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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Many quantum algorithms can be written as a composition of unitaries, some ofwhich can be exactly synthesized by a universal fault-tolerant gate set, whileothers can be approximately synthesized. A quantum compiler synthesizes eachapproximately synthesizable unitary up to some approximation error, such thatthe error of the overall unitary remains bounded by a certain amount. In thispaper we consider the case when the errors are measured in the global phaseinvariant distance. Apart from deriving a relation between this distance andthe Frobenius norm, we show that this distance composes. If a unitary iswritten as a composition (product and tensor product) of other unitaries, wederive bounds on the error of the overall unitary as a function of the errorsof the composed unitaries. Our bound is better than the sum-of-error bound(Bernstein,Vazirani,1997), derived for the operator norm. This indicates thatsynthesizing a circuit using global phase invariant distance maybe done withless number of resources.  Next we consider the following problem. Suppose we are given a decompositionof a unitary. The task is to distribute the errors in each component such thatthe T-count is optimized. Specifically, we consider those decompositions where$R_z(\theta)$ gates are the only approximately synthesizable component. Weprove analytically that for both the operator norm and global phase invariantdistance, the error should be distributed equally among these components (givensome approximations). The optimal number of T-gates obtained by using theglobal phase invariant distance is less. Furthermore, we show that in case ofapproximate Quantum Fourier Transform, the error obtained by pruning rotationgates is less when measured in this distance.

Composability of global phase invariant distance and its application to approximation error management