The geometry of quantum computation

@article{Dowling2008TheGO,
  title={The geometry of quantum computation},
  author={M. Dowling and M. Nielsen},
  journal={Quantum Inf. Comput.},
  year={2008},
  volume={8},
  pages={861-899}
}
Determining the quantum circuit complexity of a unitary operation is closely related to the problem of finding minimal length paths in a particular curved geometry [Nielsen et al, Science 311, 1133-1135 (2006)]. This paper investigates many of the basic geometric objects associated to this space, including the Levi-Civita connection, the geodesic equation, the curvature, and the Jacobi equation. We show that the optimal Hamiltonian evolution for synthesis of a desired unitary necessarily obeys… Expand
Tools in the Riemannian geometry of quantum computation
  • H. Brandt
  • Mathematics, Computer Science
  • Quantum Inf. Process.
  • 2012
Dual field theories of quantum computation
Quantum complexity of time evolution with chaotic Hamiltonians
Riemannian geometry of quantum computation
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