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International Journal of Theoretical Physics

A New Approach for Optimization of Distributed Quantum Circuits

Davood Dadkhah, Mariam Zomorodi Moghadam, Seyed Ebrahim Hosseini

Published Jul 27, 2021• 22 citations
Publisher

Abstract

Abstract In the present work, a novel approach was proposed to optimize the teleportation cost in Distributed Quantum Circuits (DQCs) by applying a new approach. To overcome the difficulty with keeping a large number of qubits next to each other, DQCs, as a well-known solution, have always been employed. In a distributed quantum system, qubits are transferred from a subsystem to another subsystem by a quantum protocol such as teleportation. First, we proposed a heuristic approach through which we could replace the equivalent circuits in the initial quantum circuit. Then, we used a genetic algorithm to partition the placement of qubits so that the number of teleportations could be optimized for the communications of a DQC. Finally, results showed that the proposed approach could impressively work.

DOI
10.1007/s10773-021-04904-y

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Abstract In the present work, a novel approach was proposed to optimize the teleportation cost in Distributed Quantum Circuits (DQCs) by applying a new approach. To overcome the difficulty with keeping a large number of qubits next to each other, DQCs, as a well-known solution, have always been employed. In a distributed quantum system, qubits are transferred from a subsystem to another subsystem by a quantum protocol such as teleportation. First, we proposed a heuristic approach through which we could replace the equivalent circuits in the initial quantum circuit. Then, we used a genetic algorithm to partition the placement of qubits so that the number of teleportations could be optimized for the communications of a DQC. Finally, results showed that the proposed approach could impressively work.
A new approach to reduce the teleportation cost and execution time in Distributed Quantum Circuits (DQCs) was proposed in the present paper. DQCs, a well-known solution, have been applied to solve the problem of maintaining a large number of qubits next to each other. In the distributed quantum system, the qubits are transferred to another subsystem by a quantum protocol like teleportation. Hence, a novel method was proposed to optimize the number of teleportation and to reduce the execution time for generating DQC. To this end, first, the quantum circuit was reordered according to the qubits placement to improve the computational execution time, and then the quantum circuit was modeled as a graph. Finally, we combined the genetic algorithm (GA) and the modified tabu search algorithm (MTS) to partition the graph model in order to obtain a distributed quantum circuit aimed at reducing the number of teleportation costs. A significant reduction in teleportation cost (TC) and execution time (ET) was obtained in benchmark circuits. In particular, we performed a more accurate optimization than the previous approaches, and the proposed approach yielded the best results for several benchmark circuits.
The presented work provides a procedure for optimizing the communication cost of a distributed quantum circuit (DQC) in terms of the number of qubit teleportations. Because of technology limitations which do not allow large quantum computers to work as a single processing element, distributed quantum computation is an appropriate solution to overcome this difficulty. Previous studies have applied ad-hoc solutions to distribute a quantum system for special cases and applications. In this study, a general approach is proposed to optimize the number of teleportations for a DQC consisting of two spatially separated and long-distance quantum subsystems. To this end, different configurations of locations for executing gates whose qubits are in distinct subsystems are considered and for each of these configurations, the proposed algorithm is run to find the minimum number of required teleportations. Finally, the configuration which leads to the minimum number of teleportations is reported. The proposed method can be used as an automated procedure to find the configuration with the optimal communication cost for the DQC.
Distributed quantum computing has been well-known for many years as a system composed of a number of small-capacity quantum circuits. Limitations in the capacity of monolithic quantum computing systems can be overcome by using distributed quantum systems which communicate with each other through known communication links. In our previous study, an algorithm with an exponential complexity was proposed to optimize the number of qubit teleportations required for the communications between two partitions of a distributed quantum circuit. In this work, a genetic algorithm is used to solve the optimization problem in a more efficient way. The results are compared with the previous study and we show that our approach works almost the same with a remarkable speed-up. Moreover, the comparison of the proposed approach based on GA with a random search over the search space verifies the effectiveness of GA.
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.
Distributed Quantum Computing (DQC) provides a means for scaling available quantum computation by interconnecting multiple quantum processor units (QPUs). A key challenge in this domain is efficiently allocating logical qubits from quantum circuits to the physical qubits within QPUs, a task known to be NP-hard. Traditional approaches, primarily focused on graph partitioning strategies, have sought to reduce the number of required Bell pairs for executing non-local CNOT operations, a form of gate teleportation. However, these methods have limitations in terms of efficiency and scalability. Addressing this, our work jointly considers gate and qubit teleportations introducing a novel meta-heuristic algorithm to minimise the network cost of executing a quantum circuit. By allowing dynamic reallocation of qubits along with gate teleportations during circuit execution, our method significantly enhances the overall efficacy and potential scalability of DQC frameworks. In our numerical analysis, we demonstrate that integrating qubit teleportations into our genetic algorithm for optimising circuit blocking reduces the required resources, specifically the number of EPR pairs, compared to traditional graph partitioning methods. Our results, derived from both benchmark and randomly generated circuits, show that as circuit complexity increases - demanding more qubit teleportations - our approach effectively optimises these teleportations throughout the execution, thereby enhancing performance through strategic circuit partitioning. This is a step forward in the pursuit of a global quantum compiler which will ultimately enable the efficient use of a 'quantum data center' in the future.
Distributed quantum computing (DQC) is a new paradigm aimed at scaling up quantum computing via the interconnection of smaller quantum processing units (QPUs). Shared entanglement allows teleportation of both states and gates between QPUs. This leads to an attractive horizontal scaling of quantum processing power that comes at the expense of the additional time and noise introduced by entanglement sharing protocols. Consequently, protocols for partitioning quantum circuits should aim to minimise the amount of entanglement-based communication required between distributed QPUs. Existing protocols tend to focus primarily on optimising entanglement costs for gate teleportation or state teleportation to cover operations between QPUs, rather than both at the same time. The most general form of the problem should treat gate and state teleportation on the same footing, allowing minimal cost circuit partitions through a combination of the two. This work introduces a graph-based formulation that allows joint optimisation of gate and state teleportation cost. The formulation permits lowe-bit cost for a variety of circuit types. Using a genetic algorithm, improved performance over state-of-the-art methods is obtained in terms of both average e-bit cost and time scaling.