Quantum Neural Network Realization of XOR on a Desktop Quantum Computer

Area of Science:

• Quantum Computing
• Machine Learning
• Quantum Information Science

Background:

• Classical computing faces limitations in solving complex machine learning problems.
• Quantum neural networks offer a novel approach by leveraging quantum computation.
• The exclusive OR (XOR) function is a nonlinear benchmark problem unsuitable for single-layer classical perceptrons.

Purpose of the Study:

• To demonstrate a quantum neural network capable of learning the nonlinear exclusive OR function.
• To evaluate the performance of a quantum neural network on actual quantum hardware.
• To establish a minimal, physically meaningful benchmark for quantum machine learning.

Main Methods:

• Trained a variational quantum circuit model using the PennyLane framework in a simulation.
• Deployed the trained quantum neural network on a two-qubit Nuclear Magnetic Resonance (NMR)-based desktop quantum computer.
• Evaluated hardware performance by measuring quantum state fidelity and purity.

Main Results:

• Achieved high quantum state fidelity: approximately 98.85% (Ry) and 99.35% (Rx).
• Obtained high average purity: 95.16% (Ry) and 97.43% (Rx).
• Demonstrated excellent agreement between simulated and experimental results.

Conclusions:

• Quantum machine learning is feasible on small-scale, room-temperature quantum hardware.
• The successful learning of the XOR function serves as a critical benchmark for quantum machine learning.
• This study highlights the potential of quantum computing for advancing machine learning capabilities.