A Depth-Independent Linear Chain Ansatz for Large-Scale Quantum Approximate Optimization

Abstract: Combinatorial optimization lies at the heart of numerous real-world applications. For a broad category of optimization problems, quantum computing is expected to exhibit quantum speed-up over classic computing. Among various quantum algorithms, the Quantum Approximate Optimization Algorithm (QAOA), as one of variational quantum algorithms, shows promise on demonstrating quantum advantage on noisy intermediate-scale quantum (NISQ) hardware. However, with increasing problem size, the circuit depth demanded by original QAOA scales rapidly and quickly surpasses the threshold at which meaningful results can be obtained. To address this challenge, in this work, we propose a variant of QAOA (termed linear chain QAOA) and demonstrate its advantages over original QAOA on paradigmatic MaxCut problems. In original QAOA, each graph edge is encoded with one entangling gate. In our ansatz, we locate a linear chain from the original MaxCut graph and place entangling gates sequentially along this chain. This linear-chain ansatz is featured by shallow quantum circuits and with the low execution time that scales independently of the problem size. Leveraging this ansatz, we demonstrate an approximation ratio of 0.78 (without post-processing) on non-hardware-native random regular MaxCut instances with 100 vertices in a digital quantum processor using 100 qubits. Our findings offer new insights into the design of hardware-efficient ansatz and point toward a promising route for tackling large-scale combinatorial optimization problems on NISQ devices.