Measurement induced entanglement transition in two dimensional shallow circuit

TL;DR

This paper investigates measurement-induced entanglement transitions in two-dimensional shallow quantum circuits, revealing phase transitions between entangled and disentangled states through numerical analysis and theoretical interpretation.

Contribution

It introduces two models demonstrating entanglement phase transitions in shallow circuits, including a competition-driven transition and a gate density-driven transition, with generalization to qudits.

Findings

Observation of entanglement phase transition between volume law and area law phases.

Numerical evaluation of critical exponents for the phase transition.

Interpretation of the transition via a random bond Ising model.

Abstract

We prepare two dimensional states generated by shallow circuits composed of (1) one layer of two-qubit CZ gate or (2) a few layers of two-qubit random Clifford gate. After measuring all of the bulk qubits, we study the entanglement structure of the remaining qubits on the one dimensional boundary. In the first model, we observe that the competition between the bulk X and Z measurements can lead to an entanglement phase transition between an entangled volume law phase and a disentangled area law phase. We numerically evaluate the critical exponents and generalize this idea to other qudit systems with local Hilbert space dimension larger than 2. In the second model, we observe the entanglement transition by varying the density of the two-qubit gate in each layer. We give an interpretation of this transition in terms of random bond Ising model in a similar shallow circuit composed of random Haar gates.