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1. A 3.3904-Competitive Online Algorithm for List Update with Uniform Costs

   https://doi.org/10.4230/lipics.esa.2025.76  

   Basiak, Mateusz; Bienkowski, Marcin; Böhm, Martin; Chrobak, Marek; Jeż, Łukasz; Sgall, Jiří; Tatarczuk, Agnieszka (January 2025, Schloss Dagstuhl – Leibniz-Zentrum für Informatik)

   Benoit, Anne; Kaplan, Haim; Wild, Sebastian; Herman, Grzegorz (Ed.)

   Abstract: We consider the List Update problem where the cost of each swap is assumed to be 1. This is in contrast to the "standard" model, in which an algorithm is allowed to swap the requested item with previous items for free. We construct an online algorithm Full-Or-Partial-Move (FPM), whose competitive ratio is at most 3.3904, improving over the previous best known bound of 4. 

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2. Quantum routing with fast reversals

   https://doi.org/10.22331/q-2021-08-31-533  

   Bapat, Aniruddha; Childs, Andrew M.; Gorshkov, Alexey V.; King, Samuel; Schoute, Eddie; Shastri, Hrishee (August 2021, Quantum)

   null (Ed.)

   We present methods for implementing arbitrary permutations of qubits under interaction constraints. Our protocols make use of previous methods for rapidly reversing the order of qubits along a path. Given nearest-neighbor interactions on a path of length n , we show that there exists a constant ϵ ≈ 0.034 such that the quantum routing time is at most ( 1 − ϵ ) n , whereas any swap-based protocol needs at least time n − 1 . This represents the first known quantum advantage over swap-based routing methods and also gives improved quantum routing times for realistic architectures such as grids. Furthermore, we show that our algorithm approaches a quantum routing time of 2 n / 3 in expectation for uniformly random permutations, whereas swap-based protocols require time n asymptotically. Additionally, we consider sparse permutations that route k ≤ n qubits and give algorithms with quantum routing time at most n / 3 + O ( k 2 ) on paths and at most 2 r / 3 + O ( k 2 ) on general graphs with radius r . 

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3. Towards Fidelity-Optimal Qubit Mapping on NISQ Computers

   https://doi.org/10.1109/QCE57702.2023.00019  

   Khandavilli, Sri; Palanisamy, Indu; Nguyen, Manh V.; Le, Thinh V.; Nguyen, Tu N.; Dinh, Thang N. (September 2023, 2023 IEEE International Conference on Quantum Computing and Engineering (QCE))

   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. 

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4. Not All SWAPs Have the Same Cost: A Case for Optimization-Aware Qubit Routing

   https://doi.org/10.1109/HPCA53966.2022.00058  

   Liu, Ji; Li, Peiyi; Zhou, Huiyang (April 2022, 2022 IEEE International Symposium on High-Performance Computer Architecture (HPCA))

   Despite rapid advances in quantum computing technologies, the qubit connectivity limitation remains to be a critical challenge. Both near-term NISQ quantum computers and relatively long-term scalable quantum architectures do not offer full connectivity. As a result, quantum circuits may not be directly executed on quantum hardware, and a quantum compiler needs to perform qubit routing to make the circuit compatible with the device layout. During the qubit routing step, the compiler inserts SWAP gates and performs circuit transformations. Given the connectivity topology of the target hardware, there are typically multiple qubit routing candidates. The state-of-the-art compilers use a cost function to evaluate the number of SWAP gates for different routes and then select the one with the minimum number of SWAP gates. After qubit routing, the quantum compiler performs gate optimizations upon the circuit with the newly inserted SWAP gates. In this paper, we observe that the aforementioned qubit routing is not optimal, and qubit routing should not be independent on subsequent gate optimizations. We find that with the consideration of gate optimizations, not all of the SWAP gates have the same basis-gate cost. These insights lead to the development of our qubit routing algorithm, NASSC (Not All Swaps have the Same Cost). NASSC is the first algorithm that considers the subsequent optimizations during the routing step. Our optimization-aware qubit routing leads to better routing decisions and benefits subsequent optimizations. We also propose a new optimization-aware decomposition for the inserted SWAP gates. Our experiments show that the routing overhead compiled with our routing algorithm is reduced by up to 69.30% (21.30% on average) in the number of CNOT gates and up to 43.50% (7.61% on average) in the circuit depth compared with the state-of-the-art scheme, SABRE. 

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5. Quantum Circuit Mapping Based on Incremental and Parallel SAT Solving

   https://doi.org/10.4230/LIPIcs.SAT.2024.29  

   Yang, Jiong; Kharkov, Yaroslav A; Shi, Yunong; Heule, Marijn J_H; Dutertre, Bruno (August 2024, Schloss Dagstuhl – Leibniz-Zentrum für Informatik)

   Chakraborty, Supratik; Jiang, Jie-Hong Roland (Ed.)

   Quantum Computing (QC) is a new computational paradigm that promises significant speedup over classical computing in various domains. However, near-term QC faces numerous challenges, including limited qubit connectivity and noisy quantum operations. To address the qubit connectivity constraint, circuit mapping is required for executing quantum circuits on quantum computers. This process involves performing initial qubit placement and using the quantum SWAP operations to relocate non-adjacent qubits for nearest-neighbor interaction. Reducing the SWAP count in circuit mapping is essential for improving the success rate of quantum circuit execution as SWAPs are costly and error-prone. In this work, we introduce a novel circuit mapping method by combining incremental and parallel solving for Boolean Satisfiability (SAT). We present an innovative SAT encoding for circuit mapping problems, which significantly improves solver-based mapping methods and provides a smooth trade-off between compilation quality and compilation time. Through comprehensive benchmarking of 78 instances covering 3 quantum algorithms on 2 distinct quantum computer topologies, we demonstrate that our method is 26× faster than state-of-the-art solver-based methods, reducing the compilation time from hours to minutes for important quantum applications. Our method also surpasses the existing heuristics algorithm by 26% in SWAP count. 

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