# Separations in query complexity using cheat sheets

@inproceedings{Aaronson2016SeparationsIQ, title={Separations in query complexity using cheat sheets}, author={S. Aaronson and Shalev Ben-David and Robin Kothari}, booktitle={STOC 2016}, year={2016} }

We show a power 2.5 separation between bounded-error randomized and quantum query complexity for a total Boolean function, refuting the widely believed conjecture that the best such separation could only be quadratic (from Grover's algorithm). We also present a total function with a power 4 separation between quantum query complexity and approximate polynomial degree, showing severe limitations on the power of the polynomial method. Finally, we exhibit a total function with a quadratic gap… CONTINUE READING

#### Supplemental Presentations

#### Paper Mentions

BLOG POST

BLOG POST

BLOG POST

BLOG POST

BLOG POST

62 Citations

Separations in Communication Complexity Using Cheat Sheets and Information Complexity

- Computer Science, Physics
- 2016

- 24
- PDF

Towards Optimal Separations between Quantum and Randomized Query Complexities

- Computer Science, Physics
- 2019

- 4
- PDF

Nearly optimal separations between communication (or query) complexity and partitions

- Computer Science, Mathematics
- 2015

- 25
- PDF

Optimal separation and strong direct sum for randomized query complexity

- Computer Science, Mathematics
- 2019

- 4
- PDF

Understanding Quantum Algorithms via Query Complexity

- Computer Science, Physics
- 2017

- 22
- Highly Influenced
- PDF

#### References

##### Publications referenced by this paper.

SHOWING 1-5 OF 5 REFERENCES

Deterministic Communication vs. Partition Number

- Computer Science, Mathematics
- 2015

- 108
- Highly Influential
- PDF

Separations in query complexity based on pointer functions

- Computer Science, Mathematics
- 2016

- 42
- Highly Influential

Approximating the AND-OR tree. Theory of Computing

- 2013