Quantum State Learning via Single-Shot Measurements.

Area of Science:

• Quantum information science
• Machine learning
• Quantum computing

Background:

• Quantum state tomography is essential for quantum information processing.
• Existing methods often require numerous measurements and significant computational resources.
• Developing efficient and accurate quantum state learning techniques is crucial.

Purpose of the Study:

• To introduce a novel machine learning algorithm for quantum state learning using single-shot measurements.
• To demonstrate the theoretical optimal accuracy and experimental efficiency of the proposed method.
• To explore the algorithm's performance in high-dimensional quantum systems.

Main Methods:

• Development of a single-shot measurement learning algorithm incorporating weighted randomness.
• Experimental validation using a linear-optical setup for qubit-state learning and reproduction.
• Simulations to assess the extension of the method to high-dimensional systems.

Main Results:

• The single-shot measurement learning algorithm achieved theoretical optimal accuracy.
• Experimental results demonstrated high accuracy in qubit-state learning and reproduction, with infidelity scaling of O(N^{-0.983}) down to <10^{-5}.
• The method proved more computationally efficient than existing tomographic schemes.

Conclusions:

• The proposed single-shot measurement learning algorithm offers a computationally efficient and highly accurate approach for quantum state learning.
• Weighted randomness in the learning rule is key to the method's superior performance.
• The algorithm shows promise for scalable quantum information processing and high-dimensional applications.