The multi-scale entanglement renormalization ansatz (MERA) postulates the existence of quantum circuits that renormalize entanglement in real space at different length scales. Chern insulators, however, cannot have scale-invariant discrete MERA circuits with finite bond dimension. In this Letter, we show that the continuous MERA (cMERA), a modified version of MERA adapted for field theories, possesses a fixed point wavefunction with nonzero Chern number. Additionally, it is well known that reversed MERA circuits can be used to prepare quantum states efficiently in time that scales logarithmically with the size of the system. However, state preparation via MERA typically requires the advent of a full-fledged universal quantum computer. In this Letter, we demonstrate that our cMERA circuit can potentially be realized in existing analog quantum computers, i.e., an ultracold atomic Fermi gas in an optical lattice with light-induced spin-orbit coupling.

%B Phys. Rev. Lett %V 122 %8 03/27/2019 %G eng %U https://arxiv.org/abs/1807.11486 %N 120502 %R https://doi.org/10.1103/PhysRevLett.122.120502 %0 Journal Article %J Physical Review A %D 2011 %T Chern numbers hiding in time-of-flight images %A Erhai Zhao %A Noah Bray-Ali %A Carl J. Williams %A I. B. Spielman %A Indubala I. Satija %X We present a technique for detecting topological invariants -- Chern numbers -- from time-of-flight images of ultra-cold atoms. We show that the Chern numbers of integer quantum Hall states of lattice fermions leave their fingerprints in the atoms' momentum distribution. We analytically demonstrate that the number of local maxima in the momentum distribution is equal to the Chern number in two limiting cases, for large hopping anisotropy and in the continuum limit. In addition, our numerical simulations beyond these two limits show that these local maxima persist for a range of parameters. Thus, an everyday observable in cold atom experiments can serve as a useful tool to characterize and visualize quantum states with non-trivial topology. %B Physical Review A %V 84 %8 2011/12/21 %G eng %U http://arxiv.org/abs/1105.3100v3 %N 6 %! Phys. Rev. A %R 10.1103/PhysRevA.84.063629