Neural Network-Guided Extrapolation Technique for Quantum Variational Algorithms

In the noisy intermediate-scale quantum (NISQ) era, the Variational Quantum Eigensolver (VQE) comes out as an effective algorithm for addressing complex quantum challenges. However, the presence of noise in quantum devices frequently reduces the accuracy and reliability of VQE outcomes. This paper presents an innovative method to address this issue by using a neural network-based extrapolation technique in VQE calculation. By utilizing the Qiskit framework, we designed parameterized quantum circuits using the RY-RZ ansatz, and their performance was analyzed under different levels of depolarizing noise with bit-flip errors, phase-flip errors, and amplitude damping errors. Our inquiry involved analyzing the expected outcomes of a Hamiltonian across various levels of noise intensity with the objective of deducing the ground state energy (GSE). To connect the observed noisy outcomes with the ideal noise-free condition, a Feedforward Neural Network (FFNN) was trained using the error probabilities and their corresponding expectation values. This model accurately predicted the VQE results in an ideal noise-free scenario. Comparison of the result of simulation and real quantum hardware executions revealed noise-induced inconsistencies, highlighting the effectiveness of this neural network-based extrapolation approach in correcting them. This comprehensive method improves the accuracy of VQE calculation on NISQ devices and highlights the significant potential of blending quantum and classical methods to address the threats imposed by quantum noise. The comparison of results between FFNN, convolutional neural network (CNN), and long short-term memory (LSTM) network reveals that FFNN predicts outcomes with more accuracy but in less time.