Expressivity of deterministic quantum computation with one qubit
This work addresses the challenge of leveraging limited quantum resources for machine learning, offering a practical and versatile platform that could rival more complex quantum models, though it appears incremental in extending DQC1 to parameterized learning tasks.
The authors tackled the problem of using deterministic quantum computation with one qubit (DQC1) as a quantum machine learning model by introducing parameterized DQC1 circuits and showing that gradients can be computed directly within the DQC1 protocol, enabling gradient-based optimization and demonstrating that DQC1-based ML is as powerful as universal quantum neural networks.
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.