论文标题
量子鲍尔茨曼机器的小组理论
Group theory on quantum Boltzmann machine
论文作者
论文摘要
小组理论在表征量子系统中的对称性方面非常成功，这极大地简化了我们对量子系统的处理。在这里，我们介绍了量子玻尔兹曼机器的对称性概念，并开发了一个组理论来描述对称性。这种对称性不仅意味着与对称转换相关的所有目标状态都是等效的，而且对于给定的目标状态，所有与保持目标状态不变的对称转换相关的最佳解决方案都是等效的。对于基于Qubit的玻尔兹曼机器，我们提出了一个系统的程序来构建该组，并开发一种数值算法来验证我们的构建的完整性。
Group theory is extremely successful in characterizing the symmetries in quantum systems, which greatly simplifies and unifies our treatments of quantum systems. Here we introduce the concept of the symmetry for a quantum Boltzmann machine and develop a group theory to describe the symmetry. This symmetry implies not only that all the target states related with the symmetry transformations are equivalent, but also that for a given target state all the optimal solutions related with the symmetry transformations that keeps the target state invariant are equivalent. For the Boltzmann machines built on qubits, we propose a systematic procedure to construct the group, and develop a numerical algorithm to verify the completeness of our construction.
