Coherence and entanglement in Grover and Harrow-Hassidim-Lloyd algorithm
Changchun Feng, Lin Chen, Lijun Zhao
TL;DR
This paper analyzes the evolution of quantum resources like coherence and entanglement during Grover's and HHL algorithms, revealing patterns of resource change at different algorithm steps.
Contribution
It provides a detailed step-by-step analysis of coherence, discord, and entanglement in Grover and HHL algorithms, highlighting their dynamic behavior.
Findings
Resources decrease at oracle steps in Grover's algorithm
Resources increase or remain invariant at diffuser steps in Grover's algorithm
Patterns of resource change are similar for entanglement and other quantum resources
Abstract
Coherence, discord and geometric measure of entanglement are important tools for measuring physical resources. We compute them at every steps of the Grover's algorithm. We summarize these resources's patterns of change. These resources are getting smaller at the step oracle and are getting bigger or invariant at the step diffuser. This result is similar to the entanglement's pattern of change in Grover's algorithm. Furthermore, we compute GM at every steps of the Harrow-Hassidim-Lloyd algorithm.
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Taxonomy
TopicsAdvanced Thermodynamics and Statistical Mechanics · Quantum Mechanics and Applications · Statistical Mechanics and Entropy