[Paper Review] Learning quantum phases via single-qubit disentanglement

Zheng An, Chenfeng Cao+2 more|arXiv (Cornell University)|Jul 8, 2021

Neural Networks and Reservoir Computing70 references4 citations

TL;DR

This paper proposes a reinforcement learning (RL)-based method to identify quantum phases by training single-qubit disentangling circuits that reveal distinct entanglement structures in the transverse field Ising model (TFIM) and XXZ model. The RL agent learns optimal local unitary operations to disentangle qubits, successfully detecting phase transitions with high robustness and scalability across system sizes, while also uncovering Kramers-Wannier duality in the TFIM.

ABSTRACT

Identifying phases of matter presents considerable challenges, particularly within the domain of quantum theory, where the complexity of ground states appears to increase exponentially with system size. Quantum many-body systems exhibit an array of complex entanglement structures spanning distinct phases. Although extensive research has explored the relationship between quantum phase transitions and quantum entanglement, establishing a direct, pragmatic connection between them remains a critical challenge. In this work, we present a novel and efficient quantum phase transition classifier, utilizing disentanglement with reinforcement learning-optimized variational quantum circuits. We demonstrate the effectiveness of this method on quantum phase transitions in the transverse field Ising model (TFIM) and the XXZ model. Moreover, we observe the algorithm's ability to learn the Kramers-Wannier duality pertaining to entanglement structures in the TFIM. Our approach not only identifies phase transitions based on the performance of the disentangling circuits but also exhibits impressive scalability, facilitating its application in larger and more complex quantum systems. This study sheds light on the characterization of quantum phases through the entanglement structures inherent in quantum many-body systems.

Motivation & Objective

• To develop a scalable, local method for identifying quantum phases using entanglement structure detection.
• To overcome the exponential complexity of many-body ground state characterization in quantum systems.
• To leverage reinforcement learning to design variational quantum circuits that extract key entanglement features without global optimization.
• To demonstrate the method's robustness and transferability across different system sizes and model parameters.
• To explore whether the RL agent learns fundamental symmetries, such as Kramers-Wannier duality, from entanglement patterns.

Proposed method

• A reinforcement learning agent is trained to design a variational quantum circuit that performs single-qubit disentanglement on a target qubit.
• The RL agent optimizes local unitary operations to minimize entanglement entropy between the target qubit and the rest of the system.
• The disentangling circuit is trained on ground states from different phases of the TFIM and XXZ models at varying parameters.
• The performance of the trained circuit is evaluated by measuring residual entanglement entropy across phase transitions.
• The method uses only local operations and single-qubit measurements, enabling scalability to larger systems.
• The trained circuit from small systems (N=8) is applied to larger systems (N=10,12,14), testing transferability and robustness.

Experimental results

Research questions

• RQ1 Can a reinforcement learning agent design a disentangling circuit that effectively distinguishes quantum phases based on entanglement structure?
• RQ2 Does the RL-designed circuit exhibit robustness to variations in training parameters and system size?
• RQ3 Can the RL agent learn fundamental symmetries, such as Kramers-Wannier duality, from entanglement patterns in the TFIM?
• RQ4 Is the disentangling circuit trained on small systems transferable to larger systems without retraining?
• RQ5 How does the entanglement entropy of the disentangled state reflect the underlying quantum phase transition?

Key findings

• The RL-designed disentangling circuit successfully identifies phase transitions in both the transverse field Ising model and the XXZ model with high accuracy.
• The method demonstrates robustness: performance remains consistent across different training parameters and system sizes.
• The disentangling circuit trained on N=8 systems generalizes effectively to N=10, 12, and 14 qubits, indicating scalability.
• For the TFIM, the RL agent learns a two-body optimal disentanglement structure when λ > 1, and reveals Kramers-Wannier duality when λ < 1.
• The entanglement entropy of the disentangled state shows a clear peak at the phase transition point, serving as a reliable indicator.
• The results suggest that the entanglement structure is intrinsic to the quantum phase and independent of system size, not a finite-size artifact.