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IEEE Access

Quantum Multi-Strategy Fusion Mapping Optimization: An Algorithm for Quantum Circuit

Zhenguo Yuan, Jiepeng Wang, Hui Li, Yutong Chen

Published Jan 1, 2025• 1 citation
Publisher

Abstract

In response to the current challenges in quantum circuit mapping algorithms, such as low mapping quality, insufficient diversity, and the difficulty in balancing mapping quality and diversity, a Quantum Multi-Strategy Fusion Mapping Optimization Algorithm (QMS-FMO) is proposed in this paper. This algorithm enhances population diversity by integrating the neighboring gate strategy of Genetic Algorithm-based Quantum Circuit Mapping (GAQCM), the quantum state characteristics of QPSO, and the parameter adjustment strategy of GSQPSO. The fitness function, which comprehensively considers SWAP gates, CNOT gate costs, particle position information, and quantum behavioral factors, is designed with an adaptive adjustment mechanism to accurately evaluate mapping solutions. During solution updating, individuals are selected using the GAQCM selection strategy, and position update formulas from QPSO and GSQPSO are combined with crossover and mutation operations based on qubit coupling strength, leveraging quantum characteristics to avoid local optima. Experimental results demonstrate that, compared with the t|ket> and Qiskit compilers, QMS-FMO reduces the number of inserted SWAP gates by 46.1% compared to t|ket> and 65.2% compared to Qiskit for specific qubit scales, significantly improving the quality and efficiency of quantum circuit mapping.

