We investigate the possibility of solving continuous non-convex optimization problems using a network of interacting quantum optical oscillators. We propose a native encoding of continuous variables in analog signals associated with the quadrature operators of a set of quantum optical modes. Optical coupling of the modes and noise introduced by vacuum fluctuations from external reservoirs or by weak measurements of the modes are used to optically simulate a diffusion process on a set of continuous random variables. The process is run sufficiently long for it to relax into the steady state of an energy potential defined on a continuous domain. As a first demonstration, we numerically benchmark solving box-constrained quadratic programming (BoxQP) problems using these settings. We consider delay-line and measurement-feedback variants of the experiment. Our benchmarking results demonstrate that in both cases the optical network is capable of solving BoxQP problems over three orders of magnitude faster than a state-of-the-art classical heuristic.

翻译：我们研究使用相互作用的量子光学振荡器网络求解连续非凸优化问题的可能性。我们提出一种原生编码方式，将连续变量编码为与一组量子光学模式的正交算符相关联的模拟信号。通过光学模式耦合以及由外部储层真空涨落或弱测量引入的噪声，在连续随机变量集合上光学模拟扩散过程。该过程运行足够长时间，使其松弛至定义在连续域上的能量势稳态。作为首次验证，我们利用这些设置对带约束二次规划（BoxQP）问题进行数值基准测试。我们考虑了延迟线型和测量反馈型两种实验变体。基准测试结果表明，在两种情况下，光学网络求解BoxQP问题的速度均比最先进的经典启发式算法快三个数量级以上。