Quantum algorithms for invariants of triangulated manifolds

@article{Alagic2012QuantumAF,
  title={Quantum algorithms for invariants of triangulated manifolds},
  author={G. Alagic and E. Bering},
  journal={Quantum Inf. Comput.},
  year={2012},
  volume={12},
  pages={843-863}
}
  • G. Alagic, E. Bering
  • Published 2012
  • Computer Science, Mathematics, Physics
  • Quantum Inf. Comput.
One of the apparent advantages of quantum computers over their classical counterparts is their ability to efficiently contract tensor networks. In this article, we study some implications of this fact in the case of topological tensor networks. The graph underlying these networks is given by the triangulation of a manifold, and the structure of the tensors ensures that the overall tensor is independent of the choice of internal triangulation. This leads to quantum algorithms for additively… Expand
1 Citations
Quantum Invariants of 3-manifolds and NP vs #P
  • 1
  • PDF

References

SHOWING 1-10 OF 55 REFERENCES
Efficient quantum processing of 3-manifold topological invariants
  • 9
  • PDF
State sum invariants of 3 manifolds and quantum 6j symbols
  • 896
  • PDF
Mednykh's Formula via Lattice Topological Quantum Field Theories
  • 8
  • PDF
Simulation of Topological Field Theories¶by Quantum Computers
  • 233
  • PDF
P.L. Homeomorphic Manifolds are Equivalent by Elementary 5hellingst
  • U. Pachner
  • Computer Science, Mathematics
  • Eur. J. Comb.
  • 1991
  • 286
The Jones polynomial: quantum algorithms and applications in quantum complexity theory
  • 77
  • PDF
...
1
2
3
4
5
...