用单量子比特实现可训练的量子机器学习，性能媲美通用量子神经网络。
Expressivity of deterministic quantum computation with one qubit
- 将参数化量子门引入DQC1，实现梯度直接计算与优化。
- 证明其可学习函数集与通用量子神经网络等价，表达能力强。
- 适合资源受限场景，是轻量级量子机器学习的理想平台。
确定性量子计算仅用一个量子比特（DQC1）因其在特定问题上的计算优势而备受关注，尽管其量子资源有限且不具普适性。本文将参数化DQC1作为量子机器学习模型，证明可通过DQC1协议直接计算测量结果对门参数的梯度，从而实现梯度驱动的电路优化，使DQC1成为唯一同时支持训练与推理的量子协议。我们进一步分析参数化DQC1电路的表达能力，刻画其可学习函数的集合，并表明基于DQC1的机器学习在能力上等同于基于通用计算的量子神经网络。研究结果凸显了DQC1作为实用且灵活的机器学习平台潜力，仅需更简单的量子资源即可媲美复杂量子计算模型。
原文摘要 · Abstract (English)
Deterministic quantum computation with one qubit (DQC1) is of significant theoretical and practical interest due to its computational advantages in certain problems, despite its subuniversality with limited quantum resources. In this work, we introduce parameterized DQC1 as a quantum machine learning model. We demonstrate that the gradient of the measurement outcome of a DQC1 circuit with respect to its gate parameters can be computed directly using the DQC1 protocol. This allows for gradient-based optimization of DQC1 circuits, positioning DQC1 as the sole quantum protocol for both training and inference. We then analyze the expressivity of the parameterized DQC1 circuits, characterizing the set of learnable functions, and show that DQC1-based machine learning (ML) is as powerful as quantum neural networks based on universal computation. Our findings highlight the potential of DQC1 as a practical and versatile platform for ML, capable of rivaling more complex quantum computing models while utilizing simpler quantum resources.
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