# Interactive quantum advantage with noisy, shallow Clifford circuits

@article{Grier2021InteractiveQA, title={Interactive quantum advantage with noisy, shallow Clifford circuits}, author={Daniel Grier and Nathan Ju and L. Schaeffer}, journal={ArXiv}, year={2021}, volume={abs/2102.06833} }

Recent work by Bravyi et al. constructs a relation problem that a noisy constant-depth quantum circuit (QNC) can solve with near certainty (probability 1 − o(1)), but that any bounded fan-in constant-depth classical circuit (NC) fails with some constant probability. We show that this robustness to noise can be achieved in the other low-depth quantum/classical circuit separations in this area. In particular, we show a general strategy for adding noise tolerance to the interactive protocols of… Expand

#### References

SHOWING 1-10 OF 21 REFERENCES

Interactive shallow Clifford circuits: quantum advantage against NC¹ and beyond

- Physics, Computer Science
- STOC
- 2020

Average-case quantum advantage with shallow circuits

- Mathematics, Computer Science
- Computational Complexity Conference
- 2019

Quantum Advantage with Noisy Shallow Circuits in 3D

- Physics, Computer Science
- 2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS)
- 2019

Exponential separation between shallow quantum circuits and unbounded fan-in shallow classical circuits

- Computer Science, Physics
- STOC
- 2019

Trading Locality for Time: Certifiable Randomness from Low-Depth Circuits

- Medicine, Computer Science
- Communications in mathematical physics
- 2021

Constant Overhead Quantum Fault-Tolerance with Quantum Expander Codes

- Computer Science, Physics
- 2018 IEEE 59th Annual Symposium on Foundations of Computer Science (FOCS)
- 2018

Classical simulation of commuting quantum computations implies collapse of the polynomial hierarchy

- Physics, Mathematics
- Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- 2010