Curator's Take
This research provides crucial insights into how quantum coherence behaves during Simon's algorithm, one of the foundational quantum algorithms that demonstrated exponential speedup over classical methods. The finding that coherence increases with system size (when N>4) but decreases for smaller systems reveals an important threshold effect that could inform optimal qubit allocation strategies for quantum processors. Understanding these coherence dynamics is particularly valuable as quantum hardware developers work to minimize decoherence and maximize algorithmic performance on NISQ devices. The work also offers theoretical tools using Tsallis entropy measures that could be applied to analyze coherence patterns in other quantum algorithms, potentially guiding the design of more robust quantum computations.
— Mark Eatherly
Summary
Quantum coherence plays a pivotal role in quantum algorithms. We study the coherence dynamics of the evolved states in Simon's quantum algorithm based on Tsallis relative $α$ entropy and $l_{1,p}$ norm. We prove that the coherences of the first register and the second register both rely on the dimension $N$ of the state spaces of the $n$ qubit systems, and increase with the increase of $N$. We show that the oracle operator $O$ does not change the coherence. Moreover, we study the coherence dynamics in the Simon's quantum algorithm and prove that in overall the coherence is in production when $N>4$ and in depletion when $N<4$.