Boosted Imaginary Time Evolution of Matrix Product States

Abstract: In this work, we consider the imaginary time evolution of matrix product states. We present a novel quantum-inspired classical method that, when combined with time evolving block decimation (TEBD), is able to potentially speed-up the convergence to a ground state compared to TEBD alone. Our method, referred to as boosted imaginary time evolution, relies on the use of reflections to boost to lower energy states. Interleaving TEBD steps with boosts reduces the total number of TEBD steps and potentially the computational cost required to imaginary time evolve a matrix product state to a ground state. We give the mathematical details of the method followed by an algorithmic implementation and finally some results for a simple test case.