As first proposed for the adiabatic quantum information processing by Wu et al (2002 Phys. Rev. Lett. 89 057904), the Trotterization technique is a very useful tool for universal quantum computing, and in particular, the adiabatic quantum simulation of quantum systems. Given a boson Hamiltonian involving arbitrary bilinear interactions, we propose a static version of this technique to perform an optical simulation that would enable the identification of the ground state of the Hamiltonian. By this method, the dynamical process of the adiabatic evolution is mapped to a static linear optical array which is robust to the errors caused by dynamical fluctuations. We examine the cost of the physical implementation of the Trotterization, i.e. the number of discrete steps required for a given accuracy. Two conclusions are drawn. One is that the number of required steps grows much more slowly than the system size if the number of non-zero matrix elements of Hamiltonian is not too large. The second is that small fluctuations of the parameters of optical elements do not affect the first conclusion. This implies that the method is robust against the certain type of errors as we considered. Last but not least, we present an example of implementation of the simulation on a photonic chip as well as an optimized scheme. By such examples, we show a reduction of the costs compared to its classical counterpart and the potential for further improvement, which promotes a more general application.

中文翻译：

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Trotterized绝热量子模拟及其在简单全光系统中的应用

正如 Wu 等人 (2002 Phys. Rev. Lett. 89 057904) 首次提出的绝热量子信息处理技术，Trotterization 技术是一种非常有用的通用量子计算工具，尤其是量子系统的绝热量子模拟。给定一个涉及任意双线性相互作用的玻色子哈密顿量，我们提出了该技术的静态版本来执行光学模拟，从而能够识别哈密顿量的基态。通过这种方法，绝热演化的动力学过程被映射到静态线性光学阵列，该阵列对动态波动引起的误差具有鲁棒性。我们检查了 Trotterization 的物理实现的成本，即给定精度所需的离散步骤的数量。得出两个结论。一是如果哈密顿量的非零矩阵元素的数量不是太大，则所需步骤的数量增长比系统规模慢得多。二是光学元件参数的微小波动不影响第一个结论。这意味着该方法对于我们所考虑的某些类型的错误具有鲁棒性。最后但并非最不重要的一点是，我们提供了一个在光子芯片上实现模拟的示例以及优化方案。通过这样的例子，我们展示了与其经典对应物相比成本的降低以及进一步改进的潜力，这促进了更普遍的应用。二是光学元件参数的微小波动不影响第一个结论。这意味着该方法对于我们所考虑的某些类型的错误具有鲁棒性。最后但并非最不重要的一点是，我们提供了一个在光子芯片上实现模拟的示例以及优化方案。通过这样的例子，我们展示了与其经典对应物相比成本的降低以及进一步改进的潜力，这促进了更普遍的应用。二是光学元件参数的小幅波动不影响第一个结论。这意味着该方法对于我们所考虑的某些类型的错误具有鲁棒性。最后但并非最不重要的一点是，我们提供了一个在光子芯片上实现模拟的示例以及优化方案。通过这样的例子，我们展示了与其经典对应物相比成本的降低以及进一步改进的潜力，这促进了更普遍的应用。