启发式量子振幅放大：交通QUBO案例研究

中文摘要 AI 辅助

量子振幅放大（QAA）是Grover算法的推广，非常适合组合优化问题，尤其对二次无约束二元优化（QUBO）问题具有前景。QAA的吸引力在于其能够将量子系统驱动到目标状态，以超过90%以上的概率产生全局最优解。然而，将QAA实现于应用规模的优化目前超出了量子硬件的能力，且自由参数选择的未解决算法挑战进一步加剧了这一问题。在本研究中，我们通过利用一个真实的交通流QUBO问题来探究QAA作为启发式求解器的实现，从而解决这些问题。具体而言，允许扩散算子参数取非π值扩展了QAA的能力。这解锁了一种新的多次射击、低迭代策略，旨在追求高累积概率而非最大化单个基态的概率。通过使用25量子比特的模拟，我们的结果表明启发式QAA解决了先前研究中提到的两个主要挑战。首先，启发式QAA即使在单次迭代下也能工作，与标准QAA相比，电路深度降低了几个数量级。其次，我们表明，达到最优算法性能所需的问题相关参数可以通过最少的前期经典计算开销可靠地近似。

英文摘要

Quantum Amplitude Amplification (QAA), the generalization of Grover's algorithm, is well-positioned for combinatorial optimization and is particularly promising for Quadratic Unconstrained Binary Optimization (QUBO) problems. QAA is appealing due to its ability to drive the quantum system to a target state, yielding the globally optimal solution with probability over $90$+%. However, realizing QAA for application-scale optimization currently exceeds quantum hardware capacity, which is further compounded by unresolved algorithmic challenges regarding the choice of free parameters. In this study, we address these issues by utilizing a realistic traffic flow QUBO problem to investigate the implementation of QAA as a heuristic solver. Specifically, allowing the diffusion operator parameter to take non-$π$ values expands the capabilities of QAA. This unlocks a new multiple-shot, low-iteration strategy that aims for a high cumulative probability rather than maximizing the probability of a single basis state. Using $25$-qubit simulations, our results demonstrate that heuristic QAA addresses two of the main challenges cited in previous studies. Firstly, heuristic QAA works even at a single iteration, reducing circuit depth by orders of magnitude compared to standard QAA. And secondly, we show that the problem-dependent parameters necessary for reaching optimal algorithmic performance can be reliably approximated with minimal upfront classical computing overhead.

发表机构

• National Academies（美国国家科学院）
• Air Force Research Laboratory（空军研究实验室）

机构由 AI 辅助整理，请以论文原文为准。