A Variational Approach to Quantum Error Mitigation*

Variational Quantum Algorithms (VQAs) are relatively robust to noise, but errors are still a significant detriment to VQAs on near-term quantum machines. It is imperative to employ error mitigation techniques (EMs) to improve VQA fidelity. While existing EMs built from theory provide gains, the disconnect between theory and real machine execution limits their benefits.

We propose a novel “variational approach to EM”, which dynamically tailors EMs to be optimal for the actual noisy execution of the VQA on the target machine. We do so by tuning specific EM features, in a manner similar to tuning VQA’s traditional angle parameters, targeting improvements in VQA expectation.

We utilize the variational approach to optimize two EMs: 1-qubit gate scheduling and insertion of dynamical decoupling sequences, tuning gate positions and number of sequences respectively. This achieves 3x improvements in VQA expectation for applications on IBM machines.

Importantly, the variational approach is general and can be extended to multiple EMs whose configurations are hard to select apriori, potentially enabling practically useful VQA in the NISQ era.