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Area of Science:

  • Quantum Information Science
  • Computational Physics
  • Quantum Computing

Background:

  • Understanding the computational complexity of simulating quantum systems is crucial for advancing quantum technologies.
  • Entanglement breaking noise is a key factor influencing the dynamics and simulation of quantum spin systems.

Purpose of the Study:

  • To analyze the complexity of classically simulating continuous-time dynamics of quantum spin systems under entanglement breaking noise.
  • To determine the conditions under which classical simulation is efficient or computationally hard.

Main Methods:

  • Analysis of quantum spin system dynamics with a constant rate of entanglement breaking noise.
  • Encoding 1D fault-tolerant quantum computation into spin systems on 2D or higher dimensional grids.

Main Results:

  • A polynomial-time classical algorithm can sample spin states when noise rate exceeds a specific threshold.
  • Weakly simulating Hamiltonian and dissipative dynamics is expected to be hard in the low-noise regime.

Conclusions:

  • The complexity of simulating quantum spin systems depends critically on the noise level.
  • High noise levels can render complex quantum dynamics classically tractable, while low noise poses significant computational challenges.