Monte Carlo fidelity certification and variational tomography : a walkthrough

Olivier Landon-Cardinal, David Poulin

Université de Sherbrooke

Characterizing a quantum state is essential to benchmark quantum devices and to compare theoretical predictions to experimental realizations. However, standard techniques fundamentally require a number of experiments and a post-processing effort that scales exponentially with the number of particles. Recently, we've developed schemes that circumvent the exponential cost of tomography.

Monte Carlo fidelity certification (MCFC) estimates the fidelity between a predicted pure state and an arbitrary experimental state using only a constant number of Pauli expectation values selected at random according to an importance-weighting rule.

Variational tomography identifies a state inside interesting variational classes such as matrix product states (MPS) [2], which include GHZ, W and cluster states, and multi-scale entanglement renormalisation ansatz (MERA) [3], which describes critical quantum systems.

In this poster, I will describe the details of the procedures, in particular
- how to choose the single-particle observables to measure experimentally
- how to efficiently perform the post-processing in order to estimate the experimental state

[1] da Silva, Landon-Cardinal and Poulin, PRL 107, 210404 (2011)
[2] Cramer, Plenio, Flammia, Somma, Gross, Bartlett, Landon-Cardinal, Poulin, Liu, Nature Commun. 1, 149 (2010)
[3] Landon-Cardinal, Poulin, arXiv:1204.0792