数字量子信息的几何方法
Geometric Approach to Digital Quantum Information
摘要：
我们提出了均匀离散连续N-量子比特希尔伯特空间的几何方法。当被视为几何图形的顶点时，所得到的状态形成了柏拉图固体的等价物。离散化技术本质上描述了一类连接集合中相邻状态的pi/2旋转，即保持几何图形不变。这些旋转被示出为生成Clifford群，这是N个量子比特上的离散变换的一般群。离散N量子比特希尔伯特空间允许我们定义其数字量子信息内容，并且我们表明该信息内容随N^2增长。虽然我们相信离散集是有趣的，因为它们允许额外的经典行为-如量子纠缠和量子并行-被探索，同时绕过希尔伯特空间的连续性，我们也展示了它们如何可能是一个有用的工具，在传统的量子计算的问题。我们详细描述了一个和两个量子比特的离散集。
英文摘要：
We present geometric methods for uniformly discretizing the continuous N-qubit Hilbert space. When considered as the vertices of a geometrical figure, the resulting states form the equivalent of a Platonic solid. The discretization technique inherently describes a class of pi/2 rotations that connect neighboring states in the set, i.e. that leave the geometrical figures invariant. These rotations are shown to generate the Clifford group, a general group of discrete transformations on N qubits. Discretizing the N-qubit Hilbert space allows us to define its digital quantum information content, and we show that this information content grows as N^2. While we believe the discrete sets are interesting because they allow extra-classical behavior--such as quantum entanglement and quantum parallelism--to be explored while circumventing the continuity of Hilbert space, we also show how they may be a useful tool for problems in traditional quantum computation. We describe in detail the discrete sets for one and two qubits.
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