An MINLP Model for Scheduling and Placement of Quantum Circuits with a Heuristic Solution Approach

Recent works on quantum physical design have pushed the scheduling and placement of quantum circuit into their prominent positions. In this article, a mixed integer nonlinear programming model is proposed for the placement and scheduling of quantum circuits in such a way that latency is minimized. The proposed model determines locations of gates and the sequence of operations. The proposed model is proved reducible to a quadratic assignment problem which is a well-known NP-complete combinatorial optimization problem. Since it is impossible to find the optimal solution of this NP-complete problem for large quantum circuits within a reasonable amount of time, a metaheuristic solution method is developed for the proposed model. Some experiments are conducted to evaluate the performance of the developed solution approach. Experimental results show that the proposed approach improves average latency by about 24.09% for the attempted benchmarks.