Institute for Quantum Information Seminar

Characterizing a quantum state is essential to benchmark quantum devices and, more broadly, 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.

Taking a more targeted approach, we have developed schemes that enable (i) estimating the fidelity of an experiment to a theoretical ideal description [1], (ii) learning which description within a variational class of states best matches the experimental data [2-3].

In this talk, I will focus on task (ii), which we call variational tomography. I will present methods for identifying a state inside interesting variational classes such as matrix product states (MPS) [2], and multi-scale entanglement renormalisation ansatz (MERA) [3]. For MERA, I will describe how to learn a state from a small number of efficiently-implementable measurements and fast post-processing, without requiring unitary control.

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