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. This work shows 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). The study carefully analyzes and elucidates the asymptotic scaling of this unique QEM capacity in VQNHE from both theoretical and experimental perspectives. Finally, a variational basis transformation is proposed 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.

Automated summary

Quantum error mitigation (QEM) is essential for reliable results on quantum computers, especially in the noisy intermediate scale quantum (NISQ) era. Combining QEM with quantum-classical hybrid schemes shows promise for practical quantum advantages. The study introduces the variational quantum-neural hybrid eigensolver (VQNHE) algorithm, which combines a parameterized quantum circuit with a neural network and has inherent noise resilience and unique QEM capacity. The study analyzes the scaling of this unique QEM capacity in VQNHE and proposes a variational basis transformation for enhanced error mitigation.