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arXiv · 2407.11782

Quantum Dissipative Search via Lindbladians

Peter J. Eder·Jernej Rudi Finžgar·Sarah Braun·Christian B. Mendl
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Abstract

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.

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Peter J. Eder, Jernej Rudi Finžgar, Sarah Braun, Christian B. Mendl. 2025-03-14. Quantum Dissipative Search via Lindbladians. https://doi.org/10.1103/physreva.111.042430

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