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Neural networks provide a prospective tool for error mitigation in quantumsimulation of physical systems. However, we need both noisy and noise-free datato train neural networks to mitigate errors in quantum computing results. Here,we propose a physics-motivated method to generate training data for quantumerror mitigation via neural networks, which does not require classicalsimulation and target circuit simplification. In particular, we propose to usethe echo evolution of a quantum system to collect noisy and noise-free data fortraining a neural network. Under this method, the initial state evolves forwardand backward in time, returning to the initial state at the end of evolution.When run on the noisy quantum processor, the resulting state will be influencedby with quantum noise accumulated during evolution. Having a vector ofobservable values of the initial (noise-free) state and the resulting (noisy)state allows us to compose training data for a neural network. We demonstratethat a feed-forward fully connected neural network trained onecho-evolution-generated data can correct results of forward-in-time evolution.Our findings can enhance the application of neural networks to error mitigationin quantum computing.

Echo-evolution data generation for quantum error mitigation via neural networks