Topological Order and Criticality in (2+1)D Monitored Random Quantum Circuits

Area of Science:

• Quantum information science
• Condensed matter physics
• Statistical mechanics

Background:

• Random quantum circuits offer a novel framework for exploring complex entanglement phenomena.
• Standard operator expectation values often obscure rich entanglement phase diagrams.
• Understanding these diagrams is crucial for advancing quantum computing and fundamental physics.

Purpose of the Study:

• To investigate the entanglement phase diagrams generated by (2+1)D random quantum circuits with Clifford gates and specific measurements.
• To identify and characterize critical points and novel phases within these circuits.
• To explore the connection between quantum circuit measurements and classical statistical mechanics models like percolation.

Main Methods:

• Utilizing (2+1)D random circuits with random Clifford unitary gates.
• Implementing competing single-qubit measurements (Pauli-Z and Pauli-Y) and toric code stabilizer measurements.
• Analyzing the resulting phase diagrams, including critical phenomena and entanglement properties.

Main Results:

• A phase diagram featuring a tricritical point mapping to (2+1)D percolation, alongside trivial, topologically ordered, critical, and volume law phases.
• Discovery of an anisotropic self-dual tricritical point with Pauli-Y measurements, exhibiting logarithmic area law violation and anomalous topological entanglement entropy.
• Observation of a measurement-induced volume law entangled phase even without unitary dynamics.

Conclusions:

• Random quantum circuits with carefully chosen measurements can host intricate and non-trivial entanglement phases.
• The study reveals a deep connection between quantum entanglement and classical percolation phenomena.
• Novel critical behaviors and phases emerge, distinct from known universality classes, highlighting the richness of measurement-driven quantum dynamics.