Efficient simulation of sparse Markovian quantum dynamics

TL;DR

This paper introduces the first efficient quantum algorithms for simulating sparse Markovian quantum dynamics generated by Lindbladians, expanding quantum simulation capabilities beyond Hamiltonian systems.

Contribution

It presents two novel approaches for simulating sparse Lindbladians and establishes fundamental limitations through a no-fast-forwarding theorem.

Findings

Efficient algorithms for simulating sparse Lindbladians.

Simulation of Lindbladians within small invariant subspaces.

Limitations established via no-fast-forwarding theorem.

Abstract

Quantum algorithms for simulating Hamiltonian dynamics have been extensively developed, but there has been much less work on quantum algorithms for simulating the dynamics of open quantum systems. We give the first efficient quantum algorithms for simulating Markovian quantum dynamics generated by Lindbladians that are not necessarily local. We introduce two approaches to simulating sparse Lindbladians. First, we show how to simulate Lindbladians that act within small invariant subspaces using a quantum algorithm to implement sparse Stinespring isometries. Second, we develop a method for simulating sparse Lindblad operators by concatenating a sequence of short-time evolutions. We also show limitations on Lindbladian simulation by proving a no-fast-forwarding theorem for simulating sparse Lindbladians in black-box models.