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The vehicle routing problem with time windows (VRPTW) is a commonoptimization problem faced within the logistics industry. In this work, weexplore the use of a previously-introduced qubit encoding scheme to reduce thenumber of binary variables, to evaluate the effectiveness of NISQ devices whenapplied to industry relevant optimization problems. We apply a quantumvariational approach to a testbed of multiple VRPTW instances ranging from 11to 3964 routes. These intances were formulated as quadratic unconstrainedbinary optimization (QUBO) problems based on realistic shipping scenarios. Wecompare our results with standard binary-to-qubit mappings after executing onsimulators as well as various quantum hardware platforms, including IBMQ, AWS(Rigetti), and IonQ. These results are benchmarked against the classicalsolver, Gurobi. Our approach can find approximate solutions to the VRPTWcomparable to those obtained from quantum algorithms using the full encoding,despite the reduction in qubits required. These results suggest that using theencoding scheme to fit larger problem sizes into fewer qubits is a promisingstep in using NISQ devices to find approximate solutions for industry-basedoptimization problems, although additional resources are still required to ekeout the performance from larger problem sizes.

Qubit efficient quantum algorithms for the vehicle routing problem on NISQ processors