Regressions on quantum neural networks at maximal expressivity

Area of Science:

• Quantum computing
• Artificial intelligence
• Machine learning

Background:

• Deep neural networks (DNNs) are powerful function approximators.
• Quantum neural networks (QNNs) offer potential advantages in computational power.
• Understanding QNN expressivity is crucial for practical applications.

Purpose of the Study:

• To analyze the expressivity of a universal deep neural network structured with nested qubit rotations.
• To quantify the network's ability to approximate continuous functions in regression tasks.
• To investigate the impact of measurement strategies on QNN performance.

Main Methods:

• Utilizing a universal deep neural network with adjustable data re-uploads and nested qubit rotations.
• Quantifying expressivity via partial Fourier decomposition of the output.
• Benchmarking performance using a teacher-student scheme.
• Comparing global-entangling measurements with local qubit readouts.

Main Results:

• Network expressivity scales with depth and qubit count but is limited by data encoding.
• Measurement techniques significantly influence the attainment of maximal expressive bounds.
• Global-entangling measurements saturate expressive bounds, enhancing approximation capabilities.
• This enhancement is linked to a broader survival set of Fourier harmonics.

Conclusions:

• Global-entangling measurements are key to unlocking the full potential of quantum neural networks.
• Optimizing measurement strategies can significantly boost the performance of quantum machine learning models.
• The findings provide insights into designing more powerful and efficient quantum neural network architectures.