Quantum (Dec 2023)

Measurement-based quantum computation in finite one-dimensional systems: string order implies computational power

  • Robert Raussendorf,
  • Wang Yang,
  • Arnab Adhikary

DOI
https://doi.org/10.22331/q-2023-12-28-1215
Journal volume & issue
Vol. 7
p. 1215

Abstract

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We present a new framework for assessing the power of measurement-based quantum computation (MBQC) on short-range entangled symmetric resource states, in spatial dimension one. It requires fewer assumptions than previously known. The formalism can handle finitely extended systems (as opposed to the thermodynamic limit), and does not require translation-invariance. Further, we strengthen the connection between MBQC computational power and string order. Namely, we establish that whenever a suitable set of string order parameters is non-zero, a corresponding set of unitary gates can be realized with fidelity arbitrarily close to unity.