Traveling Salesman Problem Solved with One Qbit

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 tsp

from qiskit.optimization.applications.ising.common import sample_most_likely

from qiskit.optimization.algorithms import MinimumEigenOptimizer

from qiskit.aqua.algorithms import VQE

from qiskit.aqua.components.optimizers import COBYLA

from qiskit.aqua.components.variational_forms import RY

from 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.

Agreed. I don't know that the algorithm used in the article to analyze their Bloch sphere representation is published. I thought i was interesting that they compare it to Grover's algorithm.