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

While quantum state tomography is notoriously hard, most states hold littleinterest to practically-minded tomographers. Given that states and unitariesappearing in Nature are of bounded gate complexity, it is natural to ask ifefficient learning becomes possible. In this work, we prove that to learn astate generated by a quantum circuit with $G$ two-qubit gates to a small tracedistance, a sample complexity scaling linearly in $G$ is necessary andsufficient. We also prove that the optimal query complexity to learn a unitarygenerated by $G$ gates to a small average-case error scales linearly in $G$.While sample-efficient learning can be achieved, we show that under reasonablecryptographic conjectures, the computational complexity for learning states andunitaries of gate complexity $G$ must scale exponentially in $G$. We illustratehow these results establish fundamental limitations on the expressivity ofquantum machine learning models and provide new perspectives on no-free-lunchtheorems in unitary learning. Together, our results answer how the complexityof learning quantum states and unitaries relate to the complexity of creatingthese states and unitaries.

Learning quantum states and unitaries of bounded gate complexity