Neural Network-Guided Extrapolation Technique for Quantum Variational Algorithms

Area of Science:

• Quantum Computing
• Artificial Intelligence
• Computational Physics

Background:

• The Variational Quantum Eigensolver (VQE) is a key algorithm for quantum computation in the Noisy Intermediate-Scale Quantum (NISQ) era.
• Quantum device noise significantly degrades VQE accuracy and reliability.
• Accurate ground state energy (GSE) determination is crucial for many quantum applications.

Purpose of the Study:

• To develop and evaluate a novel neural network-based extrapolation method for mitigating noise in VQE calculations.
• To enhance the accuracy and reliability of VQE outcomes on NISQ devices.
• To compare the performance of different neural network architectures for noise extrapolation.

Main Methods:

• Parameterized quantum circuits were designed using the RY-RZ ansatz within the Qiskit framework.
• The performance of these circuits was analyzed under various depolarizing noise models (bit-flip, phase-flip, amplitude damping).
• A Feedforward Neural Network (FFNN) was trained using error probabilities and corresponding expectation values to extrapolate noise-free VQE results.

Main Results:

• The FFNN model accurately predicted VQE results under ideal, noise-free conditions.
• Simulations and real quantum hardware executions showed noise-induced inconsistencies, which the neural network approach effectively corrected.
• FFNN demonstrated superior accuracy and speed compared to Convolutional Neural Network (CNN) and Long Short-Term Memory (LSTM) networks for this task.

Conclusions:

• Neural network-based extrapolation is a promising technique for improving VQE accuracy on NISQ devices.
• Combining quantum and classical methods, particularly neural networks, offers a powerful strategy to overcome quantum noise challenges.
• FFNN provides an efficient and accurate solution for noise correction in VQE calculations.