I meant to add: To solve TSP using Qiskit, you can follow the steps outlined in the Qiskit Optimization documentation. The example below demonstrates how to encode the TSP as a Quadratic Unconstrained Binary Optimization (QUBO) problem and then solve it using a quantum algorithm like Variational Quantum Eigensolver (VQE).
# Import necessary libraries
from qiskit.optimization.applications.ising import tspfrom qiskit.optimization.applications.ising.common import sample_most_likelyfrom qiskit.optimization.algorithms import MinimumEigenOptimizerfrom qiskit.aqua.algorithms import VQEfrom qiskit.aqua.components.optimizers import COBYLAfrom qiskit.aqua.components.variational_forms import RYfrom qiskit import Aer
# Define the distance matrix for the TSP problem
distance_matrix = [ [0, 207, 92, 131], [207, 0, 300, 350], [92, 300, 0, 82], [131, 350, 82, 0]]
# Number of cities
num_cities = len(distance_matrix)
# Convert the TSP problem to an Ising Hamiltonian
tsp_qubo, offset = tsp.get_tsp_qubo(num_cities, distance_matrix)
# Set up the VQE algorithm
var_form = RY(num_cities**2, reps=3)optimizer = COBYLA(maxiter=100)vqe = VQE(var_form, optimizer, 'paulis', callback=callback_fn)
# Use the VQE algorithm to find the minimum eigenvalue of the Hamiltonian
algo = MinimumEigenOptimizer(vqe)result = algo.solve(tsp_qubo)
# Decode the result to get the optimal route
x = sample_most_likely(result.eigenstate)sol = tsp.sample_most_likely(x)
# Print the optimal route and its cost
print("Optimal route: ", sol)print("Total distance: ", tsp.tsp_value(sol, num_cities, distance_matrix))
This example uses a distance matrix for four cities and applies the VQE algorithm to find the optimal route. The tsp.get_tsp_qubo function converts the TSP problem into a QUBO problem, which is then solved using VQE. The optimal route and its total distance are printed at the end.
Note that the number of qubits required for this problem is (n−1) squared, where n is the number of cities. For four cities, this results in 9 qubits.
