[论文解读] A Universal Training Algorithm for Quantum Deep Learning

Guillaume Verdon, Jason Pye+1 more|arXiv (Cornell University)|Jun 25, 2018

Quantum Computing Algorithms and Architecture参考文献 6被引用 73

一句话总结

本文提出 Baqprop，一种量子原生反向传播原理，并构建两种通用量子优化启发式方法——Quantum Dynamical Descent (QDD) 与 Momentum Measurement Gradient Descent (MoMGrad)——用于在量子硬件上训练量子参数化电路和经典神经网络，并在代表性应用上给出数值示例。

ABSTRACT

We introduce the Backwards Quantum Propagation of Phase errors (Baqprop) principle, a central theme upon which we construct multiple universal optimization heuristics for training both parametrized quantum circuits and classical deep neural networks on a quantum computer. Baqprop encodes error information in relative phases of a quantum wavefunction defined over the space of network parameters; it can be thought of as the unification of the phase kickback principle of quantum computation and of the backpropagation algorithm from classical deep learning. We propose two core heuristics which leverage Baqprop for quantum-enhanced optimization of network parameters: Quantum Dynamical Descent (QDD) and Momentum Measurement Gradient Descent (MoMGrad). QDD uses simulated quantum coherent dynamics for parameter optimization, allowing for quantum tunneling through the hypothesis space landscape. MoMGrad leverages Baqprop to estimate gradients and thereby perform gradient descent on the parameter landscape; it can be thought of as the quantum-classical analogue of QDD. In addition to these core optimization strategies, we propose various methods for parallelization, regularization, and meta-learning as augmentations to MoMGrad and QDD. We introduce several quantum-coherent adaptations of canonical classical feedforward neural networks, and study how Baqprop can be used to optimize such networks. We develop multiple applications of parametric circuit learning for quantum data, and show how to perform Baqprop in each case. One such application allows for the training of hybrid quantum-classical neural-circuit networks, via the seamless integration of Baqprop with classical backpropagation. Finally, for a representative subset of these proposed applications, we demonstrate the training of these networks via numerical simulations of implementations of QDD and MoMGrad.

研究动机与目标

• Motivate and formulate a quantum-native backpropagation principle (Baqprop) that unifies phase kickback with classical backpropagation for training quantum-parametric networks.
• Develop two core optimization heuristics (QDD and MoMGrad) that leverage Baqprop to train both quantum and hybrid classical-quantum networks.
• Propose augmentation techniques (parallelization, regularization, meta-learning) and apply Baqprop to a range of quantum neural and parametric circuit models.
• Demonstrate, via numerical simulations, the feasibility of training representative applications with QDD and MoMGrad.
• Bridge classical and quantum deep learning theories to enable seamless optimization across quantum and hybrid architectures.

提出的方法

• Introduce Baqprop as the encoding of error information in relative phases of a quantum wavefunction over network parameters.
• Define Quantum Dynamical Descent (QDD) as fully quantum-coherent parameter optimization using simulated Schrödinger dynamics under an effective potential.
• Define Momentum Measurement Gradient Descent (MoMGrad) as a quantum-classical method that measures Baqprop-induced phase kicks to estimate gradients for classical-like parameter updates.
• Provide quantum-coherent adaptations of classical neural network architectures and discuss their training via Baqprop.
• Outline parallelization, regularization, and meta-learning schemes to augment QDD and MoMGrad.
• Relate QDD to QAOA and QAA concepts to situate the methods within known quantum optimization paradigms.

实验结果

研究问题

• RQ1 How can Baqprop encode gradient information in a quantum-native way to train parametric networks on quantum hardware?
• RQ2 Can QDD and MoMGrad effectively optimize quantum parametric circuits and hybrid quantum-classical networks with comparable or improved performance to classical backpropagation?
• RQ3 What augmentation strategies (parallelization, regularization, meta-learning) enhance Baqprop-based training?
• RQ4 Do representative quantum neural network and parametric circuit tasks trainable under Baqprop as demonstrated by numerical simulations?

主要发现

• Baqprop provides a unified view linking phase kickback and backpropagation, enabling gradient information to propagate through quantum-parametric networks.
• Two core optimization strategies are proposed: Quantum Dynamical Descent (QDD) and Momentum Measurement Gradient Descent (MoMGrad).
• QDD uses coherent quantum dynamics to navigate the hypothesis space, potentially enabling tunneling through rough landscapes; MoMGrad estimates gradients via phase kicks measured quantum-classically.
• The framework supports quantum-coherent neural networks, quantum parametric circuits, and hybrid quantum-classical networks, including integration with classical backpropagation.
• The paper presents numerical simulations demonstrating training for a representative subset of proposed applications using QDD and MoMGrad.
• Augmentations such as batching, parallelization, regularization (weight decay, dropout), and quantum meta-learning are discussed to enhance performance.