This paper introduces the DIRSH algorithm for the Qubit Routing Problem (QRP), using a heuristic-guided randomized divide-and-conquer strategy. The method splits the circuit into chunks and optimizes each one with a stochastic selection of gates and swaps. It balances global search, via restarts and adaptive tuning of bandit parameters with depth-sensitive local pruning. Tested on RevLib benchmarks mapped to the 20-qubit IBMQ Tokyo topology, DIRSH outperformed three LightSABRE variants across different time budgets, achieving shorter depths and fewer swaps. These results confirm that combining chunk-based decomposition with bandit-driven heuristics is effective for routing quantum circuits on NISQ devices.
This paper introduces the DIRSH algorithm for the Qubit Routing Problem (QRP), using a heuristic-guided randomized divide-and-conquer strategy. The method splits the circuit into chunks and optimizes each one with a stochastic selection of gates and swaps. It balances global search, via restarts and adaptive tuning of bandit parameters with depth-sensitive local pruning. Tested on RevLib benchmarks mapped to the 20-qubit IBMQ Tokyo topology, DIRSH outperformed three LightSABRE variants across different time budgets, achieving shorter depths and fewer swaps. These results confirm that combining chunk-based decomposition with bandit-driven heuristics is effective for routing quantum circuits on NISQ devices.
In the Noisy Intermediate-Scale Quantum (NISQ) era, the topological constraints present in many of the currently available quantum devices pose a physical limit on the feasible interactions between qubits. To comply with such limitations, the compilation of quantum circuits requires solving the Qubit Routing Problem (QRP), by inserting SWAP operations among qubits. The State of the Art provides heuristic algorithms addressing this task, yet the depth of the output circuits is often incompatible with the current limits of quantum hardware. Therefore, we propose DDRoute, a novel heuristic algorithm to solve QRP, designed to reduce the depth overhead introduced by the routing process in the compiled circuits. Our experimental evaluation proves the efficiency of our approach, with a depth reduction of up to 70% with respect to the state-of-the-art routing procedures.
Quantum optimization has recently drawn considerable attention as one of the possible applications of noisy intermediate-scale quantum computation, yet the problem of qubit requirement remains a major bottleneck when combinatorial optimization problems are converted into quantum circuits. This issue becomes especially critical in solving the capacitated vehicle routing problem (CVRP) with the quantum approximate optimization algorithm (QAOA), since the number of required qubits increases polynomially with respect to the number of nodes. This study investigates whether a heuristic divide-and-conquer strategy can be adapted to the quantum setting so as to improve qubit efficiency while preserving the optimization capability to a reasonable extent. The proposed method decomposes a single CVRP into multiple traveling salesman problems (TSPs) by the sweeping-based clustering method, searches for the sector configuration with the smallest angle sum by Grover’s search algorithm, and then solves each sector-wise TSP with the QAOA aided by the gravitational search algorithm. Experiments on five benchmark datasets show that the proposed approach attains feasible solutions within 3.4 to 12.7% of the reinforcement-learning baseline on the main test set. These results suggest that the proposed approach serves as a plausible quantum heuristic framework for constrained routing optimization, with the advantage of reducing the qubit burden by decomposing the original problem into smaller subproblems.
Quantum computers with a limited qubit connectivity require inserting SWAP gates for qubit routing, which increases gate execution errors and the impact of environmental noise due to an overhead in circuit depth. In this work, we benchmark various routing techniques considering random quantum circuits on one-dimensional and square lattice connectivities, employing both analytical and numerical methods. We introduce circuit fidelity as a comprehensive metric that captures the effects of SWAP and circuit depth overheads. Leveraging a novel approach based on the SABRE algorithm, we achieve up to 84% higher average circuit fidelity for large devices within the NISQ range, compared to previously existing methods. Additionally, our results highlight that the optimal routing choice critically depends on the qubit count and the hardware characteristics, including gate fidelities and coherence times.
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.
The design of quantum circuits is often idealized, however, executing these circuits on quantum devices necessitates meeting the connectivity constraints imposed on physical devices by inserting SWAP gates. Various methods based on exact and heuristic solutions have been proposed to address the challenge of minimizing the degradation of quantum circuit performance due to factors such as circuit depth and the number of inserted SWAP gates while solving the qubit mapping problem. However, exact methods suffer from long runtime, lack of flexibility, and difficulty in scaling to larger circuits, while heuristic methods struggle to find the global optimum. Recently, solving the qubit mapping problem using machine learning approaches has emerged as a novel and promising solution. This paper studies qubit mapping optimization techniques based on machine learning, optimizing a model that solves the qubit mapping problem using the Deep Q-Network (DQN) algorithm, resulting in a SA-DQN model with superior performance in terms of circuit depth. The optimization efforts include improving the SWAP insertion strategy during the qubit mapping process and optimizing the model's initial mapping. Our SA-DQN model, tested on the IBM QX5 architecture and Rigetti 19Q Acorn architecture with a set of test circuits, achieved an improvement of 7.62% to 8.51% and 8.37% to 9.17% in circuit depth ratio compared to the original DQN model, respectively.
In current quantum devices, physical qubits are not fully connected so that two-qubit interaction can only be performed between specific pairs of physical qubits. To execute a quantum circuit, it is necessary to transform it into a functionally equivalent one that respects the constraints imposed by the target architecture. Quantum circuit transformation inevitably introduces additional gates which reduces the fidelity of the circuit. Therefore, it is important that the transformation method completes the transformation with minimal overheads. Quantum circuit transformation consists of two steps, initial mapping and qubit routing, and here we propose a DEAR (Dynamically-Extract-and-Route) framework to solve the qubit routing problem. A key insight of DEAR is that by maintaining a sufficient lookahead ability all the time, we can make much better routing decisions while effectively controlling the runtime. In our DEAR framework, we periodically extract a subcircuit by identifying a set of remaining gates that should be executed earlier than the others, and then applies A* search to determine how to insert a sequence of additional SWAP and BRIDGE operations into the subcircuit to obtain a high quality routing solution with minimum number of additional gates. In this work, we consider the insertion of both SWAP and BRIDGE operations while most previous works deal with SWAP insertion only. We evaluate our approach with four benchmark sets with different characterization on IBM Tokyo. The experimental results show that our approach outperforms the state-of-the-art work utilizing SWAP and BRIDGE insertion with 19.1% and 77.5% average reduction in the number of additional gates and runtime, respectively, starting from the same initial mapping. We also performed experiments on larger quantum devices such as Google Sycamore and IBM Rochester both with 53 physical qubits that have largely different architectures from one another and from IBM Tokyo. Again, DEAR was much faster and required significantly less amount of additional gates.