Efficient Circuit Implementations of Continuous-Time Quantum Walks for Quantum Search
Quantum walks are a powerful framework for simulating complex quantum systems and designing quantum algorithms, particularly for spatial search on graphs, where the goal is to find a marked vertex efficiently. In this work, we present efficient quantum circuits that implement the evolution operator...
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MDPI AG
2025-04-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/27/5/454 |
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| author | Renato Portugal Jalil Khatibi Moqadam |
| author_facet | Renato Portugal Jalil Khatibi Moqadam |
| author_sort | Renato Portugal |
| collection | DOAJ |
| description | Quantum walks are a powerful framework for simulating complex quantum systems and designing quantum algorithms, particularly for spatial search on graphs, where the goal is to find a marked vertex efficiently. In this work, we present efficient quantum circuits that implement the evolution operator of continuous-time quantum-walk-based search algorithms for three graph families: complete graphs, complete bipartite graphs, and hypercubes. For complete and complete bipartite graphs, our circuits exactly implement the evolution operator. For hypercubes, we propose an approximate implementation that closely matches the exact evolution operator as the number of vertices increases. Our Qiskit simulations demonstrate that even for low-dimensional hypercubes, the algorithm effectively identifies the marked vertex. Furthermore, the approximate implementation developed for hypercubes can be extended to a broad class of graphs, enabling efficient quantum search in scenarios where exact implementations are impractical. |
| format | Article |
| id | doaj-art-3a8b29ea847640468e6dd9f8e2c6bba9 |
| institution | OA Journals |
| issn | 1099-4300 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj-art-3a8b29ea847640468e6dd9f8e2c6bba92025-08-20T02:33:54ZengMDPI AGEntropy1099-43002025-04-0127545410.3390/e27050454Efficient Circuit Implementations of Continuous-Time Quantum Walks for Quantum SearchRenato Portugal0Jalil Khatibi Moqadam1National Laboratory of Scientific Computing (LNCC), Av. Getulio Vargas 333, Petrópolis 25651-075, BrazilNational Laboratory of Scientific Computing (LNCC), Av. Getulio Vargas 333, Petrópolis 25651-075, BrazilQuantum walks are a powerful framework for simulating complex quantum systems and designing quantum algorithms, particularly for spatial search on graphs, where the goal is to find a marked vertex efficiently. In this work, we present efficient quantum circuits that implement the evolution operator of continuous-time quantum-walk-based search algorithms for three graph families: complete graphs, complete bipartite graphs, and hypercubes. For complete and complete bipartite graphs, our circuits exactly implement the evolution operator. For hypercubes, we propose an approximate implementation that closely matches the exact evolution operator as the number of vertices increases. Our Qiskit simulations demonstrate that even for low-dimensional hypercubes, the algorithm effectively identifies the marked vertex. Furthermore, the approximate implementation developed for hypercubes can be extended to a broad class of graphs, enabling efficient quantum search in scenarios where exact implementations are impractical.https://www.mdpi.com/1099-4300/27/5/454quantum computerquantum walkspatial search algorithmcomplete graphbipartite graphhypercube |
| spellingShingle | Renato Portugal Jalil Khatibi Moqadam Efficient Circuit Implementations of Continuous-Time Quantum Walks for Quantum Search Entropy quantum computer quantum walk spatial search algorithm complete graph bipartite graph hypercube |
| title | Efficient Circuit Implementations of Continuous-Time Quantum Walks for Quantum Search |
| title_full | Efficient Circuit Implementations of Continuous-Time Quantum Walks for Quantum Search |
| title_fullStr | Efficient Circuit Implementations of Continuous-Time Quantum Walks for Quantum Search |
| title_full_unstemmed | Efficient Circuit Implementations of Continuous-Time Quantum Walks for Quantum Search |
| title_short | Efficient Circuit Implementations of Continuous-Time Quantum Walks for Quantum Search |
| title_sort | efficient circuit implementations of continuous time quantum walks for quantum search |
| topic | quantum computer quantum walk spatial search algorithm complete graph bipartite graph hypercube |
| url | https://www.mdpi.com/1099-4300/27/5/454 |
| work_keys_str_mv | AT renatoportugal efficientcircuitimplementationsofcontinuoustimequantumwalksforquantumsearch AT jalilkhatibimoqadam efficientcircuitimplementationsofcontinuoustimequantumwalksforquantumsearch |