Efficient Learning for Deep Quantum Neural Networks (1902.10445v1)

Abstract: Neural networks enjoy widespread success in both research and industry and, with the imminent advent of quantum technology, it is now a crucial challenge to design quantum neural networks for fully quantum learning tasks. Here we propose the use of quantum neurons as a building block for quantum feed-forward neural networks capable of universal quantum computation. We describe the efficient training of these networks using the fidelity as a cost function and provide both classical and efficient quantum implementations. Our method allows for fast optimisation with reduced memory requirements: the number of qudits required scales with only the width, allowing the optimisation of deep networks. We benchmark our proposal for the quantum task of learning an unknown unitary and find remarkable generalisation behaviour and a striking robustness to noisy training data.

• The paper proposes a novel framework that constructs deep quantum neural networks using quantum neurons with a fidelity-based cost function.
• It leverages a quantum analogue of classical backpropagation with CP layer transition maps, reducing memory requirements by scaling with network width.
• Empirical evaluations demonstrate robust learning of unknown unitary operations and resilience against noisy data, showcasing practical advancements for NISQ devices.

Efficient Learning for Deep Quantum Neural Networks

The manuscript titled "Efficient Learning for Deep Quantum Neural Networks" by Kerstin Beer et al., addresses the emerging field of quantum neural networks (QNNs) and proposes a framework for efficient training on quantum computing platforms. As quantum computing continues to advance, integrating machine learning with quantum mechanics presents significant opportunities, particularly in enhancing computational capabilities beyond classical limits.

Overview of Proposed Framework

The authors introduce quantum neurons as the essential units for constructing QNNs capable of universal quantum computation. These neurons are designed to operate within a quantum feed-forward neural network structure, employing the fidelity measure as a cost function to optimize training procedures. A unique characteristic of this architecture is the reduction in memory requirements, as the number of qudits required scales with the network width rather than its depth, facilitating the deployment of deeper networks.

Training and Optimization

The paper advances an efficient methodology for training QNNs, applicable to the task of learning unknown unitary operations. The training exploits a quantum analogue of the classical backpropagation algorithm, leveraging completely positive layer transition maps. Notably, this training mechanism demonstrates strong generalization capabilities and robustness against noisy training sets—features that are crucial for quantum applications where decoherence and imprecision might be significant.

Numerical Results and Observations

Empirical results substantiate the QNN's capacity to learn and generalize effectively from a limited set of training samples. Tests reveal that QNNs trained on random unitaries match theoretical estimates of optimal cost functions remarkably well. Additionally, the networks exhibit robustness to corrupted training data, with a slower degradation in performance as noise increases.

Implications and Future Directions

The architectural and training innovations presented lay foundational work for implementing QNNs on Noisy Intermediate Scale Quantum (NISQ) devices. The potential for reduced memory overhead promises greater scalability on emerging quantum hardware. Future research directions proposed include further generalization of quantum perceptrons to accommodate general CP maps, addressing overfitting, and optimizing implementations on forthcoming quantum technologies.

Overall, this paper makes a substantive contribution to quantum machine learning, offering practical insights into the design and training of deep QNNs. By setting the stage for more efficient utilization of NISQ devices, it heralds an era where quantum computing could drive more sophisticated machine learning applications, potentially redefining computational limits in the process.