Owing to the advancements in low-power consumption processors and high-power storage in a small-sized battery, the cost of handheld mobile devices, eg, mobiles, tabs, or personal digital assistants, have reduced to a great extent. This has enabled people to have at least 1 smartphone in general with this number increasing exponentially. However, the increasing use of these mobile devices results in an equal increase in the underused processing capacity of these devices too. This encourages the research aiming to use this processing power by forming a mobile computational grid. Because of the inherent limitations of bandwidth, battery, and computational power, job scheduling on these devices demands an efficient scheduling approach to harness the true potential of the grid. The problem becomes even more challenging considering the dynamic nature of these mobile devices. Job scheduling being nondeterministic polynomial time-complete allows the use of evolutionary approaches by exploring and exploiting the search space efficiently. The exploration gets boosted even more with the use of quantum-computing concepts. This work proposes a quantum-inspired Newtonian approach of attraction based on gravitational search algorithm for scheduling the jobs on mobile computational grid. Simulation study has been performed to evaluate the performance of the model over various dimensions. A comparative study has been performed with quantum-genetic algorithm. Simulation result establishes the effectiveness of model under various test conditions. KEYWORDS genetic algorithm (GA), gravitational search algorithm (GSA), mobile grid computing (MGC), quantum computing (QC), quantum-inspired genetic algorithm (QGA), turnaround time (TAT)