![]() There are different types of errors that may occur, such as errors in the ion’s state’s population or errors in the quantum state’s phase. The physical interactions that underlie the occurrence of noise depend on the implementation of the quantum computer. Studying the effects of noise in quantum information is necessary, as they have undesirable but inevitable effects on the quantum system, which leads to decoherence. Due to the diversity of tasks where QRW is used, a variety of experimental implementations have been considered, such as optical quantum computers, optical lattice, circuit QED, and ion traps. The latter algorithm is used to search different topologies, such as simplex and star, graphs, trees, square grids, and hypercubes. ![]() ![]() Faster hitting time and the ability to traverse arbitrary structures make QRW a good basis for a variety of quantum algorithms, such as the one for finding triangles in a graph, calculating Boolean formulas, quantum unsupervised machine learning, quantum neural networks, quantum signature schemes, and the quantum random walk search algorithm (QRWS). Later, QRW was used to study more complex structures, such as square and hexagonal grids, cylinders, torus, and hypercubes. This was initially tested on simple structures such as line and circle. Quantum interferences allow quadratically faster graph traversal compared to the classical walk. The Quantum Random Walk (QRW) is one of them. Many examples of the differences between the classical and quantum worlds can be given.
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