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 $t\ket{ket}$ and Qiskit compilers, respectively.
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⟩ and Qiskit compilers, respectively.
In the era of noisy intermediate-scale quantum (NISQ) computing, the limited connectivity between qubits is one of the common physical limitations faced by current quantum computing devices. Quantum circuit mapping methods transform quantum circuits into equivalent circuits that satisfy physical connectivity constraints by remapping logical qubits, making them executable. The optimization problem of quantum circuit mapping has NP-hard computational complexity, and existing heuristic mapping algorithms still have significant potential for optimization in terms of the number of quantum gates generated. To reduce the number of SWAP gates inserted during mapping, the solution space of the mapping problem is represented as a tree structure, and the mapping process is equivalent to traversing this tree structure. To effectively and efficiently complete the search process, a beam search framework (BSF) is proposed for solving quantum circuit mapping. By iteratively selecting, expanding, and making decisions, high-quality target circuits are generated. Experimental results show that this method can significantly reduce the number of inserted SWAP gates on medium to large circuits, achieving an average reduction of 44% compared to baseline methods, and is applicable to circuits of various sizes and complexities.
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.
Quantum computing has already demonstrated great computational potential across multiple domains and has received more and more attention. However, due to the connectivity limitations of Noisy Intermediate-Scale Quantum (NISQ) devices, most of the quantum algorithms cannot be directly executed without the help of inserting SWAP gates. Nevertheless, more SWAP gates lead to a longer execution time and, inevitably, lower fidelity of the algorithm. To this end, this paper proposes an optimized qubit mapping algorithm based on a dynamic look-ahead strategy to minimize the number of SWAP gates inserted. Firstly, a heuristic algorithm is proposed based on maximizing physical qubit connectivity to generate the optimal initial qubit mapping, which reduces the need for logical qubit shifts during subsequent SWAP gate insertion. Secondly, in the form of directed acyclic graphs, we identify quantum gates that violate the constraints of physical coupling and insert SWAP gates to remap qubits, thereby overcoming the limitations of qubit interactions. Finally, the optimal SWAP gate insertion strategy is built by comparing the cost of different SWAP gate insertion strategies through a multi-window look-ahead strategy to reduce the number of SWAP gates inserted. The experimental results show that the strategy in this paper decreases the number of SWAP gate insertions and significantly reduces the depth of quantum circuits when performing qubit mapping compared with state-of-the-art methods.
In the Quantum computing era of Noisy Intermediate-Scale Quantum (NISQ) devices, conventional qubit mapping strategies typically rely on specific heuristic rules to solve the mapping problem, overlooking the impact of other factors on the mapping, which leads to increased overhead from extra SWAP gates. To address this issue, we propose a SWAP optimization strategy based on the Centric-Shortest Quantum Gate Set (C-SQGS) and applies it to qubit mapping. In this approach, the centric qubit is determined by analyzing the maximum flexibility qubit set and the physical distances between the associated CNOT gates, leading to the identification of the Centric-Shortest Quantum Gate Set. To overcome the limitations of traditional cost functions that consider only single factors, a multi-factor cost function is introduced to evaluate the overall overhead of candidate SWAP operations and determine pending SWAP gate Set. Based on qubit flexibility analysis, executable SWAP gate is identified and inserted into the circuit. Experimental results demonstrate that the C-SQGS strategy effectively reduces both SWAP gate and two-qubit gate overhead. Specifically, it achieves an average SWAP gate reduction of 36.9% and 47.7%, and a two-qubit gate reduction of 13.8% and 13.5% on the t|ket⟩ and Qiskit compilers, respectively. These results highlight the potential of the C-SQGS strategy in enhancing the efficiency of qubit mapping for NISQ devices.
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.
Quantum algorithm design usually assumes access to a perfect quantum computer with ideal properties like full connectivity, noise-freedom, and arbitrarily long coherence time. In noisy intermediate-scale quantum (NISQ) devices, however, the number of qubits is highly limited and quantum operation error and qubit coherence are not negligible. Besides, the connectivity of physical qubits in a quantum processing unit (QPU) is also strictly constrained. Thereby, additional operations like SWAP gates have to be inserted to satisfy this constraint while preserving the functionality of the original circuit. This process is known as quantum circuit transformation. Adding additional gates will increase both the size and depth of a quantum circuit and, therefore, cause further decay of the performance of a quantum circuit. Thus, it is crucial to minimize the number of added gates. In this article, we propose an efficient method to solve this problem. We first choose by using simulated annealing an initial mapping which fits well with the input circuit and then, with the help of a heuristic cost function, stepwise apply the best-selected SWAP gates until all quantum gates in the circuit can be executed. Our algorithm runs in time polynomial in all parameters, including the size and the qubit number of the input circuit, and the qubit number in the QPU. Its space complexity is quadratic to the number of edges in the QPU. The experimental results on extensive realistic circuits confirm that the proposed method is efficient and the number of added gates of our algorithm is, on average, only 57% of that of state-of-the-art algorithms on IBM Q20 (Tokyo), the most recent IBM quantum device.