Figure 1: Quantum circuit to obtain matrix product state.

The circuit transforms . The unitaries Ûi successively disentangle the particles and the state |η〉 on the last sites acts as a boundary condition to determine the MPS description of |φ〉.
The circuit transforms . The unitaries Ûi successively disentangle the particles and the state |η〉 on the last sites acts as a boundary condition to determine the MPS description of |φ〉.