Due to little considerations in the hardware constraints, e.g., limited connections between physical qubits to enable two-qubit gates, most quantum algorithms cannot be directly executed on the Noisy Intermediate-Scale Quantum (NISQ) devices. Dynamically remapping logical qubits to physical qubits in the compiler is needed to enable the two-qubit gates in the algorithm, which introduces additional operations and inevitably reduces the fidelity of the algorithm. Previous solutions in finding such remapping suffer from high complexity, poor initial mapping quality, and limited flexibility and control. To address these drawbacks mentioned above, this paper proposes a SWAP-based Bidirectional heuristic search algorithm (SABRE), which is applicable to NISQ devices with arbitrary connections between qubits. By optimizing every search attempt, globally optimizing the initial mapping using a novel reverse traversal technique, introducing the decay effect to enable the trade-off between the depth and the number of gates of the entire algorithm, SABRE outperforms the best known algorithm with exponential speedup and comparable or better results on various benchmarks.
Due to little considerations in the hardware constraints, e.g., limited connections between physical qubits to enable two-qubit gates, most quantum algorithms cannot be directly executed on the Noisy Intermediate-Scale Quantum (NISQ) devices. Dynamically remapping logical qubits to physical qubits in the compiler is needed to enable the two-qubit gates in the algorithm, which introduces additional operations and inevitably reduces the fidelity of the algorithm. Previous solutions in finding such remapping suffer from high complexity, poor initial mapping quality, and limited flexibility and control. To address these drawbacks mentioned above, this paper proposes a SWAP-based Bidirectional heuristic search algorithm (SABRE), which is applicable to NISQ devices with arbitrary connections between qubits. By optimizing every search attempt, globally optimizing the initial mapping using a novel reverse traversal technique, introducing the decay effect to enable the trade-off between the depth and the number of gates of the entire algorithm, SABRE outperforms the best known algorithm with exponential speedup and comparable or better results on various benchmarks.
Quantum computing promises to solve certain problems more efficiently than classical computation. Realizing this potential on noisy, intermediate-scale quantum (NISQ) devices remains challenging. Among other things, hardware connectivity constraints necessitate additional routing operations that degrade circuit fidelity. The qubit mapping problem - assigning logical qubits to physical qubits while minimizing inserted SWAP gates - is thus critical in quantum circuit transpilation. Exact methods scale poorly, and heuristic approaches like the SABRE algorithm, though efficient, rely on local decisions that can miss globally optimal solutions. In this thesis, we propose K-SWAP SABRE that integrates bounded exhaustive search over sequences of up to k SWAPs into the SABRE algorithm. A modified heuristic ensures global progress while maintaining comparability between explored branches. Experiments on benchmark circuits show that increasing k reduces required SWAP gates, especially on highly connected devices, though at the cost of longer runtime. Our results demonstrate that K-SWAP SABRE can improve heuristic qubit mapping quality without sacrificing scalability, offering a practical approach for mapping circuits to near-term and emerging quantum architectures.
Quantum computing is gaining momentum in revolutionizing the way we approach complex problem-solving. However, the practical implementation of quantum algorithms remains a significant challenge due to the error-prone and hardware limits of near-term quantum devices. For instance, physical qubit connections are limited, which necessitates the use of quantum SWAP gates to dynamically transform the logical topology during execution. In addition, to optimize fidelity, it is essential to ensure that 1) the allocated hardware has a low error rate and 2) the number of SWAP gates injected into the circuit is minimized. To address these challenges, we propose a suite of algorithms: the Fidelity-aware Graph Extraction Algorithm (FGEA) is used to identify the hardware region with the lowest probability of error, the Frequency-based Mapping Algorithm (FMA) allocates logical-physical qubits that reduce the potential distance of topological transformation, and the Heuristic Routing Algorithm (HRA) searches for an optimal swapping injection strategy. We evaluate the proposed algorithms on the IBM-provided Noisy Intermediate-Scale Quantum (NISQ) computer, using a dataset consisting of 17 different quantum circuits of various sizes. The circuits are executed on the IBM Toronto Falcon processor. The three proposed algorithms outperform the existing SABRE algorithm in reducing the number of SWAP gates required. Therefore, our proposed algorithms hold significant promise in enhancing the fidelity and reducing the number of SWAP gates required in implementing Quantum algorithms.
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 past few years, several quantum computers realized by the noisy intermediate-scale quantum (NISQ) technology have been released. However, there exists a significant limitation to using such computers, i.e., the connectivity constraint between physical qubits. To perform a 2-qubit quantum operation on such NISQ computers, its two logical qubits have to be mapped to a pair of physical qubits that satisfy the connectivity constraint. This mapping procedure requires additional operations to be introduced into the original quantum circuit, reducing its fidelity. Therefore, it is of great significance to design an algorithm that is able to complete the mapping task with minimal additional operations. In this article, we propose an efficient algorithm to solve this problem. Our algorithm consists of two core components, an expansion-from-center scheme to determine the initial mapping and a SWAP-based heuristic search algorithm to update the mapping. We introduce the maximum consecutive positive effect of a SWAP operation as the heuristic cost function, allowing our search algorithm to look ahead dynamically. Our algorithm is evaluated on IBM Q 20. The experimental results show that our algorithm can complete the mapping task in a very short time even for large-scale benchmarks with hundreds of thousands of operations, and outperforms the state-of-the-art in terms of the number of additional operations for most benchmarks considered.
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.
The noisy intermediate-scale quantum (NISQ) computer significantly advances quantum computing technology. Due to the physical connectivity constraints of the NISQ device, its induced qubit mapping problem becomes more challenging. Recent works employ heuristics to achieve promising outcomes. However, they are limited to using only one type of center for graph matching, and their exhaustive traversal of the coupling graph results in high computation time. This paper strategically generates specific subgraphs during the initial mapping stage to reduce the solution space for the coupling graph. Then, we employ a bidirectional graph isomorphism search to improve initial mapping. In the main mapping stage, we develop an efficient search algorithm to minimize the number of inserted gates. Experimental results show that our method significantly outperforms the state-of-the-art work in reducing the number of inserted CNOT gates by 13.22% and the runtime by 19.61%.