Soft-Quantum Algorithms

TL;DR

This paper introduces a novel method for training matrices directly in quantum machine learning, maintaining unitarity with a regularization term, leading to faster training and improved performance in classification and reinforcement learning tasks.

Contribution

The authors propose a two-step training approach for soft-unitary matrices that enhances efficiency and performance in quantum neural networks and hybrid quantum-classical systems.

Findings

Training matrices directly is faster than gate decomposition for small datasets.

The two-step process achieves lower loss in a five-qubit classification task.

Hybrid quantum-classical agents outperform classical baselines in reinforcement learning.

Abstract

Quantum operations on pure states can be fully represented by unitary matrices. Variational quantum circuits, also known as quantum neural networks, embed data and trainable parameters into gate-based operations and optimize the parameters via gradient descent. The high cost of training and low fidelity of current quantum devices, however, restricts much of quantum machine learning to classical simulation. For few-qubit problems with large datasets, training the matrix elements directly, as is done with weight matrices in classical neural networks, can be faster than decomposing data and parameters into gates. We propose a method that trains matrices directly while maintaining unitarity through a single regularization term added to the loss function. A second training step, circuit alignment, then recovers a gate-based architecture from the resulting soft-unitary. On a five-qubit supervised classification task with 1000 datapoints, this two-step process produces a trained variational circuit in under four minutes, compared to over two hours for direct circuit training, while achieving lower binary cross-entropy loss. In a second experiment, soft-unitaries are embedded in a hybrid quantum-classical network for a reinforcement learning cartpole task, where the hybrid agent outperforms a purely classical baseline of comparable size.