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Measurement-based quantum computation on symmetry breaking thermal States.

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Measurement-based quantum computation (MBQC) is more robust against thermal noise in interacting cluster states. Long-range order in thermal states below a critical temperature enhances MBQC stability, even at higher temperatures.

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Area of Science:

  • Quantum Information Science
  • Condensed Matter Physics

Background:

  • Measurement-based quantum computation (MBQC) is a leading model for quantum computing.
  • Thermal states and phase transitions in quantum systems pose challenges for robust computation.
  • The cluster Hamiltonian is a key resource state for MBQC.

Purpose of the Study:

  • To investigate the impact of thermal phase transitions on MBQC robustness.
  • To explore the role of long-range order in symmetry-breaking thermal states for quantum computation.
  • To determine the potential for performing MBQC at higher temperatures using interacting Hamiltonians.

Main Methods:

  • Analysis of the interacting cluster Hamiltonian and its thermal phase transitions.
  • Studying the properties of thermal states below a critical temperature.
  • Investigating the robustness of MBQC against thermal excitations in 2D and 3D systems.

Main Results:

  • Long-range order in symmetry-breaking thermal states significantly enhances MBQC robustness.
  • MBQC exhibits enhanced stability in 2D systems with interacting cluster states.
  • Topological protection of MBQC is proven in 3D systems below the critical temperature.
  • The interacting cluster Hamiltonian enables MBQC at temperatures one order of magnitude higher than the free cluster Hamiltonian.

Conclusions:

  • Interacting cluster Hamiltonians offer a pathway to robust quantum computation in the presence of thermal noise.
  • Symmetry-breaking thermal states with long-range order provide inherent protection for MBQC.
  • These findings pave the way for practical quantum computation at elevated temperatures.