All reports by Author Alex Grilo:

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TR20-185
| 1st December 2020
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Srinivasan Arunachalam, Alex Grilo, Tom Gur, Igor Oliveira, Aarthi Sundaram#### Quantum learning algorithms imply circuit lower bounds

Revisions: 1

Srinivasan Arunachalam, Alex Grilo, Tom Gur, Igor Oliveira, Aarthi Sundaram

We establish the first general connection between the design of quantum algorithms and circuit lower bounds. Specifically, let $\mathrm{C}$ be a class of polynomial-size concepts, and suppose that $\mathrm{C}$ can be PAC-learned with membership queries under the uniform distribution with error $1/2 - \gamma$ by a time $T$ quantum algorithm. ... more >>>