Limitations of quantum coset states for graph isomorphism

Abstract

It has been known for some time that graph isomorphism reduces to the hidden subgroup problem (HSP). What is more, most exponential speedups in quantum computation are obtained by solving instances of the HSP. A common feature of the resulting algorithms is the use of quantum coset states, which encode the hidden subgroup. An open question has been how hard it is to use these states to solve graph isomorphism. It was recently shown by Moore et al. [2005] that only an exponentially small amount of information is available from one, or a pair of coset states. A potential source of power to exploit are entangled quantum measurements that act jointly on many states at once.

Document Details

Document Type
Pub Defense Publication
Publication Date
Oct 01, 2010
Source ID
10.1145/1857914.1857918

Entities

People

  • Alexander Russell
  • Cristopher Moore
  • Martin Rötteler
  • Pranab Sen
  • Sean Hallgren

Organizations

  • Army Research Office
  • Division of Computing and Communication Foundations
  • NEC Laboratories America
  • National Science Foundation
  • Pennsylvania State University
  • Tata Institute of Fundamental Research
  • University of Connecticut
  • University of New Mexico

Tags

Readers

  • Graph Algorithms and Convex Optimization.
  • Neural Network Machine Learning.
  • Quantum Dot Semiconductor Device Photonics and Graphene Optoelectronic Materials and THz Physics.

Technology Areas

  • Quantum Computing