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A Single-shot Measurement of the Energy of Product States in a Translation Invariant Spin Chain Can Replace Any Quantum Computation

2008

Article

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In measurement-based quantum computation, quantum algorithms are implemented via sequences of measurements. We describe a translationally invariant finite-range interaction on a one-dimensional qudit chain and prove that a single-shot measurement of the energy of an appropriate computational basis state with respect to this Hamiltonian provides the output of any quantum circuit. The required measurement accuracy scales inverse polynomially with the size of the simulated quantum circuit. This shows that the implementation of energy measurements on generic qudit chains is as hard as the realization of quantum computation. Here, a ‘measurement‘ is any procedure that samples from the spectral measurement induced by the observable and the state under consideration. As opposed to measurement-based quantum computation, the post-measurement state is irrelevant.

Author(s): Janzing, D. and Wocjan, P. and Zhang, S.
Journal: New Journal of Physics
Volume: 10
Number (issue): 093004
Pages: 1-18
Year: 2008
Month: September
Day: 0

Department(s): Empirical Inference
Bibtex Type: Article (article)

Digital: 0
DOI: 10.1088/1367-2630/10/9/093004
Language: en
Organization: Max-Planck-Gesellschaft
School: Biologische Kybernetik

Links: PDF

BibTex

@article{5395,
  title = {A Single-shot Measurement of the Energy of Product States in a Translation Invariant Spin Chain Can Replace Any Quantum Computation},
  author = {Janzing, D. and Wocjan, P. and Zhang, S.},
  journal = {New Journal of Physics},
  volume = {10},
  number = {093004},
  pages = {1-18},
  organization = {Max-Planck-Gesellschaft},
  school = {Biologische Kybernetik},
  month = sep,
  year = {2008},
  month_numeric = {9}
}