End-to-End Efficiency in Dissipative Preparation of Thermal and Ground States

Inspired by natural cooling processes, dissipation has emerged as a powerful paradigm for preparing low-energy states of quantum systems, including thermal and ground states. In contrast to traditional quantum algorithms that rely on coherent evolution followed by final measurement and postselection, dissipative state preparation involves repeated mid-circuit measurements. This makes runtime analysis significantly more challenging, especially for non-commuting Hamiltonians. Recent advances, such as the development of Kubo-Martin-Schwinger (KMS) detailed-balanced Lindbladians and protocols for dissipative ground state preparation, have enabled not only efficient algorithms, as measured by the simulation cost per unit time, but also end-to-end runtime guarantees, as measured by the mixing time—the timescale required to reach the target quantum state from any initial state. In certain cases, sharp estimates on mixing times can be rigorously established. I will present these developments, and discuss how to simplify such protocols for efficient implementation on early fault-tolerant quantum devices while maintaining end-to-end efficiency.