A drop of ink in a glass of water spreads in intricate swirls. Similarly, a quantum particle exchanging energy with its environment changes its state in a complex and entangled manner. Describing this dance between particle and environment has long baffled scientists.

Earlier calculations relied on crude assumptions: the environment was thought to 'forget' the particle almost instantly, like water quickly mixing ink. But in many cases, the environment remembers longer, and simple methods fail. Tensor networks are a way to record the history of particle–environment interactions without gaps. They resemble a knitted fabric, where each loop holds connections to its neighbors, and through these connections, influence passes from the past to the present.

The review's authors brought together various versions of such 'knitted' calculations and showed that one can now numerically track, with controlled accuracy, a quantum system continuously interacting with the outside world. This paves the way for precise modeling of molecules in liquids, energy transfer in photosynthesis, or the operation of tiny transistors where heat leakage can no longer be ignored.