Virtual distillation with neural quantum states

Virtual Distillation (VD) is one of the promising Quantum Error Mitigation (QEM) protocols that can exponentially attenuate computational bias by increasing the number of replicated quantum states. On the other hand, VD faces several challenges such as the difficulties in generating quantum state replicas and in globally entangled measurement. In this work, we address these two issues and propose a novel method to mitigate errors in computational outcomes based on Neural Quantum State (NQS).NQS enables efficient representation of large quantum states of interests with neural networks. Once NQS learns quantum states, we can increase the samples in Monte-Carlo sampling without re-executing quantum experiments, and the globally entangled measurement can be achieved without quantum errors. We numerically evaluated the performance of the technique. The calculated expectation value for the Bell state under stochastic and unitary errors indicate our methods can suppress the bias more efficiently than the existing methods. Thus, our method can be used as a QEM methods for unknown errors with a mechanism similar to VD with resolving its drawbacks.