Nearly tight bounds for testing tree tensor network states

par Benjamin Lovitz (Northeastern University)

jeudi 19 déc. 2024, 15:00 → 16:00 Europe/Paris

https://cnrs.zoom.us/j/96639500410?pwd=xUzC1wGCdSj0aGhCi8CC5lza4fV4ze.1 (Online)

Tree tensor network states (TTNS) form a class of physically motivated quantum states. We study the task of testing TTNS in the property testing framework, wherein one is handed multiple copies of an unknown quantum state, and performs measurements to determine whether the state forms a TTNS (of a given bond dimension) or is epsilon-far from TTNS. The minimum number of copies required is called the copy complexity of the task. We prove nearly tight bounds on the copy complexity of testing TTNS. This generalizes prior works on testing matrix product states (MPS), and closes a gap left in these works. No prior knowledge of quantum computing will be assumed. Based on joint work with Angus Lowe.