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

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.

arXiv comment59 pages, 11 figures, submission to the second journal special issue dedicated to the memory of Göran Lindblad, sequel to arXiv:2307.14932

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Cited by in corpus (6)

• Quantum-centric Supercomputing for Materials Science: A Perspective on Challenges and Future Directions
• Quantum Dynamic Programming
• Sample-based Hamiltonian and Lindbladian simulation: Non-asymptotic analysis of sample complexity
• Simulating quantum collision models with Hamiltonian simulations using early fault-tolerant quantum computers
• Digital Quantum Simulations of the Non-Resonant Open Tavis-Cummings Model
• Quantum Imaginary-Time Evolution with Polynomial Resources in Evolution Time