Quantum Dissipative Search via Lindbladians

• URL: http://arxiv.org/abs/2407.11782v1
• Date: Tue, 16 Jul 2024 14:39:18 GMT
• Title: Quantum Dissipative Search via Lindbladians
• Authors: Peter J. Eder, Jernej Rudi Finžgar, Sarah Braun, Christian B. Mendl,
• Abstract summary: We analyze the convergence criteria and the convergence speed of a Markovian, purely dissipative quantum random walk on an unstructured search space. We map the results onto an actual implementation to correctly estimate the potential and show that it is no more efficient than classical search.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 the convergence speed of a Markovian, purely dissipative quantum random walk on an unstructured search space. We analytically derive the mixing time for continuous- and discrete-time processes for different coupling regimes that control the random walk. Then, we map the results onto an actual implementation to correctly estimate the potential and show that it is no more efficient than classical search. Despite this, we highlight the connections between the classical random walks and open quantum random walks and demonstrate how to recover a quadratic speedup in the unitary limit. Moreover, the study of the Grover problem reveals how the hyperparameters affect the cost of implementation. This helps us refine the complexity analysis of the investigated algorithm to simulate the Lindblad equation.

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