Combinatorial optimization with a smooth and convex objective function arises naturally in applications such as discrete mean-variance portfolio optimization, where assets must be traded in integer quantities. Although optimal solutions to the associated smooth problem can be computed efficiently, existing adiabatic quantum optimization methods cannot leverage this information. Moreover, while various warm-starting strategies have been proposed for gate-based quantum optimization, none of them explicitly integrate insights from the relaxed continuous solution into the QUBO formulation. In this work, a novel approach is introduced that restricts the search space to discrete solutions in the vicinity of the continuous optimum by constructing a compact Hilbert space, thereby reducing the number of required qubits. Experiments on software solvers and a D-Wave Advantage quantum annealer demonstrate that our method outperforms state-of-the-art techniques.

翻译：在离散均值-方差投资组合优化等应用中，当资产必须以整数单位交易时，自然会产生具有光滑凸目标函数的组合优化问题。尽管相关光滑问题的最优解可被高效计算，现有的绝热量子优化方法却无法利用这一信息。此外，尽管已针对基于门电路的量子优化提出了多种热启动策略，但尚无方法将松弛连续解的洞见明确整合至QUBO（二次无约束二进制优化）表述中。本研究提出一种创新方法，通过构建紧凑的希尔伯特空间，将搜索空间限制在连续最优解附近的离散解集，从而减少所需量子比特数。在软件求解器与D-Wave Advantage量子退火器上的实验表明，本方法性能优于现有最先进技术。