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

We provide practical and powerful schemes for learning many properties of anunknown n-qubit quantum state using a sparing number of copies of the state.Specifically, we present a depth-modulated randomized measurement scheme thatinterpolates between two known classical shadows schemes based on random Paulimeasurements and random Clifford measurements. These can be seen within ourscheme as the special cases of zero and infinite depth, respectively. We focuson the regime where depth scales logarithmically in n and provide evidence thatthis retains the desirable properties of both extremal schemes whilst, incontrast to the random Clifford scheme, also being experimentally feasible. Wepresent methods for two key tasks; estimating expectation values of certainobservables from generated classical shadows and, computing upper bounds on thedepth-modulated shadow norm, thus providing rigorous guarantees on the accuracyof the output estimates. We consider observables that can be written as alinear combination of poly(n) Paulis and observables that can be written as alow bond dimension matrix product operator. For the former class of observablesboth tasks are solved efficiently in n. For the latter class, we do notguarantee efficiency but present a method that works in practice; byvariationally computing a heralded approximate inverses of a tensor networkthat can then be used for efficiently executing both these tasks.

Shallow shadows: Expectation estimation using low-depth random Clifford circuits