Wave Matrix Lindbladization II: General Lindbladians, Linear Combinations, and Polynomials

TL;DR

This paper extends wave matrix Lindbladization to simulate general Lindbladians, including linear combinations and polynomials, offering a dimension-independent approach with efficient sample complexity compared to full operator tomography.

Contribution

It introduces quantum algorithms for simulating general Lindbladians using program states, expanding the method to more complex operator structures and analyzing their sample complexity.

Findings

Sample complexity is dimension independent.

Algorithms efficiently simulate general Lindbladians.

Compared favorably to full operator tomography.

Abstract

In this paper, we investigate the problem of simulating open system dynamics governed by the well-known Lindblad master equation. In our prequel paper, we introduced an input model in which Lindblad operators are encoded into pure quantum states, called program states, and we also introduced a method, called wave matrix Lindbladization, for simulating Lindbladian evolution by means of interacting the system of interest with these program states. Therein, we focused on a simple case in which the Lindbladian consists of only one Lindblad operator and a Hamiltonian. Here, 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.