Connectivity matrix model of quantum circuits and its application to distributed quantum circuit optimization

Abstract

As quantum computation grows, the number of qubits involved in a given quantum computer increases. But due to the physical limitations in the number of qubits of a single quantum device, the computation should be performed in a distributed system. In this paper, a new model of quantum computation based on the matrix representation of quantum circuits is proposed. Then, using this model, we propose a novel approach for reducing the number of teleportations in a distributed quantum circuit. The proposed method consists of two phases: the pre-processing phase and the optimization phase. In the pre-processing phase, it considers the bi-partitioning of quantum circuits by Non-Dominated Sorting Genetic Algorithm (NSGA-III) to minimize the number of global gates and to distribute the quantum circuit into two balanced parts with equal number of qubits and minimum number of global gates. In the optimization phase, two heuristics named Heuristic I and Heuristic II are proposed to optimize the number of teleportations according to the partitioning obtained from the pre-processing phase. Finally, the proposed approach is evaluated on many benchmark quantum circuits. The results of these evaluations show an average of 22.16% improvement in the teleportation cost of the proposed approach compared to the existing works in the literature.

A hierarchical approach for building distributed quantum systems

“…The main purpose of the algorithm was to determine which qubit of a non-local gate should be teleported to the other system and when the teleported qubit should be returned back to its home partition. Also, in our another work 41 , we presented a two-phase algorithm based on NSGA-II to bi-partition the qubits in the first phase and suggested two heuristics to optimize the number of non-local gates in the second phase. The authors in 42 , 44 also discussed the issue of reducing communication cost in a distributed quantum circuit composing of up to three-qubit gates and presented a new heuristic method to solve it.…”

Reordering and Partitioning of Distributed Quantum Circuits

“…Afterward, we implemented our optimization approach in several distributed quantum circuits. In this paper, as a benchmark, quantum circuits were selected from the RevLib website [13] and Quipper's library [14], [15] to test the proposed optimization. In all circuits, we focused on the number of teleportation and the execution time to optimize for the distributed quantum circuit.…”