Operator Learning Renormalization Group for Quantum Simulation

By generalizing Wilson's Numerical Renormalization Group (NRG) and Density Matrix Renormalization Group (DMRG) from a learning perspective, we find a new variational principle that allows one to use a more flexible ansätze in the DMRG style, which we term the "operator learning renormalization group" (OLRG). We first prove the general convergence condition called "scale consistency". Subsequently, we establish a theorem that demonstrates an area-law scaled error upper bound in instances of time evolution resulting from locality. We then showcase this variational principle using some toy ansätze and models to illustrate its convergence. We believe this opens new opportunities in exploring the simulation of many-body systems by utilizing their locality and modern differentiable solvers on small systems. Additionally, we find this variational principle leads to new types of digital analog quantum simulation algorithms with adjustable digital resource requirements. Finally, we will discuss some open problems that arise from this new setup.