Quantum Dissipative Search via Lindbladians

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 eq...

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Bibliographic Details
Published in:arXiv.org 2024-11
Main Authors: Eder, Peter J, Jernej Rudi Finžgar, Braun, Sarah, Mendl, Christian B
Format: Article
Language:English
Subjects:
Algorithms
Convergence
Cost analysis
Dissipation
Quantum computers
Qubits (quantum computing)
Random walk
Searching
System dynamics
Online Access:Get full text
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Summary: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.
ISSN:2331-8422