Barren plateaus in quantum neural network training landscapes

Area of Science:

• Quantum Computing
• Quantum Machine Learning
• Quantum Optimization

Background:

• Hybrid quantum-classical algorithms train parameterized quantum circuits using classical optimization.
• Random circuits are often used as initial guesses due to their simplicity and hardware efficiency.
• These algorithms are applied in quantum simulation, optimization, and machine learning.

Purpose of the Study:

• To investigate the suitability of random circuits as initial guesses for hybrid quantum-classical algorithms.
• To analyze the gradient estimation complexity for parameterized quantum circuits on noisy intermediate-scale quantum devices.

Main Methods:

• Analysis of the probability of non-zero gradients for parameterized quantum circuits.
• Examination of the relationship between gradient estimation complexity and the number of qubits.
• Connection to the 2-design characteristic of random circuits.

Main Results:

• The probability of a non-zero gradient decreases exponentially with the number of qubits for many parameterized quantum circuits.
• This gradient vanishing issue makes random circuits unsuitable for hybrid quantum-classical algorithms on more than a few qubits.
• The complexity arises from the exponential dimension of Hilbert space and gradient estimation challenges.

Conclusions:

• Random circuits are not effective initializations for training quantum machine learning or optimization models on larger quantum devices.
• The 2-design property of random circuits contributes to the vanishing gradient problem.
• Further research is needed to find suitable parameterized quantum circuits and training strategies for scalable quantum computation.