A quantum dynamic programming circuit prepares the uniform superposition of all Hamiltonian cycles in polynomial gates, reducing Grover-based TSP search complexity to O(sqrt((N-1)!).
The above enumeration process has a terrible time complexity of O((N − 1)!), which makes it a NP-hard problem to find all valid HCs [38]
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A quantum speedup algorithm for TSP based on quantum dynamic programming with very few qubits
A quantum dynamic programming circuit prepares the uniform superposition of all Hamiltonian cycles in polynomial gates, reducing Grover-based TSP search complexity to O(sqrt((N-1)!).