QOptCraft: A Python package for the design and study of linear optical quantum systems

The manipulation of the quantum states of light in linear optical systems has multiple applications in quantum optics and quantum computation. The package QOptCraft gives a collection of methods to solve some of the most usual problems when designing quantum experiments with linear interferometers. The methods include functions that compute the quantum evolution matrix for n photons from the classical description of the system and inverse methods that, for any desired quantum evolution, will either give the complete description of the experimental system that realizes that unitary evolution or, when this is impossible, the complete description of the linear system which approximates the desired unitary with a locally minimal error. The functions in the package include implementations of different known decompositions that translate the classical scattering matrix of a linear system into a list of beam splitters and phase shifters and methods to compute the effective Hamiltonian that describes the quantum evolution of states with n photons. The package is completed with routines for useful tasks like generating random linear optical systems, computing matrix logarithms, and quantum state entanglement measurement via metrics such as the Schmidt rank. The routines are chosen to avoid usual numerical problems when dealing with the unitary matrices that appear in the description of linear systems.在线性光学系统中开展光量子态操控，在量子光学与量子计算领域具备多重应用价值。QOptCraft软件包提供了一系列方法，用于解决线性干涉仪量子实验设计中常见的若干问题。该套件包含的函数可从系统的经典描述出发，计算n光子的量子演化矩阵；同时还提供逆求解方法：针对任意期望的量子演化，要么给出实现该幺正演化的完整实验系统描述，若无法实现精确匹配，则输出以局部最小误差逼近目标幺正变换的线性系统完整参数。套件内的函数涵盖多种经典分解算法的实现，可将系统的经典散射矩阵转换为分束器与移相器的组合列表；同时提供用于计算描述n光子态量子演化的有效哈密顿量的相关方法。该套件还附带了诸多实用工具例程，可完成随机线性光学系统生成、矩阵对数计算，以及通过施密特秩（Schmidt rank）等指标开展量子态纠缠度量等任务。所选例程均针对线性系统描述中出现的幺正矩阵，规避了常见的数值计算难题。