The utility of classical neural networks as universal approximators suggests that their quantum analogues could play an important role in quantum generalizations of machine-learningmethods. Inspired by the proposal in [Torrontegui and GarcĂa-Ripoll 2019 EPL 125 30004], we demonstrate a superconducting qubit implementation of an adiabatic controlled gate, which generalizes the action of a classical perceptron as the basic building block of a quantum neural network. We show full control over the steepness of the perceptron activation function, the input weight and the bias by tuning the adiabatic gate length, the coupling between the qubits and the frequency of the applied drive, respectively. In its general form, the gate realizes a multi-qubit entangling operation in a single step, whose decomposition into single- and two-qubit gates would require a number of gates that is exponential in the number of qubits. Its demonstrated direct implementation as perceptron in quantum hardware may therefore lead to more powerful quantum neural networks when combined with suitable additional standard gates.

Quantum simulators are attractive as a means to study many-body quantum systems that are not amenable to classical numerical treatment. A versatile framework for quantum simulationis offered by superconducting circuits. In this perspective, we discuss how superconducting circuits allow the engineering of a wide variety of interactions, which in turn allows the simulation of a wide variety of model Hamiltonians. In particular we focus on strong photon-photon interactions mediated by nonlinear elements. This includes on-site, nearest-neighbour and four-body interactions in lattice models, allowing the implementation of extended Bose-Hubbard models and the toric code. We discuss not only the present state in analogue quantum simulation, but also future perspectives of superconducting quantum simulation that open up when concatenating quantum gates in emerging quantum computing platforms.

Motivated by recent experiments on Josephson junction arrays in microwave cavities, we construct a quantum phase model and calculate the susceptibility of this model in linear response.Both charge and vortex degrees of freedom are considered, as well as circuits containing either Josephson junctions or coherent quantum phase slip elements. The effects of decoherence are considered via a Lindblad master equation.