Expressivity of deterministic quantum computation with one qubit

TL;DR

This paper introduces parameterized DQC1 as a quantum machine learning model, demonstrating its ability to perform gradient-based training and inference, and establishing its expressivity as comparable to universal quantum neural networks.

Contribution

It develops a method to compute gradients in DQC1 circuits and analyzes their expressivity, positioning DQC1 as a practical alternative for quantum machine learning.

Findings

Gradient of DQC1 measurement outcomes can be computed directly.

DQC1-based ML is as expressive as universal quantum neural networks.

DQC1 can be used for both training and inference in quantum ML.

Abstract

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.