Preparing matrix product states via fusion: constraints and extensions

Understand

In the era of noisy, intermediate-scale quantum (NISQ) devices, the efficient preparation of many-body resource states is a task of paramount importance.

• In this paper we focus on the deterministic preparation of matrix-product states (MPS) in constant depth by utilizing measurements and classical communication to fuse smaller states into larger ones.
• We place strong constraints on the MPS that can be prepared using this method, which we refer to as MPS fusion.
• Namely, we establish that it is necessary for the MPS to have a flat entanglement spectrum.