Variational Quantum-Neural Hybrid Error Mitigation

Quantum error mitigation (QEM) is crucial for obtaining reliable results on quantum computers by suppressing quantum noise with moderate resources. It is a key factor for successful and practical quantum algorithm implementations in the noisy intermediate scale quantum (NISQ) era. Since quantum-classical hybrid algorithms can be executed with moderate and noisy quantum resources, combining QEM with quantum-classical hybrid schemes is one of the most promising directions toward practical quantum advantages. In this work, we show how the variational quantum-neural hybrid eigensolver (VQNHE) algorithm, which seamlessly combines the expressive power of a parameterized quantum circuit with a neural network, is inherently noise resilient with a unique QEM capacity, which is absent in vanilla variational quantum eigensolvers (VQE). We carefully analyze and elucidate the asymptotic scaling of this unique QEM capacity in VQNHE from both theoretical and experimental perspectives. Finally, we propose a variational basis transformation for the Hamiltonian to be measured under the VQNHE framework, yielding a powerful tri-optimization setup, dubbed as VQNHE++. VQNHE++ can further enhance the quantum-neural hybrid expressive power and error mitigation capacity.