论文标题
费米子边界运算符的代表
Representation of the Fermionic Boundary Operator
论文作者
论文摘要
边界运算符是一个线性操作员，可用于高维二进制点（简单）的集合，并将其映射到边界。该边界图是许多应用程序中的关键组件之一，包括微分方程，机器学习，计算几何，机器视觉和控制系统。我们考虑在量子计算机上代表完整边界运算符的问题。我们首先证明边界运营商的特殊结构的完整形式是费米子创建和an灭操作员的特殊结构。然后，我们使用以下事实：这些运算符成对抗耐用性产生一个$ O（n）$ - 深度电路，该电路准确地实现了边界运算符，而无需任何Trotterterization或Taylor系列近似错误。误差较少会减少获得所需精度所需的镜头数量。
The boundary operator is a linear operator that acts on a collection of high-dimensional binary points (simplices) and maps them to their boundaries. This boundary map is one of the key components in numerous applications, including differential equations, machine learning, computational geometry, machine vision and control systems. We consider the problem of representing the full boundary operator on a quantum computer. We first prove that the boundary operator has a special structure in the form of a complete sum of fermionic creation and annihilation operators. We then use the fact that these operators pairwise anticommute to produce an $O(n)$-depth circuit that exactly implements the boundary operator without any Trotterization or Taylor series approximation errors. Having fewer errors reduces the number of shots required to obtain desired accuracies.
