Enhancing Quantum Variational Algorithms with Zero Noise Extrapolation
  via Neural Networks
Subhasree Bhattacharjee Soumyadip Sarkar Kunal Das Bikramjit Sarkar
In the emergent realm of quantum computing, the Variational Quantum
Eigensolver (VQE) stands out as a promising algorithm for solving complex
quantum problems, especially in the noisy intermediate-scale quantum (NISQ)
era. However, the ubiquitous presence of noise in quantum devices often limits
the accuracy and reliability of VQE outcomes. This research introduces a novel
approach to ameliorate this challenge by utilizing neural networks for zero
noise extrapolation (ZNE) in VQE computations. By employing the Qiskit
framework, we crafted parameterized quantum circuits using the RY-RZ ansatz and
examined their behavior under varying levels of depolarizing noise. Our
investigations spanned from determining the expectation values of a
Hamiltonian, defined as a tensor product of Z operators, under different noise
intensities to extracting the ground state energy. To bridge the observed
outcomes under noise with the ideal noise-free scenario, we trained a Feed
Forward Neural Network on the error probabilities and their associated
expectation values. Remarkably, our model proficiently predicted the VQE
outcome under hypothetical noise-free conditions. By juxtaposing the simulation
results with real quantum device executions, we unveiled the discrepancies
induced by noise and showcased the efficacy of our neural network-based ZNE
technique in rectifying them. This integrative approach not only paves the way
for enhanced accuracy in VQE computations on NISQ devices but also underlines
the immense potential of hybrid quantum-classical paradigms in circumventing
the challenges posed by quantum noise. Through this research, we envision a
future where quantum algorithms can be reliably executed on noisy devices,
bringing us one step closer to realizing the full potential of quantum
computing.