# A quantum algorithm to estimate the Gowers U2 norm and linearity testing of Boolean functions

@article{Jothishwaran2020AQA, title={A quantum algorithm to estimate the Gowers U2 norm and linearity testing of Boolean functions}, author={C. A. Jothishwaran and Anton Tkachenko and Sugata Gangopadhyay and Constanza Riera and Pantelimon Stănică}, journal={ArXiv}, year={2020}, volume={abs/2006.16523} }

We propose a quantum algorithm to estimate the Gowers U2 norm of a Boolean function, and extend it into a second algorithm to distinguish between linear Boolean functions and Boolean functions that are ǫ-far from the set of linear Boolean functions, which seems to perform better than the classical BLR algorithm. Finally, we outline an algorithm to estimate Gowers U3 norms of Boolean functions.

#### Topics from this paper.

#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 14 REFERENCES

## A new proof of Szemerédi's theorem

VIEW 2 EXCERPTS

## An inverse theorem for the Gowers U3 norm, 2005, https://arxiv.org/abs/math/0503014

VIEW 1 EXCERPT

## Cryptographic Boolean functions and Applications, 2nd Edition, Elsevier (2017)

VIEW 1 EXCERPT

## Quantum Computation and Quantum Information (10th ed.)

VIEW 1 EXCERPT

## Quantum Computing: A Gentle Introduction, The MIT Press, 1st ed

VIEW 1 EXCERPT