Variational decision diagrams for quantum-inspired machine learning applications

Decision diagrams (DDs) have emerged as an efficient tool for simulating quantum circuits due to their capacity to exploit data redundancies in quantum states and quantum operations, enabling the efficient computation of probability amplitudes. However, their application in quantum machine learning (QML) has remained unexplored. This paper introduces variational decision diagrams (VDDs), a novel graph structure that combines the structural benefits of DDs with the adaptability of variational methods for efficiently representing quantum states. We investigate the trainability of VDDs by applying them to the ground state estimation problem for transverse-field Ising and Heisenberg Hamiltonians. Analysis of gradient variance suggests that training VDDs is possible, as no signs of vanishing gradients--also known as barren plateaus--are observed. This work provides new insights into the use of decision diagrams in QML as an alternative to design and train variational ans\"atze.

MEMO-QCD: Quantum Density Estimation through Memetic Optimisation for Quantum Circuit Design

This paper presents a strategy for efficient quantum circuit design for density estimation. The strategy is based on a quantum-inspired algorithm for density estimation and a circuit optimisation routine based on memetic algorithms. The model maps a training dataset to a quantum state represented by a density matrix through a quantum feature map. This training state encodes the probability distribution of the dataset in a quantum state, such that the density of a new sample can be estimated by projecting its corresponding quantum state onto the training state. We propose the application of a memetic algorithm to find the architecture and parameters of a variational quantum circuit that implements the quantum feature map, along with a variational learning strategy to prepare the training state. Demonstrations of the proposed strategy show an accurate approximation of the Gaussian kernel density estimation method through shallow quantum circuits illustrating the feasibility of the algorithm for near-term quantum hardware.

Road Network Deterioration Monitoring Using Aerial Images and Computer Vision

Road maintenance is an essential process for guaranteeing the quality of transportation in any city. A crucial step towards effective road maintenance is the ability to update the inventory of the road network. We present a proof of concept of a protocol for maintaining said inventory based on the use of unmanned aerial vehicles to quickly collect images which are processed by a computer vision program that automatically identifies potholes and their severity. Our protocol aims to provide information to local governments to prioritise the road network maintenance budget, and to be able to detect early stages of road deterioration so as to minimise maintenance expenditure.

An Empirical Study of Quantum Dynamics as a Ground State Problem with Neural Quantum States

Neural quantum states are variational wave functions parameterised by artificial neural networks, a mathematical model studied for decades in the machine learning community. In the context of many-body physics, methods such as variational Monte Carlo with neural quantum states as variational wave functions are successful in approximating, with great accuracy, the ground-state of a quantum Hamiltonian. However, all the difficulties of proposing neural network architectures, along with exploring their expressivity and trainability, permeate their application as neural quantum states. In this paper, we consider the Feynman-Kitaev Hamiltonian for the transverse field Ising model, whose ground state encodes the time evolution of a spin chain at discrete time steps. We show how this ground state problem specifically challenges the neural quantum state trainability as the time steps increase because the true ground state becomes more entangled, and the probability distribution starts to spread across the Hilbert space. Our results indicate that the considered neural quantum states are capable of accurately approximating the true ground state of the system, i.e., they are expressive enough. However, extensive hyper-parameter tuning experiments point towards the empirical fact that it is poor trainability--in the variational Monte Carlo setup--that prevents a faithful approximation of the true ground state.

Optimisation-free Classification and Density Estimation with Quantum Circuits

We demonstrate the implementation of a novel machine learning framework for probability density estimation and classification using quantum circuits. The framework maps a training data set or a single data sample to the quantum state of a physical system through quantum feature maps. The quantum state of the arbitrarily large training data set summarises its probability distribution in a finite-dimensional quantum wave function. By projecting the quantum state of a new data sample onto the quantum state of the training data set, one can derive statistics to classify or estimate the density of the new data sample. Remarkably, the implementation of our framework on a real quantum device does not require any optimisation of quantum circuit parameters. Nonetheless, we discuss a variational quantum circuit approach that could leverage quantum advantage for our framework.

Supervised Learning with Quantum Measurements

This letter reports a novel method for supervised machine learning based on the mathematical formalism that supports quantum mechanics. The method uses projective quantum measurement as a way of building a prediction function. Specifically, the correlation between input and output variables is represented as the state of a bipartite quantum system. The state is estimated from training samples through an averaging process that produces a density matrix. Prediction of the label for a new sample is made by performing a projective measurement on the bipartite system with an operator, prepared from the new input sample, and applying a partial trace to obtain the state of the subsystem representing the outputs. The method can be seen as a generalization of Bayesian inference classification and as a type of kernel-based learning method. One remarkable characteristic of the method is that it does not require learning any parameters through optimization. We illustrate the method with different 2-D classification benchmark problems and different quantum information encodings.

Event detection in Colombian security Twitter news using fine-grained latent topic analysis

Cultural and social dynamics are important concepts that must be understood in order to grasp what a community cares about. To that end, an excellent source of information on what occurs in a community is the news, especially in recent years, when mass media giants use social networks to communicate and interact with their audience. In this work, we use a method to discover latent topics in tweets from Colombian Twitter news accounts in order to identify the most prominent events in the country. We pay particular attention to security, violence and crime-related tweets because of the violent environment that surrounds Colombian society. The latent topic discovery method that we use builds vector representations of the tweets by using FastText and finds clusters of tweets through the K-means clustering algorithm. The number of clusters is found by measuring the $C_V$ coherence for a range of number of topics of the Latent Dirichlet Allocation (LDA) model. We finally use Uniform Manifold Approximation and Projection (UMAP) for dimensionality reduction to visualise the tweets vectors. Once the clusters related to security, violence and crime are identified, we proceed to apply the same method within each cluster to perform a fine-grained analysis in which specific events mentioned in the news are grouped together. Our method is able to discover event-specific sets of news, which is the baseline to perform an extensive analysis of how people engage in Twitter threads on the different types of news, with an emphasis on security, violence and crime-related tweets.