QFlux: An Open-Source Toolkit for Quantum Dynamics Simulations on Quantum Computers. Part V - Adaptive Variational Quantum Algorithms for Open Quantum Systems

Simulating open quantum systems remains one of the most demanding problems in quantum dynamics, as environmental interactions lead to non-unitary evolution that challenges standard quantum simulation techniques. Variational quantum algorithms (VQAs) offer a practical way forward by combining classical optimization with quantum hardware, making them well suited for near-term devices. Here, in Part V of the QFlux implementation series, we introduce adaptive variational-ansatz methods for solving the Lindblad master equation. This tutorial presents the Python-based qmad module of the QFlux toolkit, which is designed to help students and researchers easily build and explore adaptive VQA strategies. The tutorial walks through each step of the workflow and applies the methods to two illustrative examples. The first is the amplitude-damping channel, which models spontaneous emission in a two-level system. The second is the Fenna-Matthews-Olson (FMO) complex, a prominent model for excitonic energy transfer in photosynthesis. The two workflows utilizing adaptive variational approaches implemented here are the unrestricted adaptive variational quantum dynamics (UAVQD) scheme and the stochastic Schrödinger equation (SSE) based trajectory method. By working through these examples, readers gain both intuition and hands-on experience with variational techniques for simulating dissipative quantum dynamics.