Interactive shallow Clifford circuits: Quantum advantage against NC¹ and beyond

  title={Interactive shallow Clifford circuits: Quantum advantage against NC¹ and beyond},
  author={Daniel Grier and Luke Schaeffer},
  journal={Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing},
  • Daniel Grier, Luke Schaeffer
  • Published 6 November 2019
  • Computer Science
  • Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing
Recent work of Bravyi et al. and follow-up work by Bene Watts et al. demonstrates a quantum advantage for shallow circuits: constant-depth quantum circuits can perform a task which constant-depth classical (i.e., 0) circuits cannot. Their results have the advantage that the quantum circuit is fairly practical, and their proofs are free of hardness assumptions (e.g., factoring is classically hard, etc.). Unfortunately, constant-depth classical circuits are too weak to yield a convincing real… 

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