Related papers: Do quantum linear solvers offer advantage for netw…
Transformers are increasingly employed for graph data, demonstrating competitive performance in diverse tasks. To incorporate graph information into these models, it is essential to enhance node and edge features with positional encodings.…
In this work, we propose novel families of positional encodings tailored to graph neural networks obtained with quantum computers. These encodings leverage the long-range correlations inherent in quantum systems that arise from mapping the…
Linear system solvers are widely used in scientific computing, with the primary goal of solving linear system problems. Classical iterative algorithms typically rely on the conjugate gradient method. The rise of quantum computing has…
The Harrow-Hassidim-Lloyd algorithm is intended for solving the system of linear equations on quantum devices. The exponential advantage of the algorithm comes with four caveats. We present a numerical study of the performance of the…
Variational Quantum Algorithms (VQAs) have emerged as promising methods for tackling complex problems on near-term quantum devices. Among these algorithms, the Variational Quantum Linear Solver (VQLS) addresses linear systems of the form…
The analysis of the computational power of single-query quantum algorithms is important because they must extract maximal information from one oracle call, revealing fundamental limits of quantum advantage and enabling optimal,…
The hybrid quantum-classical learning scheme provides a prominent way to achieve quantum advantages on near-term quantum devices. A concrete example towards this goal is the quantum neural network (QNN), which has been developed to…
We introduce a family of identities that express general linear non-unitary evolution operators as a linear combination of unitary evolution operators, each solving a Hamiltonian simulation problem. This formulation can exponentially…
The recent availability of the first commercial quantum computers has provided a promising tool to tackle NP hard problems which can only be solved heuristically with present techniques. However, it is unclear if the current state of…
Although the Harrow-Hassidim-Lloyd (HHL) algorithm offers an exponential speedup in system size for treating linear equations of the form $A\vec{x}=\vec{b}$ on quantum computers when compared to their traditional counterparts, it faces a…
Building large-scale quantum computers, essential to demonstrating quantum advantage, is a key challenge. Quantum Networks (QNs) can help address this challenge by enabling the construction of large, robust, and more capable quantum…
Solving linear systems is at the foundation of many algorithms. Recently, quantum linear system algorithms (QLSAs) have attracted great attention since they converge to a solution exponentially faster than classical algorithms in terms of…
Quantum algorithms based on quantum kernel methods have been investigated previously [1]. A quantum advantage is derived from the fact that it is possible to construct a family of datasets for which, only quantum processing can recognise…
Quantum Support Vector Machines (QSVM) play a vital role in using quantum resources for supervised machine learning tasks, such as classification. However, current methods are strongly limited in terms of scalability on Noisy Intermediate…
Binary Neural Networks are a promising technique for implementing efficient deep models with reduced storage and computational requirements. The training of these is however, still a compute-intensive problem that grows drastically with the…
In this paper, we model and solve a fundamental power system problem, i.e., DC power flow, using a practical quantum computer. The Harrow-Hassidim-Lloyd (HHL) quantum algorithm is used to solve the DC power flow problem. The HHL algorithm…
Quantum walks provide a natural framework to approach graph problems with quantum computers, exhibiting speedups over their classical counterparts for tasks such as the search for marked nodes or the prediction of missing links.…
Solving systems of linear equations is one of the most important primitives in quantum computing that has the potential to provide a practical quantum advantage in many different areas, including in optimization, simulation, and machine…
Quantum theory has shown its superiority in enhancing machine learning. However, facilitating quantum theory to enhance graph learning is in its infancy. This survey investigates the current advances in quantum graph learning (QGL) from…
The limited capabilities of current quantum hardware significantly constrain the scale of experimental demonstrations of most quantum algorithmic primitives. This makes it challenging to perform benchmarking of the current hardware using…