Finite-Time Teleportation Phase Transition in Random Quantum Circuits.

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.