The subset sum problem is a typical NP-complete problem that is hard to solve efficiently in time due to the intrinsic superpolynomial-scaling property. Increasing the problem size results in a vast amount of time consuming in conventionally available computers. Photons possess the unique features of extremely high propagation speed, weak interaction with environment and low detectable energy level, therefore can be a promising candidate to meet the challenge by constructing an a photonic computer computer. However, most of optical computing schemes, like Fourier transformation, require very high operation precision and are hard to scale up. Here, we present a chip built-in photonic computer to efficiently solve the subset sum problem. We successfully map the problem into a waveguide network in three dimensions by using femtosecond laser direct writing technique. We show that the photons are able to sufficiently dissipate into the networks and search all the possible paths for solutions in parallel. In the case of successive primes the proposed approach exhibits a dominant superiority in time consumption even compared with supercomputers. Our results confirm the ability of light to realize a complicated computational function that is intractable with conventional computers, and suggest the subset sum problem as a good benchmarking platform for the race between photonic and conventional computers on the way towards "photonic supremacy".

中文翻译：

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解决子集和问题的可扩展光子计算机

子集求和问题是典型的 NP 完全问题，由于其固有的超多项式标度特性，很难及时有效地求解。在传统可用的计算机中，增加问题的规模会导致大量的时间消耗。光子具有极高的传播速度、与环境的弱相互作用和低可检测能级的独特特征，因此通过构建光子计算机可以成为迎接挑战的有希望的候选者。然而，大多数光学计算方案，如傅立叶变换，都需要非常高的运算精度，并且难以扩展。在这里，我们提出了一种芯片内置光子计算机来有效地解决子集和问题。我们通过使用飞秒激光直写技术成功地将问题映射到三维波导网络。我们表明光子能够充分消散到网络中并并行搜索所有可能的解决方案路径。在连续素数的情况下，即使与超级计算机相比，所提出的方法在时间消耗方面也表现出显着优势。我们的结果证实了光能够实现传统计算机难以处理的复杂计算功能，并建议将子集和问题作为光子和传统计算机在“光子霸权”道路上的竞赛的良好基准平台。我们表明光子能够充分消散到网络中并并行搜索所有可能的解决方案路径。在连续素数的情况下，即使与超级计算机相比，所提出的方法在时间消耗方面也表现出显着优势。我们的结果证实了光能够实现传统计算机难以处理的复杂计算功能，并建议将子集和问题作为光子和传统计算机在“光子霸权”道路上的竞赛的良好基准平台。我们表明光子能够充分消散到网络中并并行搜索所有可能的解决方案路径。在连续素数的情况下，即使与超级计算机相比，所提出的方法在时间消耗方面也表现出显着优势。我们的结果证实了光能够实现传统计算机难以处理的复杂计算功能，并建议将子集和问题作为光子和传统计算机在“光子霸权”道路上的竞赛的良好基准平台。