



01585nas a2200145   4500008004100000245010600041210006900147260001500216520109100231100002101322700002001343700001901363700002001382856003701402       2019                        eng d00aQuantum circuit approximations and entanglement renormalization for the Dirac field in 1+1 dimensions0 aQuantum circuit approximations and entanglement renormalization   c05/21/20193 a<p>The multiscale entanglement renormalization ansatz describes quantum many-body states by a hierarchical entanglement structure organized by length scale. Numerically, it has been demonstrated to capture critical lattice models and the data of the corresponding conformal field theories with high accuracy. However, a rigorous understanding of its success and precise relation to the continuum is still lacking. To address this challenge, we provide an explicit construction of entanglement-renormalization quantum circuits that rigorously approximate correlation functions of the massless Dirac conformal field theory. We directly target the continuum theory: discreteness is introduced by our choice of how to probe the system, not by any underlying short-distance lattice regulator. To achieve this, we use multiresolution analysis from wavelet theory to obtain an approximation scheme and to implement entanglement renormalization in a natural way. This could be a starting point for constructing quantum circuit approximations for more general conformal field theories.&nbsp;</p>1 aWitteveen, Freek1 aScholz, Volkher1 aSwingle, Brian1 aWalter, Michael  uhttps://arxiv.org/abs/1905.08821