High-Accuracy Neural-Network Quantum States via Randomized Real-Time Dynamics

We introduce a new algorithm to enhance the accuracy of neural-network quantum states (NQSs) in approximating ground states of quantum systems. Our method, termed dynamical averaging, estimates expectation values by sampling a NQS as it evolves in real-time. Using techniques from quantum information, we prove an up-to-quadratic suppression of error in estimating arbitrary ground state observables. Importantly, this improved accuracy requires neither further energy minimization nor an enhanced parameterization, but rather exploits the influence of randomness on quantum states. We demonstrate the advantage of dynamical averaging on an important spin model in quantum many-body physics, where it reduces relative errors in correlation functions from $\sim 10$\% to $\lesssim 1$\%.