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

Unifying approach to the quantification of bipartite correlations by Bures distance

The notion of distance defined on the set of states of a composite quantum system can be used to quantify total, quantum and classical correlations in a unifying way. We provide new closed formulae for classical and total correlations of two-qubit Bell-diagonal states by considering the Bures distance. Complementing the known corresponding expressions for entanglement and more general quantum correlations, we thus complete the quantitative hierarchy of Bures correlations for Bell-diagonal states. We then explicitly calculate Bures correlations for two relevant families of states: Werner states and rank-2 Bell-diagonal states, highlighting the subadditivity which holds for total correlations with respect to the sum of classical and quantum ones when using Bures distance. Finally, we analyse a dynamical model of two independent qubits locally exposed to non-dissipative decoherence channels, where both quantum and classical correlations measured by Bures distance exhibit freezing phenomena, in analogy with other known quantifiers of correlations.Comment: 18 pages, 4 figures; published versio

Continuous-variable quantum neural networks

We introduce a general method for building neural networks on quantum computers. The quantum neural network is a variational quantum circuit built in the continuous-variable (CV) architecture, which encodes quantum information in continuous degrees of freedom such as the amplitudes of the electromagnetic field. This circuit contains a layered structure of continuously parameterized gates which is universal for CV quantum computation. Affine transformations and nonlinear activation functions, two key elements in neural networks, are enacted in the quantum network using Gaussian and non-Gaussian gates, respectively. The non-Gaussian gates provide both the nonlinearity and the universality of the model. Due to the structure of the CV model, the CV quantum neural network can encode highly nonlinear transformations while remaining completely unitary. We show how a classical network can be embedded into the quantum formalism and propose quantum versions of various specialized model such as convolutional, recurrent, and residual networks. Finally, we present numerous modeling experiments built with the Strawberry Fields software library. These experiments, including a classifier for fraud detection, a network which generates Tetris images, and a hybrid classical-quantum autoencoder, demonstrate the capability and adaptability of CV quantum neural networks

Navigating the quantum-classical frontier

The description of a quantum system follows a fundamentally different paradigm to that of a classical system, leading to unique yet counter-intuitive properties. In this thesis we consider some of these unique properties, here termed simply the quantum. We focus on understanding some important types of the quantum: quantum coherence and quantum correlations, as well as quantum entanglement as an important subclass of quantum correlations. Our objective is to investigate how to quantify the quantum, what it can be used for, and how it can be preserved in the adverse presence of noise. These findings help to clarify the frontier between quantum and classical systems, a crucial endeavour for understanding the applications and advantageous features of the quantum world