Quantum phase classification via partial tomography-based quantum hypothesis testing.

Area of Science:

• Quantum many-body physics
• Quantum information science
• Statistical inference

Background:

• Quantum phase classification is crucial in many-body physics.
• Traditional methods like order parameters and quantum convolutional neural networks (QCNNs) have limitations.
• These limitations include requiring extensive prior knowledge or numerous quantum state copies.

Purpose of the Study:

• To develop a more efficient and accurate quantum phase classification algorithm.
• To overcome the limitations of existing methods in terms of data requirements and computational cost.
• To leverage the theoretical optimality of the quantum Neyman-Pearson test for state discrimination.

Main Methods:

• Proposed a classification algorithm based on the quantum Neyman-Pearson test.
• Introduced a partitioning strategy to apply hypothesis tests to subsystems, avoiding full state tomography.
• Validated the approach using numerical simulations on systems up to 81 qubits.

Main Results:

• The proposed method achieves lower classification error probabilities than conventional methods.
• It requires significantly fewer quantum state copies compared to order parameter-based classifiers, QCNNs, and classical machine learning enhanced with quantum data.
• Demonstrated reduced training costs and classical computational time, along with scalability.

Conclusions:

• Quantum hypothesis testing offers a powerful tool for quantum phase classification.
• The partitioning strategy effectively reduces data requirements while maintaining accuracy.
• The method shows promise for experimental applications combining quantum measurements and classical post-processing.