Lasse Bjørn Kristensen

Philipp Schleich, Marta Skreta, Lasse B. Kristensen et al.

The feasibility of variational quantum algorithms, the most popular correspondent of neural networks on noisy, near-term quantum hardware, is highly impacted by the circuit depth of the involved parametrized quantum circuits (PQCs). Higher depth increases expressivity, but also results in a detrimental accumulation of errors. Furthermore, the number of parameters involved in the PQC significantly influences the performance through the necessary number of measurements to evaluate gradients, which scales linearly with the number of parameters. Motivated by this, we look at deep equilibrium models (DEQs), which mimic an infinite-depth, weight-tied network using a fraction of the memory by employing a root solver to find the fixed points of the network. In this work, we present Quantum Deep Equilibrium Models (QDEQs): a training paradigm that learns parameters of a quantum machine learning model given by a PQC using DEQs. To our knowledge, no work has yet explored the application of DEQs to QML models. We apply QDEQs to find the parameters of a quantum circuit in two settings: the first involves classifying MNIST-4 digits with 4 qubits; the second extends it to 10 classes of MNIST, FashionMNIST and CIFAR. We find that QDEQ is not only competitive with comparable existing baseline models, but also achieves higher performance than a network with 5 times more layers. This demonstrates that the QDEQ paradigm can be used to develop significantly more shallow quantum circuits for a given task, something which is essential for the utility of near-term quantum computers. Our code is available at https://github.com/martaskrt/qdeq.

Jakob Meldgaard Kjær, Lasse Kristensen, Mads Alberg Christensen

Access to quality travel time information for roads in a road network has become increasingly important with the rising demand for real-time travel time estimation for paths within road networks. In the context of the Danish road network (DRN) dataset used in this paper, the data coverage is sparse and skewed towards arterial roads, with a coverage of 23.88% across 850,980 road segments, which makes travel time estimation difficult. Existing solutions for graph-based data processing often neglect the size of the graph, which is an apparent problem for road networks with a large amount of connected road segments. To this end, we propose a framework for predicting road segment travel speed histograms for dataless edges, based on a latent representation generated by an adversarially regularized convolutional network. We apply a partitioning algorithm to divide the graph into dense subgraphs, and then train a model for each subgraph to predict speed histograms for the nodes. The framework achieves an accuracy of 71.5% intersection and 78.5% correlation on predicting travel speed histograms using the DRN dataset. Furthermore, experiments show that partitioning the dataset into clusters increases the performance of the framework. Specifically, partitioning the road network dataset into 100 clusters, with approximately 500 road segments in each cluster, achieves a better performance than when using 10 and 20 clusters.

Lasse Bjørn Kristensen, Matthias Degroote, Peter Wittek et al.

Artificial spiking neural networks have found applications in areas where the temporal nature of activation offers an advantage, such as time series prediction and signal processing. To improve their efficiency, spiking architectures often run on custom-designed neuromorphic hardware, but, despite their attractive properties, these implementations have been limited to digital systems. We describe an artificial quantum spiking neuron that relies on the dynamical evolution of two easy to implement Hamiltonians and subsequent local measurements. The architecture allows exploiting complex amplitudes and back-action from measurements to influence the input. This approach to learning protocols is advantageous in the case where the input and output of the system are both quantum states. We demonstrate this through the classification of Bell pairs which can be seen as a certification protocol. Stacking the introduced elementary building blocks into larger networks combines the spatiotemporal features of a spiking neural network with the non-local quantum correlations across the graph.