Quantum Dissipative Search via Lindbladians
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866908350902435840 |
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| author | Eder, Peter J. Finžgar, Jernej Rudi Braun, Sarah Mendl, Christian B. |
| author_facet | Eder, Peter J. Finžgar, Jernej Rudi Braun, Sarah Mendl, Christian B. |
| contents | Closed quantum systems follow a unitary time evolution that can be simulated on quantum computers. By incorporating non-unitary effects via, e.g., measurements on ancilla qubits, these algorithms can be extended to open-system dynamics, such as Markovian processes described by the Lindblad master equation. In this paper, we analyze the convergence criteria and speed of a Markovian, purely dissipative quantum random walk on an unstructured classical search space. Notably, we show that certain jump operators make the quantum process replicate a classical one, while others yield differences between open quantum (OQRW) and classical random walks. We also clarify a previously observed quadratic speedup, demonstrating that OQRWs are no more efficient than classical search. Finally, we analyze a dissipative discrete-time ground-state preparation algorithm with a lower implementation cost. This allows us to interpolate between the dissipative and the unitary domain and thereby illustrate the important role of coherence for the quadratic speedup. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_11782 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantum Dissipative Search via Lindbladians Eder, Peter J. Finžgar, Jernej Rudi Braun, Sarah Mendl, Christian B. Quantum Physics Closed quantum systems follow a unitary time evolution that can be simulated on quantum computers. By incorporating non-unitary effects via, e.g., measurements on ancilla qubits, these algorithms can be extended to open-system dynamics, such as Markovian processes described by the Lindblad master equation. In this paper, we analyze the convergence criteria and speed of a Markovian, purely dissipative quantum random walk on an unstructured classical search space. Notably, we show that certain jump operators make the quantum process replicate a classical one, while others yield differences between open quantum (OQRW) and classical random walks. We also clarify a previously observed quadratic speedup, demonstrating that OQRWs are no more efficient than classical search. Finally, we analyze a dissipative discrete-time ground-state preparation algorithm with a lower implementation cost. This allows us to interpolate between the dissipative and the unitary domain and thereby illustrate the important role of coherence for the quadratic speedup. |
| title | Quantum Dissipative Search via Lindbladians |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2407.11782 |