DOI
10.1109/access.2025.3638794

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In response to the current challenges in quantum circuit mapping algorithms, such as low mapping quality, insufficient diversity, and the difficulty in balancing mapping quality and diversity, a Quantum Multi-Strategy Fusion Mapping Optimization Algorithm (QMS-FMO) is proposed in this paper. This algorithm enhances population diversity by integrating the neighboring gate strategy of Genetic Algorithm-based Quantum Circuit Mapping (GAQCM), the quantum state characteristics of QPSO, and the parameter adjustment strategy of GSQPSO. The fitness function, which comprehensively considers SWAP gates, CNOT gate costs, particle position information, and quantum behavioral factors, is designed with an adaptive adjustment mechanism to accurately evaluate mapping solutions. During solution updating, individuals are selected using the GAQCM selection strategy, and position update formulas from QPSO and GSQPSO are combined with crossover and mutation operations based on qubit coupling strength, leveraging quantum characteristics to avoid local optima. Experimental results demonstrate that, compared with the t|ket> and Qiskit compilers, QMS-FMO reduces the number of inserted SWAP gates by 46.1% compared to t|ket> and 65.2% compared to Qiskit for specific qubit scales, significantly improving the quality and efficiency of quantum circuit mapping.
Abstract Most of the existing qubit mapping algorithms are deterministic, resulting in a lack of diversity in the generated quantum circuit mappings, which makes it difficult to strike a balance between quality and diversity, and prevents them from being flexibly adapted to different quantum computing tasks. To solve this problem, this paper proposes the Genetic Algorithm-based Quantum Circuit Mapping (GAQCM) framework, which is based on the idea of genetic algorithm, evaluates the quality of mapping by the fitness function, and continuously improves the mapping scheme through several iterations. The GAQCM framework is designed to be flexible, providing a variety of choices, crossover operations and several unique mutation methods are designed to improve the performance of the algorithm. The framework also introduces a neighbourhood gate-based initialisation strategy to improve the algorithm efficiency and convergence speed. Experimental results show that the GAQCM framework reduces the number of SWAP gates by an average of 44.6% and 62.0%, and reduces the hardware gate overhead by 13.8% and 14.9% in the t|ket > and Qiskit compilers, respectively, compared to 2QAN. The framework allows users to customise the fitness function and parameter settings according to their specific needs, and is suitable for a variety of quantum computing tasks.
This paper explores the application of genetic algorithms (GAs) to optimize quantum circuits. The core claim is that GA can effectively improve the efficiency and accuracy of quantum computation by strategically modifying the topology and control parameters of quantum circuits. The proposed mechanism treats a quantum circuit as a genetic individual, leveraging the principles of genetic algorithms – including crossover, mutation, and selection – to iteratively enhance circuit performance. This approach represents a novel method for quantum circuit optimization, offering a potentially robust and adaptable solution compared to traditional optimization techniques. We present a framework for implementing this approach, focusing on the algorithmic steps and considerations for successful application. The exploration will cover the challenges and potential benefits of integrating evolutionary algorithms with the unique characteristics of quantum computation. ---
Abstract In the Noisy Intermediate-Scale Quantum (NISQ) era, owing to the limitation of quantum hardware coupling constraints, only physically directly connected qubits can realize interaction. For CNOT gates that do not satisfy the coupling conditions, extra SWAP gates need to be inserted to adjust the qubit positions to ensure the executability of the quantum circuit. To reduce the extra overhead due to SWAP gates, this paper proposes a Leveraging Strategy-Driven Quantum Sparrow Search Algorithm (LS-QSSA) and applies it to quantum circuit mapping. LS-QSSA introduces the concept of qubit coupling count, and combines it with the SWAP gate overhead to jointly construct the fitness function. In the individual selection stage, the top 20% of individuals in terms of fitness value are set as “discoverers,” which are able to explore multiple solution space locations at the same time through the introduction of quantum representations, thus expanding the search space. To enhance the capability of escaping local optima, LS-QSSA introduces a Gaussian noise mechanism to perturb the follower positions. Experimental results demonstrate that LS-QSSA achieves an approximate reduction of 36.4% and 47.5% in the quantity of SWAP gates, and around 13.1% and 13.2% in hardware gate count overhead, when compared with the t∣ket⟩t\ket{ket}t∣ket⟩ and Qiskit compilers, respectively.
Quantum computing leverages the unique properties of qubits and quantum parallelism to solve problems intractable for classical systems, offering unparalleled computational potential. However, optimization of quantum circuits remains critical, especially for noisy intermediate-scale quantum (NISQ) devices with limited qubits and high error rates. Genetic algorithms (GAs) provide a promising approach for efficient quantum circuit synthesis by automating optimization tasks. This work examines the impact of various mutation strategies within a GA framework for quantum circuit synthesis. By analyzing how different mutations transform circuits, it identifies strategies that enhance efficiency and performance. Experiments utilized a fitness function emphasizing fidelity, while accounting for circuit depth and T-operations, to optimize circuits with four to six qubits. Our analysis revealed that, while the "swap, addition" strategy achieved the highest fidelity scores, it consistently increased circuit depth. In contrast, combining "swap, addition, delete" strategies offers a more balanced approach, delivering near-optimal results while also having the potential of reducing circuit depth.
The conventional approach for initial qubit mapping in the Noisy Intermediate-Scale Quantum (NISQ) era typically uses a static heuristic strategy, overlooking insufficient qubit neighborhood in subsequent operations, resulting in excess additional SWAP gates. To address this, we introduce a multifactor interaction cost function considering qubit distance, interaction time, and gate operation error rates, enhancing SWAP gate selection in the traditional strategy. Considering quantum hardware constraints, we propose Batch SWAP Optimization Strategy (BSOS). BSOS tackles qubit mapping challenges by leveraging optimal SWAP gate selection and a SWAP-based batch update technique, effectively minimizing SWAP gates throughout circuit execution. Experimental results show that BSOS significantly reduces additional gates by intelligently selecting SWAP gates and using batch updating, with a 38.1% average decrease in inserted SWAP gates, leading to a 12% reduction in hardware gate counting overhead.
Abstract Current quantum devices typically lack full qubit connectivity, making it difficult to directly execute logical circuits on quantum devices. This limitation necessitates quantum circuit mapping algorithms to insert SWAP gates, dynamically remapping logical qubits to physical qubits, and transforming logical circuits into physical circuits that comply with device connectivity constraints. However, the insertion of SWAP gates increases both the gate count and circuit depth, ultimately reducing the fidelity of quantum algorithms. To achieve a balanced optimization of these two objectives, we propose the TANGO algorithm. The algorithm first formulates an evaluation function that balances the impact of qubit mapping on both mapped and unmapped nodes is introduced to enhance initial mapping quality, thereby reducing the number of SWAP gates inserted during routing. Next, we design an innovative two-stage routing algorithm that prioritizes the number of executable gates as the primary evaluation metric while also considering quantum gate distance, circuit depth, {and a novel bidirectional-look SWAP strategy}, which optimizes SWAP gate selection in conjunction with preceding gates, improving the effectiveness of the mapping algorithm. Finally, by integrating advanced quantum gate optimization techniques, the algorithm's overall performance is further enhanced. Experimental results demonstrate that, compared to state-of-the-art methods, the proposed algorithm achieves multi-objective co-optimization of gate count and circuit depth across various benchmarks and quantum devices, exhibiting significant performance advantages.