Efficient quantum state tomography.

By M. Cramer, Martin Bodo Plenio, Steven T. Flammia, Rolando D. Somma, David Gross, Stephen D. Bartlett, Olivier Landon-Cardinal, David Poulin, Yi-Kai Liu. Nature Communications, 2010

738 citations recorded by the source corpus.

Quantum state tomography--deducing quantum states 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 unfeasible because the number of measurements and the amount of computation required to process them grows exponentially in the system size. Here, we present two tomography schemes that scale much more favourably than direct tomography with system size. One of them requires unitary operations on a constant number of subsystems, whereas the other requires only local measurements together with more elaborate post-processing. Both rely only on a linear number of experimental operations and post-processing that is polynomial in the system size. These schemes can be applied to a wide range of quantum states, in particular those that are well approximated by matrix product states. The accuracy of the reconstructed states can be rigorously certified without any a priori assumptions.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/7393b708b21c85ad6ff0ea528ca8c9c27fe85156

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

In Atomic and Molecular Physics, and Optics

Citations in the corpus

Entanglement certification from theory to experiment (2018, background): “Here, matrix product state (MPS) tomography [260–262] can provide some relief, offering a useful pure state estimate in systems with finite interaction range, e.”
Quantum computing and the entanglement frontier (2012, background): “But for a slightly entangled state, a number of measurements linear in n suffices.(13) We can perform tomography on segments of constant size, then do an efficient classical computation to determine how the pieces are stitched together.”
Efficient tomography of a quantum many-body system (2016, methodology): “This characterisation task requires resources (number of measurements and classical post-processing time) that scale exponentially in Ω and linearly in N via certified MPS tomography [6, 7].”
The randomized measurement toolbox (2022, background): “matrix product states with polynomial bond dimension [47] or neural network states [48].”
Matrix product states and projected entangled pair states: Concepts, symmetries, theorems (2020, background): “For instance, quantum tomography can become much more efficient if the states one deals with can be approximated by MPS or MPDO, as with fewer measurements one can fully characterize the many-body state (Cramer et al., 2010).”
Quantum tomography via compressed sensing: error bounds, sample complexity and efficient estimators (2012, methodology): “[61] M.”