A new method for efficiently preparing thermal states is enabling advances in fields from materials science to machine learning. Andrew Wright and colleagues at the Institute of Physics, in collaboration with Chulalongkorn University and Keio University, have developed a technique termed double-bracket thermofield double (DB-TFD) that uses double-bracket quantum algorithms to simulate thermofield double states and realise Gibbs states. The poly DB-TFD algorithm’s complexity scales favourably with inverse temperature, consistent with established techniques and confirmed by numerical simulations. Moreover, the team demonstrates DB-TFD’s potential in quantum Boltzmann machines, achieving improved performance compared with existing variational methods, and providing a strong pathway for thermal state preparation on near-term and early-fault-tolerant quantum computers. Exponential scaling unlocks thermal state preparation for complex quantum systems The poly DB-TFD algorithm now demonstrates a query complexity scaling exponentially with inverse temperature, a substantial improvement over earlier methods limited to polynomial scaling in practical regimes. Validated by numerical simulations, this exponential scaling unlocks the potential to prepare thermal states for larger, more complex systems previously inaccessible to quantum computation. Dr. Alastair Peoples and Professor Andrew Green, alongside Dr. Patrick Draper, employed a technique called double-bracket thermofield double (DB-TFD) to simulate thermofield double states, effectively creating ‘hot’ and ‘cold’ copies of a system to realise Gibbs states, crucial for modelling thermal equilibrium. Thermofield double states are a cornerstone of quantum statistical mechanics, representing a system and its replica in a fictitious Hilbert space, allowing for the elegant formulation of thermal properties. The Gibbs state, describing the probability distribution of a system in thermal equilibrium at a given temperature, is central to understanding macroscopic behaviour from microscopic quantum principles. A polynomial transformation approximating imaginary-time evolution underpins the approach, reducing the computational steps needed for thermal state creation and offering a viable pathway for both near-term and early fault-tolerant quantum