.
• Using the multi-qubit pool reduces both the number of optimization parameters and CNOT gates by about 50% compared to standard QAOA.
• Entangling mixers are frequently chosen (up to ~75–80% of the time) for multi-qubit pools, indicating higher connectivity aids convergence.
• The approach achieves faster convergence despite introducing entangling mixers, and can require fewer total CNOTs than standard QAOA.
• For larger or less connected graphs, ADAPT-QAOA with multi-qubit mixers still outperforms standard QAOA, with measurable resource savings.