Belief Propagation-based Disentanglers for Tensor Network State Preparation

Abstract

We develop a quantum circuit synthesis method for preparing a class of tensor network states. The scheme applies to states tractable with belief propagation (BP), a tensor network gauging scheme which recently allowed for classical simulations at large scales. The problem is reduced to independent, strictly local, classical variational optimizations: each nearest-neighbor two-qubit "disentangler" gate minimizes the entropy defined on an edge. Disentanglers drive the state to a product state and their Hermitian conjugate prepares the target. Each disentangling layer has depth at most $z+1$ (with $z$ the maximal number of nearest neighbors per site), the optimization has no barren plateaus, and the bond dimension stays bounded. As a demonstration, with only $3$-$5$ disentangling layers we prepare a $102$-qubit tree tensor network encoding a $17$-dimensional normal distribution and the transverse-field Ising model ground states on a $64$- to $127$-qubit heavy-hex lattice with fidelities of order $0.9-0.999$. The method opens new possibilities for quantum applications by transferring classical tensor network states onto hardware.