Variational Power of Quantum Circuit Tensor Networks

We characterize the variational power of quantum circuit tensor networks in representation physical many-body ground-states. Such are formed by replacing dense block unitaries and isometries standard local circuits. explore both matrix product states multi-scale entanglement renormalization ansatz, introduce an adaptive method to optimize resulting circuits high fidelity with more than $10^4$ parameters. benchmark their expressiveness against networks, as well other common architectures, for 1D/2D Heisenberg 1D Fermi-Hubbard models. find be substantially expressive these problems, that they can even compact networks. Extrapolating depths which no longer emulated classically, this suggests a region advantage