Frictionless quantum free energy estimation with tunable bias

We introduce a new algorithmic protocol for estimating intensive, per-particle free energy differences in locally interacting quantum systems via the fluctuation theorem. Our approach adopts a pseudo-work formulation initialized from a single product state and relies only on unitary time evolution, making it compatible with both near-term and fault-tolerant quantum platforms. A key feature of this protocol is the tunability of its bias through the duration of time evolution and the vanishing ensemble variance of the estimator enabled by the single-state initialization. We further explore the computational complexity of this protocol and examine its implications for practical implementations on quantum hardware. This work establishes a rigorous and operational framework for realizing the quantum Jarzynski equality, opening new avenues for efficient free energy estimation in many-body thermodynamics.