Partial quantisation scheme for optimising the performance of hopfield network - Song, Zhaoyang; Qu, Yingjie; Li, Ming; Liang, Junqing; Ma, Hongyang (Frontiers in Physics, 2022)
This work provides a new quantum scheme for the design of Hopfield network weight matrices. We replace the Hebbian rule by introducing the quantum perceptron to complete the design of its weight matrix. Compared with the classical Hopfield network, our scheme adds training on thresholds along with weight training, resulting in a significant improvement in the usability of the Hopfield network. We demonstrate the improvement of the proposed hybrid quantum-classical Hopfield network over the classical Hopfield network in terms of non-orthogonal simple matrix recovery, incomplete data recovery, memory capacity and model convergence speed through controlled analysis. In the recovery test of non-orthogonal simple matrices, we demonstrate that the improved Hopfield network can find a suitable weight to handle non-orthogonal simple matrices; in the recovery test of random binary-based incomplete matrices, the improved Hopfield network is significantly ahead of the classical Hopfield network, with an average improvement of 30.6% ,and a maximum improvement of 49.1%; in the memory capacity test based on the recognizability of QR codes, the memory capacity of the improved Hopfield network is 2.25 times that of the classical scheme.Finally, we also show that our optimized network has a huge improvement in convergence speed compared to the classical network, which is also significant for Hopfield network.