01192nas a2200133 4500008004100000245005800041210005800099260001500157520078600172100002900958700001600987700001801003856003701021 2010 eng d00aEfficient Direct Tomography for Matrix Product States0 aEfficient Direct Tomography for Matrix Product States c2010/02/243 a 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.
1 aLandon-Cardinal, Olivier1 aLiu, Yi-Kai1 aPoulin, David uhttp://arxiv.org/abs/1002.4632v101775nas a2200229 4500008004100000245003900041210003900080260001500119300000800134490000600142520116900148100001901317700002301336700002401359700001701383700002601400700001901426700002901445700001601474700001801490856003701508 2010 eng d00aEfficient quantum state tomography0 aEfficient quantum state tomography c2010/12/21 a1490 v13 a 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.
1 aCramer, Marcus1 aPlenio, Martin, B.1 aFlammia, Steven, T.1 aGross, David1 aBartlett, Stephen, D.1 aSomma, Rolando1 aLandon-Cardinal, Olivier1 aLiu, Yi-Kai1 aPoulin, David uhttp://arxiv.org/abs/1101.4366v1