Purification-based quantum simulations via clustering property

Quantum many-body systems that appear in natural phenomena can be efficiently simulated by quantum computers. However, the experimental limitations of near-term devices still make it challenging to perform the entire process of the quantum simulation. The purification-based quantum simulations have been proposed in order to break the limitations in experiments such as the cooling temperature and noise from the environment, whereas this method requires globally entangled measurements and an exponentially large number of measurements regarding the system size. In this work, we aim to overcome the drawbacks by restricting the entangled measurements to the vicinity of the local observables to be measured, when the locality of the system can be exploited. Under the assumption of the clustering property, we provide theoretical guarantees that the global purification operation can be replaced with local operations, in particular for the task of cooling and error mitigation. We furthermore give a numerical verification that the localized virtual purification is valid even when conditions are not satisfied. Our method fills the gaps between the fundamental concept of locality and quantum simulation, and therefore expected to open a path to unexplored quantum many-body phenomena.