The Power of Quantum Systems on a Line

@article{Aharonov2007ThePO,
  title={The Power of Quantum Systems on a Line},
  author={D. Aharonov and D. Gottesman and S. Irani and J. Kempe},
  journal={Communications in Mathematical Physics},
  year={2007},
  volume={287},
  pages={41-65}
}
We study the computational strength of quantum particles (each of finite dimensionality) arranged on a line. First, we prove that it is possible to perform universal adiabatic quantum computation using a one-dimensional quantum system (with 9 states per particle). This might have practical implications for experimentalists interested in constructing an adiabatic quantum computer. Building on the same construction, but with some additional technical effort and 12 states per particle, we show… Expand
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References

SHOWING 1-10 OF 29 REFERENCES
The Complexity of Quantum Systems on a One-dimensional Chain
  • 12
  • PDF
The complexity of quantum spin systems on a two-dimensional square lattice
  • 200
  • Highly Influential
  • PDF
Efficient approximation of the dynamics of one-dimensional quantum spin systems.
  • T. Osborne
  • Physics, Medicine
  • Physical review letters
  • 2006
  • 86
The Complexity of the Local Hamiltonian Problem
  • 433
  • PDF
Hamiltonian quantum cellular automata in one dimension
  • 44
  • PDF
Local Hamiltonians in quantum computation
  • 19
  • Highly Influential
  • PDF
Density-matrix algorithms for quantum renormalization groups.
  • White
  • Physics, Medicine
  • Physical review. B, Condensed matter
  • 1993
  • 1,685
An Area Law for One Dimensional Quantum Systems
  • 584
  • PDF
Quantum Computation by Adiabatic Evolution
  • 887
  • PDF
...
1
2
3
...