Quantum Hopfield neural network

Quantum computing allows for the potential of significant advancements in both the speed and the capacity of widely used machine learning techniques. Here we employ quantum algorithms for the Hopfield network, which can be used for pattern recognition, reconstruction, and optimization as a realization of a content-addressable memory system. We show that an exponentially large network can be stored in a polynomial number of quantum bits by encoding the network into the amplitudes of quantum states. By introducing a classical technique for operating the Hopfield network, we can leverage quantum algorithms to obtain a quantum computational complexity that is logarithmic in the dimension of the data. We also present an application of our method as a genetic sequence recognizer.Comment: 13 pages, 3 figures, final versio

On compression rate of quantum autoencoders: Control design, numerical and experimental realization

Quantum autoencoders which aim at compressing quantum information in a low-dimensional latent space lie in the heart of automatic data compression in the field of quantum information. In this paper, we establish an upper bound of the compression rate for a given quantum autoencoder and present a learning control approach for training the autoencoder to achieve the maximal compression rate. The upper bound of the compression rate is theoretically proven using eigen-decomposition and matrix differentiation, which is determined by the eigenvalues of the density matrix representation of the input states. Numerical results on 2-qubit and 3-qubit systems are presented to demonstrate how to train the quantum autoencoder to achieve the theoretically maximal compression, and the training performance using different machine learning algorithms is compared. Experimental results of a quantum autoencoder using quantum optical systems are illustrated for compressing two 2-qubit states into two 1-qubit states