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arXiv · 2501.13469

Improving Quantum Optimization to Achieve Quadratic Time Complexity

Ji Jiang·Peisheng Huang·Zhiyi Wu·Xuandong Sun·Zechen Guo·Wenhui Huang·Libo Zhang·Yuxuan Zhou·Jiawei Zhang·Weijie Guo·Xiayu Linpeng·Song Liu·Wenhui Ren·Ziyu Tao·Ji Chu·Jingjing Niu·Youpeng Zhong·Dapeng Yu
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Abstract

Quantum Approximate Optimization Algorithm (QAOA) is a promising candidate for achieving quantum advantage in combinatorial optimization. However, its variational framework presents a long-standing challenge in selecting circuit parameters. In this work, we prove that the energy expectation produced by QAOA can be expressed as a trigonometric function of the final-level mixer parameter. Leveraging this insight, we introduce Penta-O, a level-wise parameter-setting strategy that eliminates the classical outer loop, maintains minimal sampling overhead, and ensures non-decreasing performance. This method is broadly applicable to the generic quadratic unconstrained binary optimization formulated as the Ising model. For a $p$-level QAOA, Penta-O achieves an unprecedented quadratic time complexity of $\mathcal{O}(p^2)$ and a sampling overhead proportional to $5p+1$. Through experiments and simulations, we demonstrate that QAOA enhanced by Penta-O achieves near-optimal performance with exceptional circuit depth efficiency. Our work provides a versatile tool for advancing variational quantum algorithms.

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Ji Jiang, Peisheng Huang, Zhiyi Wu, Xuandong Sun, Zechen Guo, Wenhui Huang, Libo Zhang, Yuxuan Zhou, Jiawei Zhang, Weijie Guo, Xiayu Linpeng, Song Liu, Wenhui Ren, Ziyu Tao, Ji Chu, Jingjing Niu, Youpeng Zhong, Dapeng Yu. 2025-01-23. Improving Quantum Optimization to Achieve Quadratic Time Complexity. https://arxiv.org/abs/2501.13469

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