Related papers: Solving graph problems using permutation-invariant…

In the Graph Isomorphism problem two N-vertex graphs G and G' are given and the task is to determine whether there exists a permutation of the vertices of G that preserves adjacency and transforms G into G'. If yes, then G and G' are said…

The process of translating a quantum algorithm into a form suitable for implementation on a quantum computing platform is crucial but yet challenging. This entails specifying quantum operations with precision, a typically intricate task. In…

Quantum computing has been a prominent research area for decades, inspiring transformative fields such as quantum simulation, quantum teleportation, and quantum machine learning (QML), which are undergoing rapid development. Within QML,…

Quantum circuit mapping is a crucial process in the quantum circuit compilation pipeline, facilitating the transformation of a logical quantum circuit into a list of instructions directly executable on a target quantum system. Recent…

Several variational quantum circuit approaches to machine learning have been proposed in recent years, with one promising class of variational algorithms involving tensor networks operating on states resulting from local feature maps. In…

Machine learning techniques have led to broad adoption of a statistical model of computing. The statistical distributions natively available on quantum processors are a superset of those available classically. Harnessing this attribute has…

Incorporating nonlinearity into quantum machine learning is essential for learning a complicated input-output mapping. We here propose quantum algorithms for nonlinear regression, where nonlinearity is introduced with feature maps when…

Random quantum circuits take an input quantum state and randomize it. This is a task with a growing number of identified uses in quantum information processing. We suggest a scheme to implement random circuits in a weighted graph state. The…

In this work, we propose a parameterised quantum circuit learning approach to point set matching problem. In contrast to previous annealing-based methods, we propose a quantum circuit-based framework whose parameters are optimised via…

From early image processing to modern computational imaging, successful models and algorithms have relied on a fundamental property of natural signals: symmetry. Here symmetry refers to the invariance property of signal sets to…

We propose a novel benchmarking methodology for graph neural networks (GNNs) based on the graph alignment problem, a combinatorial optimization task that generalizes graph isomorphism by aligning two unlabeled graphs to maximize overlapping…

We perform a massive evaluation of neural networks with architectures corresponding to random graphs of various types. We investigate various structural and numerical properties of the graphs in relation to neural network test accuracy. We…

The quantum hidden subgroup approach is an actively studied approach to solve combinatorial problems in quantum complexity theory. With the success of the Shor's algorithm, it was hoped that similar approach may be useful to solve the other…

Quantum annealing is a proposed combinatorial optimization technique meant to exploit quantum mechanical effects such as tunneling and entanglement. Real-world quantum annealing-based solvers require a combination of annealing and classical…

Circuit design for quantum machine learning remains a formidable challenge. Inspired by the applications of tensor networks across different fields and their novel presence in the classical machine learning context, one proposed method to…

Quantum machine learning (QML) has attracted growing interest with the rapid parallel advances in large-scale classical machine learning and quantum technologies. Similar to classical machine learning, QML models also face challenges…

Representing and learning from graphs is essential for developing effective machine learning models tailored to non-Euclidean data. While Graph Neural Networks (GNNs) strive to address the challenges posed by complex, high-dimensional graph…

We review quantum chaos on graphs. We construct a unitary operator which represents the quantum evolution on the graph and study its spectral and wavefunction statistics. This operator is the analogue of the classical evolution operator on…

The symmetry of complex networks is a global property that has recently gained attention since MacArthur et al. 2008 showed that many real-world networks contain a considerable number of symmetries. These authors work with a very strict…

Quantum machines are among the most promising technologies expected to provide significant improvements in the following years. However, bridging the gap between real-world applications and their implementation on quantum hardware is still…