Noise-resilient quantum circuits

Certain quantum circuits are shown to be surprisingly resilient to noise. The circuit depth scales with the system size, but even without error correction, low-order correlation functions are perturbed at most by an amount comparable to the noise strength, independent of the system size. These circuits can be run on a noisy quantum computer of moderate size to assist variational calculations of various tensor networks. In particular, the dependence of the computational cost on the variational parameters can be exponentially reduced by the quantum computer. We estimate the computational cost based on realistic physical parameters, and find that it is far smaller than the cost of classical computation.