Wave Matrix Lindbladization as an Approach for Simulating Markovian Quantum Dynamics (via Zoom)

Abstract: We investigate the problem of simulating open system dynamics governed by the well-known Lindblad master equation. In order to do so, we introduce an input model in which Lindblad operators are encoded into pure quantum states, called program states, and we also introduce a method, called wave matrix Lindbladization, for simulating Lindbladian evolution by means of interacting the system of interest with these program states. We begin by focusing on a simple case in which the Lindbladian consists of only one Lindblad operator and a Hamiltonian. Thereafter, we extend the method to simulating general Lindbladians and other cases in which a Lindblad operator is expressed as a linear combination or a polynomial of the operators encoded into the program states. We propose quantum algorithms for all these cases and also investigate their sample complexity, i.e., the number of program states needed to simulate a given Lindbladian evolution approximately. Finally, we demonstrate that our quantum algorithms provide an efficient route for simulating Lindbladian evolution relative to full tomography of encoded operators, by proving that the sample complexity for tomography is dependent on the dimension of the system, whereas the sample complexity of wave matrix Lindbladization is dimension independent.
Bio: Dhrumil Patel is a PhD student at Cornell CIS, advised by Prof. Mark M. Wilde. The majority of his research interests revolve around two questions: first, what speed-ups can a quantum computer achieve for problems that are considered difficult to solve for modern classical computers?, and second, how to best use the current state-of-the-art quantum computers, that are noisy, to achieve some quantum advantage if any? He is also currently working as a research assistant at Los Alamos National Lab.