TY - JOUR
T1 - Efficient Direct Tomography for Matrix Product States
Y1 - 2010
A1 - Olivier Landon-Cardinal
A1 - Yi-Kai Liu
A1 - David Poulin
AB - 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.
UR - http://arxiv.org/abs/1002.4632v1
ER -
TY - JOUR
T1 - Efficient quantum state tomography
JF - Nature Communications
Y1 - 2010
A1 - Marcus Cramer
A1 - Martin B. Plenio
A1 - Steven T. Flammia
A1 - David Gross
A1 - Stephen D. Bartlett
A1 - Rolando Somma
A1 - Olivier Landon-Cardinal
A1 - Yi-Kai Liu
A1 - David Poulin
AB - 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.
VL - 1
U4 - 149
UR - http://arxiv.org/abs/1101.4366v1
CP - 9
J1 - Nat Comms
U5 - 10.1038/ncomms1147
ER -