Coherence Depletion in Quantum Algorithms

TL;DR

This paper reveals that quantum coherence depletion is a universal feature in various quantum algorithms, potentially guiding the development of new algorithms by focusing on coherence dynamics.

Contribution

It demonstrates that coherence depletion occurs across multiple quantum algorithms, highlighting a shared quantum feature not reflected by entanglement measures.

Findings

Quantum coherence reduces to minimum during successful algorithm execution.

Coherence depletion is observed in Grover's, Deutsch-Jozsa, and Shor's algorithms.

Other measures like entanglement do not show similar depletion patterns.

Abstract

Besides the superior efficiency compared to their classical counterparts, quantum algorithms known so far are basically task-dependent, and scarcely any common features are shared between them. In this work, however, we show that the depletion of quantum coherence turns out to be a common phenomenon in these algorithms. For all the quantum algorithms that we investigated including Grover's algorithm, Deutsch-Jozsa algorithm and Shor's algorithm, quantum coherence of the system states reduces to the minimum along with the successful execution of the respective processes. Notably, a similar conclusion cannot be drawn using other quantitative measures such as quantum entanglement. Thus, we expect that coherence depletion as a common feature can be useful for devising new quantum algorithms in the future.