Quantum circuit for spatial optimization

Mengyu Guo, Shaowen Wang

Amr Magdy, Ibrahim Sabek, Moustafa A. Youssef

Quantum computing has shown significant potential for addressing complex optimization and computationally intensive problems across a range of domains. Its adoption in spatial data applications presents substantial opportunities for advancing spatial computing. This tutorial provides an in-depth introduction to quantum computing, covering both the quantum circuit model (gate model) and quantum annealing, and discusses their applications in spatial computing. The tutorial is organized into three parts. The first part introduces fundamental concepts in quantum computing. The second part presents quantum gates, highlighting examples of basic gates and their use in circuits. The third part introduces quantum annealing, including Quadratic Unconstrained Binary Optimization (QUBO) modeling and hybrid solvers that combine the power of Quantum Processing Units (QPUs) with classical CPUs. The tutorial also points readers to key resources at the intersection of quantum computing and spatial computing.

George A. Kevrekidis

Jin Yan Zheng, Qing Zhong Gao, MACIEJ J. OGORZAŁEK +2 more

This article proposes a quantum spatial graph convolutional neural network (QSGCN) model that is implementable on quantum circuits, providing a novel avenue to processing non-Euclidean type data based on the state-of-the-art parameterized quantum circuit (PQC) computing platforms. Four basic blocks are constructed to formulate the whole QSGCN model, including the quantum encoding, the quantum graph convolutional layer, the quantum graph pooling layer, and the network optimization. In particular, the trainability of the QSGCN model is analyzed through discussions on the barren plateau phenomenon. Simulation results from various types of graph data are presented to demonstrate the learning, generalization, and robustness capabilities of the proposed quantum neural network (QNN) model.

Ansh Bansal

Arpan Bhattacharyya, Pratik Nandy, Aninda Sinha

We propose a modification to Nielsen's circuit complexity for Hamiltonian simulation using the Suzuki-Trotter (ST) method, which provides a network like structure for the quantum circuit. This leads to an optimized gate counting linear in the geodesic distance and spatial volume, unlike in the original proposal. The optimized ST iteration order is correlated with the error tolerance and plays the role of an anti-de Sitter radial coordinate. The density of gates is shown to be monotonic with the tolerance and a holographic interpretation using path-integral optimization is given.