publication . Conference object . Article . Preprint . 2000

quantum lower bounds by quantum arguments

Ambainis, Andris;
Open Access
  • Published: 23 Feb 2000
  • Publisher: ACM Press
Abstract
We propose a new method for proving lower bounds on quantum query algorithms. Instead of a classical adversary that runs the algorithm with one input and then modifies the input, we use a quantum adversary that runs the algorithm with a superposition of inputs. If the algorithm works correctly, its state becomes entangled with the superposition over inputs. We bound the number of queries needed to achieve a sufficient entanglement and this implies a lower bound on the number of queries for the computation. Using this method, we prove two new $\Omega(\sqrt{N})$ lower bounds on computing AND of ORs and inverting a permutation and also provide more uniform proofs f...
Subjects
free text keywords: Upper and lower bounds, Quantum error correction, Quantum operation, Computer science, Quantum computer, Quantum algorithm, Quantum capacity, Combinatorics, Quantum sort, Discrete mathematics, Quantum phase estimation algorithm, Theoretical Computer Science, Computer Networks and Communications, Computational Theory and Mathematics, Applied Mathematics, quantum computing, quantum lower bounds, quantum query algorithms., Quantum Physics, Computer Science - Computational Complexity
Funded by
NSF| A Proposal for Research on Quantum Computation and Clustering Algorithms
Project
  • Funder: National Science Foundation (NSF)
  • Project Code: 9800024
  • Funding stream: Directorate for Computer & Information Science & Engineering | Division of Computing and Communication Foundations
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