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This article aims to bring quantum computing to robotics. A quantum algorithm is developed to minimize the distance traveled in warehouses and distribution centers where order picking is applied. For this, a proof of concept is proposed through a Raspberry Pi 4, generating a quantum combinatorial optimization algorithm that saves the distance travelled and the batch of orders to be made. In case of computational need, the robot will be able to parallelize part of the operations in hybrid computing (quantum + classical), accessing CPUs and QPUs distributed in a public or private cloud. We developed a stable environment (ARM64) inside the robot (Raspberry) to run gradient operations and other quantum algorithms on IBMQ, Amazon Braket (D-Wave), and Pennylane locally or remotely. The proof of concept, when run in the above stated quantum environments, showed the execution time of our algorithm with different public access simulators on the market, computational results of our picking and batching algorithm, and analyze the quantum real-time execution. Our findings are that the behavior of the Amazon Braket D-Wave is better than Gate-based Quantum Computing over 20 qubits, and that AWS-Braket has better time performance than Qiskit or Pennylane.

We propose a new Quadratic Unconstrained Binary Optimization (QUBO) formulation of the Travelling Salesman Problem (TSP), with which we overcame the best formulation of the Vehicle Routing Problem (VRP) in terms of the minimum number of necessary variables. After, we will present a detailed study of the constraints subject to the new TSP model and benchmark it with MTZ and native formulations. Finally, we will test whether the correctness of the formulation by entering it into a QUBO problem solver. The solver chosen is a D-Wave_2000Q6 quantum computer simulator due to the connection between Quantum Annealing and QUBO formulations.

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