%0 Journal Article
%D 2010
%T Efficient Direct Tomography for Matrix Product States
%A Olivier Landon-Cardinal
%A Yi-Kai Liu
%A David Poulin
%X 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. Our method also has the advantage of recovering any MPS, while other approaches were limited to special classes of states that exclude important examples such as GHZ and W states.
%8 2010/02/24
%G eng
%U http://arxiv.org/abs/1002.4632v1
%0 Journal Article
%J Nature Communications
%D 2010
%T Efficient quantum state tomography
%A Marcus Cramer
%A Martin B. Plenio
%A Steven T. Flammia
%A David Gross
%A Stephen D. Bartlett
%A Rolando Somma
%A Olivier Landon-Cardinal
%A Yi-Kai Liu
%A David Poulin
%X Quantum state tomography, the ability to deduce the state of a quantum system from measured data, is the gold standard for verification and benchmarking of quantum devices. It has been realized in systems with few components, but for larger systems it becomes infeasible because the number of quantum measurements and the amount of computation required to process them grows exponentially in the system size. Here we show that we can do exponentially better than direct state tomography for a wide range of quantum states, in particular those that are well approximated by a matrix product state ansatz. We present two schemes for tomography in 1-D quantum systems and touch on generalizations. One scheme requires unitary operations on a constant number of subsystems, while the other requires only local measurements together with more elaborate post-processing. Both schemes rely only on a linear number of experimental operations and classical postprocessing that is polynomial in the system size. A further strength of the methods is that the accuracy of the reconstructed states can be rigorously certified without any a priori assumptions.
%B Nature Communications
%V 1
%P 149
%8 2010/12/21
%G eng
%U http://arxiv.org/abs/1101.4366v1
%N 9
%! Nat Comms
%R 10.1038/ncomms1147