Randomness-Enhanced Expressivity of Quantum Neural Networks

Area of Science:

• Quantum Computing
• Artificial Intelligence
• Machine Learning

Background:

• Quantum neural networks (QNNs) are a hybrid of AI and quantum computing, showing promise for noisy quantum devices.
• Conventional QNNs use parametrized quantum circuits for operations and measurements.

Purpose of the Study:

• To enhance the expressivity of QNNs.
• To introduce randomness into quantum circuits for improved performance.

Main Methods:

• Incorporated a novel random layer with single-qubit gates sampled from a trainable ensemble pooling.
• Utilized Uhlmann's theorem for majorization to prove accurate approximation of target operators.
• Performed numerical experiments including observable learning, Rényi entropy measurement, and image recognition.

Main Results:

• Demonstrated enhanced expressivity of QNNs by introducing randomness.
• Showcased the ability to approximate arbitrary target operators, enabling observable learning.
• Validated the approach across multiple quantum machine learning tasks.

Conclusions:

• The proposed random layer significantly enhances QNN expressivity.
• This method offers broad applications in quantum machine learning.
• Randomness is a key factor in improving QNN performance for various tasks.