Track finding is a complex optimization problem,originally introduced in particle physics for the reconstruction of the trajectories of particles.A track is typically composed of several consecutive segments,which tog...Track finding is a complex optimization problem,originally introduced in particle physics for the reconstruction of the trajectories of particles.A track is typically composed of several consecutive segments,which together form a smooth curve without any bifurcations.In this paper,we investigate various modeling approaches to assess their effectiveness and impact when applied to track finding,using both quantum and classical methods.We present implementations of three classical models using CPLEX,two quantum models on actual D-Wave quantum computers,and one quantummodel on a D-Wave simulator.The results show that,while CPLEX provides better results than D-Wave on small instances,D-Wave is able to propose solutions in shorter computation times for large instances,although the gap with the optimal solution tends to increase.To the best of our knowledge,this is the first numerical study comparing a non-quantum approach based on classical algorithms(Simplex and Branch and Bound)used in commercial software with a quantum approach offered by D-Wave.The results do not show the quantum supremacy typically expected,but they do demonstrate that quantum solutions can be competitive with classical approaches,and even more efficient than some classical modeling and solving methods.展开更多
文摘Track finding is a complex optimization problem,originally introduced in particle physics for the reconstruction of the trajectories of particles.A track is typically composed of several consecutive segments,which together form a smooth curve without any bifurcations.In this paper,we investigate various modeling approaches to assess their effectiveness and impact when applied to track finding,using both quantum and classical methods.We present implementations of three classical models using CPLEX,two quantum models on actual D-Wave quantum computers,and one quantummodel on a D-Wave simulator.The results show that,while CPLEX provides better results than D-Wave on small instances,D-Wave is able to propose solutions in shorter computation times for large instances,although the gap with the optimal solution tends to increase.To the best of our knowledge,this is the first numerical study comparing a non-quantum approach based on classical algorithms(Simplex and Branch and Bound)used in commercial software with a quantum approach offered by D-Wave.The results do not show the quantum supremacy typically expected,but they do demonstrate that quantum solutions can be competitive with classical approaches,and even more efficient than some classical modeling and solving methods.
