A Logarithm Depth Quantum Converter: From One-hot Encoding to Binary Encoding

• URL: http://arxiv.org/abs/2206.11166v2
• Date: Wed, 27 Jul 2022 06:22:56 GMT
• Title: A Logarithm Depth Quantum Converter: From One-hot Encoding to Binary Encoding
• Authors: Bingren Chen, Hanqing Wu, Haomu Yuan, Lei Wu, Xin Li
• Abstract summary: 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. Compared with the early work, our circuit achieves the exponential speedup with $O(log2 N)$ depth and $O(N)$ size.
• Score: 6.461907578088013
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Within the quantum computing, there are two ways to encode a normalized vector $\{ \alpha_i \}$. They are one-hot encoding and binary coding. The one-hot encoding state is denoted as $\left | \psi_O^{(N)} \right \rangle=\sum_{i=0}^{N-1} \alpha_i \left |0 \right \rangle^{\otimes N-i-1} \left |1 \right \rangle \left |0 \right \rangle ^{\otimes i}$ and the binary encoding state is denoted as $\left | \psi_B^{(N)} \right \rangle=\sum_{i=0}^{N-1} \alpha_i \left |b_i \right \rangle$, 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 $\left | \psi_E^{(N)} \right \rangle=\sum_{i=0}^{N-1} \alpha_i \left |0 \right \rangle^{\otimes N-i-1} \left |1 \right \rangle ^{\otimes i}$. Compared with the early work, our circuit achieves the exponential speedup with $O(\log^2 N)$ depth and $O(N)$ size.

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