论文标题
对数深度量子转换器：从一个壁编码到二进制编码
A Logarithm Depth Quantum Converter: From One-hot Encoding to Binary Encoding
论文作者
论文摘要
在量子计算中，有两种方法可以编码归一化的向量$ \ {α_i\} $。它们是一式编码和二进制编码。单热编码状态表示为$ \ left | ψ_O^{(N)} \right \rangle=\sum_{i=0}^{N-1} α_i \left |0 \right \rangle^{\otimes N-i-1} \left |1 \right \rangle \left |0 \right \rangle ^{\otimes i}$ and the binary encoding state is表示为$ \ left | ψ_b^{（n）} \ right \ rangle = \ sum_ {i = 0}^{n-1}α_i\ left | b_i \ right \ rangle $，其中$ b_i $在$ i $ $ i $ $ i $的二进制中解释为tensor of i $ tensor of i $ tensor of i $。在本文中，我们提出了一种方法，该方法通过将Edick状态作为过渡状态，在单速编码状态和二进制编码状态之间转换，其中Edick状态定义为$ \ left | ψ_e^{（n）} \ right \ rangle = \ sum_ {i = 0}^{n-1}α_i\ left | 0 \ range \ rangle^{\ otime n-i-i-imime n-i-i-rangime n-i-i-rangimes n-i-i-range^\ left | 1 \ left | 1 \ weft | 1 \ rangle^rangle^rangle^rangle^{\ otimes i i} $。与早期工作相比，我们的电路以$ o（\ log^2 n）$深度和$ o（n）$大小实现了指数加速。
Within the quantum computing, there are two ways to encode a normalized vector $\{ α_i \}$. They are one-hot encoding and binary coding. The one-hot encoding state is denoted as $\left | ψ_O^{(N)} \right \rangle=\sum_{i=0}^{N-1} α_i \left |0 \right \rangle^{\otimes N-i-1} \left |1 \right \rangle \left |0 \right \rangle ^{\otimes i}$ and the binary encoding state is denoted as $\left | ψ_B^{(N)} \right \rangle=\sum_{i=0}^{N-1} α_i \left |b_i \right \rangle$, where $b_i$ is interpreted in binary of $i$ as the tensor product sequence of qubit states. In this paper, we present a method converting between the one-hot encoding state and the binary encoding state by taking the Edick state as the transition state, where the Edick state is defined as $\left | ψ_E^{(N)} \right \rangle=\sum_{i=0}^{N-1} α_i \left |0 \right \rangle^{\otimes N-i-1} \left |1 \right \rangle ^{\otimes i}$. Compared with the early work, our circuit achieves the exponential speedup with $O(\log^2 N)$ depth and $O(N)$ size.
