The D-Wave quantum annealer has emerged as a novel computational architecture that is attracting significant interest, but there have been only a few practical algorithms exploiting the power of quantum annealers. Here we present a model predictive control (MPC) algorithm using a quantum annealer for a system allowing a finite number of input values. Such an MPC problem is classified as a non-deterministic polynomial-time-hard combinatorial problem, and thus real-time sequential optimization is difficult to obtain with conventional computational systems. We circumvent this difficulty by converting the original MPC problem into a quadratic unconstrained binary optimization problem, which is then solved by the D-Wave quantum annealer. Two practical applications, namely stabilization of a spring-mass-damper system and dynamic audio quantization, are demonstrated. For both, the D-Wave method exhibits better performance than the classical simulated annealing method. Our results suggest new applications of quantum annealers in the direction of dynamic control problems.

中文翻译：

---

使用 D-Wave 量子退火器对有限输入系统进行模型预测控制

D-Wave 量子退火器已成为一种新的计算架构，引起了极大的兴趣，但只有少数实用算法利用了量子退火器的强大功能。在这里，我们提出了一种模型预测控制 (MPC) 算法，该算法将量子退火器用于允许有限数量输入值的系统。这种 MPC 问题被归类为非确定性多项式-时间-困难组合问题，因此传统计算系统难以获得实时顺序优化。我们通过将原始 MPC 问题转换为二次无约束二元优化问题来规避这一困难，然后由 D-Wave 量子退火器解决。两个实际应用，即弹簧质量阻尼器系统的稳定和动态音频量化，被证明。对于这两种方法，D-Wave 方法表现出比经典模拟退火方法更好的性能。我们的结果表明量子退火器在动态控制问题方向上的新应用。