English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

A general quantum search algorithm aims to evolve a quantum system from aknown source state $|s\rangle$ to an unknown target state $|t\rangle$. It usesa diffusion operator $D_{s}$ having source state as one of its eigenstates and$I_{t}$, where $I_{\psi}$ denotes the selective phase inversion of$|\psi\rangle$ state. It evolves $|s\rangle$ to a particular state $|w\rangle$,call it w-state, in $O(B/\alpha)$ time steps where $\alpha$ is $|\langlet|s\rangle|$ and $B$ is a characteristic of the diffusion operator. Measuringthe w-state gives the target state with the success probability of $O(1/B^{2})$and $O(B^{2})$ applications of the algorithm can boost it from $O(1/B^{2})$ to$O(1)$, making the total time complexity $O(B^{3}/\alpha)$. In the special caseof Grover's algorithm, $D_{s}$ is $I_{s}$ and $B$ is very close to $1$. A moreefficient way to boost the success probability is quantum amplitudeamplification provided we can efficiently implement $I_{w}$. Such an efficientimplementation is not known so far. In this paper, we present an efficientalgorithm to approximate selective phase inversions of the unknown eigenstatesof an operator using phase estimation algorithm. This algorithm is used toefficiently approximate $I_{w}$ which reduces the time complexity of generalalgorithm to $O(B/\alpha)$. Though $O(B/\alpha)$ algorithms are known to exist,our algorithm offers physical implementation advantages.

Postprocessing can speed up general quantum search algorithms