Zero noise extrapolation of transport coefficients

Abstract

NISQ devices routinely estimate properties of the noiseless system from measurements at varying noise strengths $\gamma$. These zero-noise extrapolation (ZNE) schemes fail to estimate transport coefficients of conserved quantities when the noise violates the associated conservation laws. We show how to extrapolate measurements in noisy, one-dimensional, non-integrable spin chains to obtain the spin transport coefficients governing linear response in the zero-noise limit. As the wavevector of the Fourier mode of a conserved quantity goes to zero, its decay rate vanishes. The coefficient of the leading momentum dependence defines a transport coefficient in the noiseless system, and an analogous effective coefficient in the noisy one. Naive ZNE implicitly assumes that this effective coefficient is analytic in $\gamma$ as $\gamma \to 0$. Our main result is that universal non-linear corrections to hydrodynamics can produce non-analytic dependence on $\gamma$. In particular, we argue that the effective spin diffusion coefficient of a dissipative Heisenberg chain and the effective subdiffusion coefficient of a dipole-conserving fracton approach their noiseless value as ${\gamma }^{1/2}$. We benchmark these analytical predictions numerically.

arXiv comment8 + epsilon pages, 4 figures, 4 + epsilon pages supplemental material