论文标题
希尔伯特空间几何形状和有效量子计算的约束不平等
Constraint Inequalities from Hilbert Space Geometry & Efficient Quantum Computation
论文作者
论文摘要
描述给定量子系统的任意参数的有用关系可以从对相应希尔伯特空间中的向量施加的简单物理约束中得出。这是众所周知的，通常通过将大维的希尔伯特空间划分为相关的子空间，并将希尔伯特空间中的点与物理可观察物的预期值相关联。本说明的目的很小。我们描述了该过程，并指出该过程与必要的考虑相似，以使量子场进行量子模拟，并在嘈杂的中间尺度量子（NISQ）设备上进行量子量子系统进行交互。最后，我们指出了量子计算的相关部分，这些想法可能有用。这项工作以密度矩阵形式主义进行，是对参考文献中发现的材料的回顾。我们通过建议如何使用这些想法来指导和改善参数化量子电路来丰富文献。
Useful relations describing arbitrary parameters of given quantum systems can be derived from simple physical constraints imposed on the vectors in the corresponding Hilbert space. This is well known and it usually proceeds by partitioning the large dimensional Hilbert space into relevant sub spaces and relating points in the Hilbert space to the expectation values of physical observables. The aim of this note is quite modest. We describe the procedure and point out that this parallels the necessary considerations that make Quantum Simulation of quantum fields and interacting many body quantum systems on Noisy Intermediate Scale Quantum (NISQ) devices possible. We conclude by pointing out relevant parts of Quantum Computing where these ideas could be useful. This work proceeds in density matrix formalism and is a review of materials found in references. We enrich the literature by suggesting how to use these ideas to guide and improve parameterized quantum circuits.
