Many large image processing and data processing scenarios can soon develop into maze problems requiring, say, finding the longest possible path, which are unresponsive, intractable, and challenging to analyze! Such maze problems, of which the traveling salesman decision problem is a special case, are of the Non-determinate Polynomial (NPcomplete) class of problems that are often impossible to solve with finite time and storage. We propose a novel methodology to approach this class of NP-complete problems. We convert a suitably formulated maze problem into a Quantum Search Problem (QSP), and the desired solutions are then sought using the iterative Grover’s Search Algorithm. Thus, we reformulate the entire class of such NP-problems into QSPs. Our current solution deals with two-dimensional perfect mazes with no closed loops. We encode all possible individual paths from the starting point of the maze into a quantum register. A quantum fitness operator applied to the register encodes each qubit with its fitness value. We propose the design of an optical oracle that marks all entities above a certain fitness value and uses the Grover search algorithm to find the optimal marked state in an iterative manner.
Debabrata Goswami, "Sensing the insensible using optical schemes: converting the maze problem into a quantum search problem," Proc. SPIE 11388, Image Sensing Technologies: Materials, Devices, Systems, and Applications VII, 113880L (Presented at SPIE Defense + Commercial Sensing: April 28, 2020; Published: 23 April 2020); https://doi.org/10.1117/12.2563658.
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