论文标题
量子寄存器代数：用于量子计算的数学语言
Quantum Register Algebra: the mathematical language for quantum computing
论文作者
论文摘要
我们引入量子寄存器代数（QRA）作为量子计算的有效工具。我们展示了QRA与Dirac形式主义之间的直接联系。我们提出了我们方法的GAALOP（几何代数算法优化器）。使用第4节中给出的QRA基础向量定义以及基于第5节中介绍的DE WITT基础的框架，我们能够使用几何产品在GAALOP中与QRA进行充分描述和计算。我们通过在两个Qubit寄存器上呈现众所周知的掉期操作的QRA形式来说明此计算的直觉。
We introduce Quantum Register Algebra (QRA) as an efficient tool for quantum computing. We show the direct link between QRA and Dirac formalism. We present GAALOP (Geometric Algebra Algorithms Optimizer) implementation of our approach. Using the QRA basis vectors definitions given in Section 4 and the framework based on the de Witt basis presented in Section 5, we are able to fully describe and compute with QRA in GAALOP using the geometric product. We illustrate the intuitiveness of this computation by presenting the QRA form for the well known SWAP operation on a two qubit register.
