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

Ghodsollahee, Ismail; Davarzani, Zohreh; Zomorodi‐Moghadam, Mariam; Pławiak, Paweł; Houshmand, Monireh; Houshmand, Mahboobeh

doi:10.1007/s11128-021-03170-5

Cited by 12 publications

(4 citation statements)

References 41 publications

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“…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.…”

Section: Related Workmentioning

confidence: 99%

A hierarchical approach for building distributed quantum systems

Davarzani

Zomorodi‐Moghadam

Houshmand

2022

Sci Rep

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In this paper, a multi-layer hierarchical architecture is proposed for distributing quantum computation. In a distributed quantum computing (DQC), different units or subsystems communicate by teleportation in order to transfer quantum information. Quantum teleportation requires classical and quantum resources and hence, it is essential to minimize the number of communications among these subsystems. To this end, a two-level hierarchical optimization method is proposed to distribute the qubits among different parts. In Level I, an integer linear programming model is presented to distribute a monolithic quantum system into K balanced partitions which results in the minimum number of non-local gates. When a qubit is teleported to a destination part, it can be used optimally by other gates without being teleported back to the destination part. In Level II, a data structure is proposed for quantum circuit and a recursive function is applied to minimize the number of teleportations. Experimental results show that the proposed approach outperforms the previous ones.

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Section: Related Workmentioning

confidence: 99%

A hierarchical approach for building distributed quantum systems

Davarzani

Zomorodi‐Moghadam

Houshmand

2022

Sci Rep

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“…Metaheuristic optimization algorithms such as GA [39] have been widely used in solving some important optimization problems in, e.g., the field of quantum information and computation, such as in distributed quantum computing [40][41][42][43], in the design and the optimization of quantum circuits [44][45][46], and in finding stabilizers of a given subspace [47], etc.…”

Section: Introductionmentioning

confidence: 99%

A Modified Quantum-Inspired Genetic Algorithm Using Lengthening Chromosome Size and an Adaptive Look-Up Table to Avoid Local Optima

Hakemi,

Houshmand,

Hosseini

et al. 2023

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The quantum-inspired genetic algorithm (QGA), which combines quantum mechanics concepts and GA to enhance search capability, has been popular and provides an efficient search mechanism. This paper proposes a modified QGA, called dynamic QGA (DQGA). The proposed algorithm utilizes a lengthening chromosome strategy for a balanced and smooth transition between exploration and exploitation phases to avoid local optima and premature convergence. Apart from that, a novel adaptive look-up table for rotation gates is presented to boost the algorithm’s optimization abilities. To evaluate the effectiveness of these ideas, DQGA is tested by various mathematical benchmark functions as well as real-world constrained engineering problems against several well-known and state-of-the-art algorithms. The obtained results indicate the merits of the proposed algorithm and its superiority for solving multimodal benchmark functions and real-world constrained engineering problems.

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“…In addition, Houshmand et al [16] proposed an evolutionary algorithm, and Dadkhah et al [17] proposed a genetic algorithm to minimize the communication cost between two partitions inside a DQC design. Recently, based on the connectivity matrix model of QCs, Ghodsollahee et al [18] further proposed a two-phase algorithm to minimize the communication cost between two partitions inside a DQC design. However, these proposed algorithms do not consider the multiple-way partitioning on the minimization of the communication cost in a DQC design.…”

Section: Introductionmentioning

confidence: 99%

Fuzzy-Based Balanced Partitioning Under Capacity and Size-Tolerance Constraints in Distributed Quantum Circuits

Yan

2023

IEEE Trans. Quantum Eng.

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It is important for the design of a distributed quantum circuit (DQC) to minimize the communication cost in k-way balanced partitioning. In this article, given an original quantum circuit (QC), a partitioning number k, the maximum capacity δ inside each partition, and the maximum size tolerance γ between two partitions, a new k-way (δ, γ )-balanced partitioning problem can be formulated as a k-way partitioning problem under the capacity constraint δ and the size-tolerance constraint γ , and a fuzzy-based partitioning algorithm can be proposed to minimize the communication cost in k-way (δ, γ )-balanced partitioning for a DQC design. First, an edge-weighted connection graph can be constructed from the gates in a given QC. Furthermore, based on the estimation of the probabilistic connection strength between two vertices in the connection graph and the initial k-way partitioning result in the connection graph, the fuzzy memberships on k clusters can be generated in fuzzy k-means graph clustering. Finally, based on the fuzzy memberships on k clusters in the connection graph, the maximum capacity inside each partition, and the maximum size tolerance between two partitions, all the vertices in the connection graph can be assigned onto k partitions to minimize the communication cost in k-way (δ, γ )-balanced partitioning. Compared with Daei's recursive Kernighan-Lin-based algorithm in four-way balanced partitioning, the experimental results show that the proposed fuzzy-based partitioning algorithm with three size-tolerance constraints γ = 1, γ = 2, and γ = 3 can use 58.3%, 61.3%, and 64.5% of CPU time to reduce 16.1%, 21.2%, and 24.6% of the communication cost for the eight tested circuits on the average, respectively. Compared with the modified partitioning algorithm from Dadkhah's partitioning algorithm in three-way, four-way, or five-way balanced partitioning, the experimental results show that the proposed fuzzy-based partitioning algorithm with the size-tolerance constraint γ = 3 can use 35.0% of CPU time to reduce 11.1% of the communication cost for the eight tested circuits on the average, respectively. INDEX TERMSBalanced partitioning, communication cost, distributed quantum circuit (DQC), fuzzy kmeans graph clustering (FKGC). Engineering uantum Transactions on IEEE Yan: FUZZY-BASED BALANCED PARTITIONING UNDER CAPACITY AND SIZE-TOLERANCE CONSTRAINTS IN DQCS

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

Cited by 12 publications

References 41 publications

A hierarchical approach for building distributed quantum systems

A hierarchical approach for building distributed quantum systems

A Modified Quantum-Inspired Genetic Algorithm Using Lengthening Chromosome Size and an Adaptive Look-Up Table to Avoid Local Optima

Fuzzy-Based Balanced Partitioning Under Capacity and Size-Tolerance Constraints in Distributed Quantum Circuits

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