Hierarchical quantum classifiers

Quantum circuits with hierarchical structure have been used to perform binary classification of classical data encoded in a quantum state. We demonstrate that more expressive circuits in the same family achieve better accuracy and can be used to classify highly entangled quantum states, for which there is no known efficient classical method. We compare performance for several different parameterizations on two classical machine learning datasets, Iris and MNIST, and on a synthetic dataset of quantum states. Finally, we demonstrate that performance is robust to noise and deploy an Iris dataset classifier on the ibmqx4 quantum computer

A Quantum Information Theoretic View On A Deep Quantum Neural Network

We discuss a quantum version of an artificial deep neural network where the role of neurons is taken over by qubits and the role of weights is played by unitaries. The role of the non-linear activation function is taken over by subsequently tracing out layers (qubits) of the network. We study two examples and discuss the learning from a quantum information theoretic point of view. In detail, we show that the lower bound of the Heisenberg uncertainty relations is defining the change of the gradient descent in the learning process. We raise the question if the limit by Nature to two non-commuting observables, quantified in the Heisenberg uncertainty relations, is ruling the optimization of the quantum deep neural network. We find a negative answer.Comment: 8 pages, 5 figure

Differentiation of Linear Optical Circuits

Experimental setups based on linear optical circuits and single photon sources offer a promising platform for near-term quantum machine learning. However, current applications are all based on support vector machines and gradient-free optimization methods. Differentiating an optical circuit over a phase parameter poses difficulty because it results in an operator on the Fock space which is not unitary. In this paper, we show that the derivative of the expectation values of a linear optical circuit can be computed by sampling from a larger circuit, using one additional photon. In order to express the derivative in terms of expectation values, we develop a circuit extraction procedure based on unitary dilation. We end by showing that the full gradient of a universal programmable interferometer can be estimated using polynomially many queries to a boson sampling device. This is in contrast to the qubit setting, where exponentially many parameters are needed to cover the space of unitaries. Our algorithm enables applications of photonic technologies to machine learning, quantum chemistry and optimization, powered by gradient descent