PSO inspired global neighbourhood based Qubit mapping: a new approach

Abstract

Due to limited connectivity between physical qubits of quantum devices, it is a real challenge to map a logical circuit to physical hardware device. To ensure proper mapping of logical qubits to physical qubits, this research introduces particle swarm optimization (PSO) inspired global neighbourhood based (GNB) qubit mapping. Starting with an empty initial mapping, degree of each logical qubit of the circuit is computed. Degree of a qubit refers to the number of qubits with which it is connected in the entire circuit. The proposed technique maps the highest degree qubit and its global neighbours initially based on the designed heuristic and then maps the remaining logical qubits in a way that minimizes the total distance to already allocated physical qubits. The concept of "global neighbours" refers to all interconnected qubits within a circuit, regardless of the direction of their connections. Thus, the proposed fitness ensures minimization of the sum of the swap count and the degree difference between logical and mapped physical qubits for the complete mapping. The swap count is determined by the distance between mapped physical qubits for each gate. PSO based implementation of GNB yields efficient mapping of benchmark circuits to physical hardware of IBM QX5 in feasible execution time. Number of operations, depth and execution time (in second) of the mapped circuit obtained from PSO is compared with the previous methodologies and also with Genetic Algorithm (GA). PSO exhibits rapid convergence speed and thus showcase its ability to find near-optimal solution in lesser time.