Quantum simulation of Markovian and non-Markovian open quantum dynamics in heavy-ion collisions

In relativistic heavy-ion collisions, hard probes such as heavy quarks and quarkonia interact with the surrounding quark-gluon plasma (QGP). Modeling these interactions requires an open quantum system (OQS) framework that accounts for the environment's influence on the subsystem. While the Markovian approximation (where the environment loses memory rapidly) is common, it often fails during the late stages of collisions when the plasma cools and memory effects become significant. This paper explores how to simulate both Markovian and non-Markovian dynamics on quantum computers.

The authors model a two-level bound state interacting with a thermal bath. For the Markovian regime, they use Stinespring dilation to implement the Lindblad master equation as a unitary circuit, tracing out ancilla qubits at each time step. To handle non-Markovian dynamics, they introduce an auxiliary two-level pseudomode. This pseudomode acts as a memory carrier, coupling to the subsystem and a residual Markovian bath. The joint system-pseudomode state is evolved using a symmetric Lie-Trotter splitting, which allows the simulation to retain memory effects without requiring the full history of the density matrix.

The study demonstrates that the pseudomode construction effectively reproduces the exact non-Markovian evolution for an exponentially decaying memory kernel. By varying the bath correlation time, the authors show that the non-Markovian simulation smoothly converges to the Markovian limit as the memory time decreases. The quantum circuit results for survival probability show excellent agreement with classical fourth-order Runge-Kutta (RK4) numerical solutions, validating the feasibility of this framework for future high-energy physics applications.

As heavy-ion experiments provide increasingly precise data, the ability to simulate quantum dynamics beyond the Markovian approximation is essential for understanding the real-time evolution of probes in the QGP. This framework provides a scalable, circuit-compatible method to incorporate environmental memory, which is a critical step toward using quantum computers to solve complex problems in nuclear and high-energy physics that are computationally prohibitive for classical methods.