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)!).
It is clear that a quantum state encoding a feasible solution should rep- resent a N -cycle as an element of N -order permutation group
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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)!).