Efficient Direct Tomography for Matrix Product States

Understand

In this note, we describe a method for reconstructing matrix product states from a small number of efficiently-implementable measurements.

• Our method is exponentially faster than standard tomography, and it can also be used to certify that the unknown state is an MPS.
• The basic idea is to use local unitary operations to measure in the Schmidt basis, giving direct access to the MPS representation.
• This compares favorably with recently and independently proposed methods that recover the MPS tensors by performing a variational minimization, which is computationally intractable in certain cases.