Finding Hidden Numbers with Majorana-based Topological Quantum Algorithms: Simulation of the Bernstein-Vazirani Algorithm
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866929759447941120 |
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| author | Bedow, Jasmin Morr, Dirk K. |
| author_facet | Bedow, Jasmin Morr, Dirk K. |
| contents | Executing quantum algorithms using Majorana zero modes - a major milestone for the field of topological quantum computing - requires a platform that can be scaled to large quantum registers, can be controlled in real time and space, and a braiding protocol that uses the unique properties of these exotic particles. Here, we demonstrate the first successful simulation of the Bernstein-Vazirani algorithm in two-dimensional magnet-superconductor hybrid structures from initialization to read-out of the final many-body state. Utilizing the Majorana zero modes' topological properties, we introduce an optimized braiding protocol for the algorithm and a scalable architecture for its implementation with an arbitrary number of qubits. We visualize the algorithm protocol in real time and space by computing the non-equilibrium density of states, which is proportional to the time-dependent differential conductance, and the non-equilibrium charge density, which assigns a unique signature to each final state of the algorithm. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_10770 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Finding Hidden Numbers with Majorana-based Topological Quantum Algorithms: Simulation of the Bernstein-Vazirani Algorithm Bedow, Jasmin Morr, Dirk K. Mesoscale and Nanoscale Physics Superconductivity Executing quantum algorithms using Majorana zero modes - a major milestone for the field of topological quantum computing - requires a platform that can be scaled to large quantum registers, can be controlled in real time and space, and a braiding protocol that uses the unique properties of these exotic particles. Here, we demonstrate the first successful simulation of the Bernstein-Vazirani algorithm in two-dimensional magnet-superconductor hybrid structures from initialization to read-out of the final many-body state. Utilizing the Majorana zero modes' topological properties, we introduce an optimized braiding protocol for the algorithm and a scalable architecture for its implementation with an arbitrary number of qubits. We visualize the algorithm protocol in real time and space by computing the non-equilibrium density of states, which is proportional to the time-dependent differential conductance, and the non-equilibrium charge density, which assigns a unique signature to each final state of the algorithm. |
| title | Finding Hidden Numbers with Majorana-based Topological Quantum Algorithms: Simulation of the Bernstein-Vazirani Algorithm |
| topic | Mesoscale and Nanoscale Physics Superconductivity |
| url | https://arxiv.org/abs/2503.10770 |