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Area of Science:

  • Quantum Information Science
  • Condensed Matter Physics
  • Quantum Computing

Background:

  • Entanglement is a key resource for quantum computation and communication.
  • Understanding entanglement dynamics in quantum circuits is crucial for scalable quantum technologies.
  • Previous studies often focused on specific circuit types or idealized conditions.

Purpose of the Study:

  • To determine the time required to entangle two distant qubits in generic unitary quantum circuit dynamics.
  • To investigate the onset of entanglement and its relation to quantum state teleportation fidelity.
  • To provide a theoretical framework for understanding entanglement transitions in random quantum circuits.

Main Methods:

  • Analysis of random unitary circuit dynamics, including short-range 2D and long-range 1D interactions.
  • Mapping quantum evolution to a finite-temperature thermal state of an effective spin Hamiltonian.
  • Numerical simulations of Clifford circuits to verify theoretical predictions.

Main Results:

  • A finite critical time (t_c) for entanglement onset was identified, marking a phase transition.
  • Entanglement and quantum teleportation fidelity exhibit a simultaneous critical onset.
  • Entanglement corresponds to long-range ferromagnetic spin correlations below a critical temperature in the effective Hamiltonian.

Conclusions:

  • Entanglement in generic random quantum circuits can emerge at a finite time via a phase transition.
  • The theoretical framework provides insights into the thermalization and entanglement properties of quantum systems.
  • Findings have implications for quantum simulation platforms and the development of quantum communication protocols.