Southwest Quantum Information and Technology

Optimal strategies for quantum state and process tomography: efficiency versus robustness

Presenting Author: Hector Sosa Martinez, Jessen group (Arizona)
Contributing Author(s): Nathan Lysne, Charles Baldwin, Amir Kalev, Ivan Deutsch, Poul Jessen

To build useful quantum hardware one needs good ways to characterize its behavior. In principle quantum tomography (QT) is an ideal tool, capable of providing complete information about an unknown state (QST) or process (QPT). In practice, the protocols used for QT are resource intensive and scale poorly with system size. Even for modest sized Hilbert spaces corresponding to only a few qubits, this puts a premium on schemes that are as efficient as possible. Theoretical work on QST has identified sets of POVM elements that are optimal under varying assumptions, in each case prescribing a minimal number of measurements of a given structure. Laboratory exploration of these POVM constructions has, however, been constrained by the ability to control SPAM errors and generate accurate test states and processes in all but the simplest quantum systems. Here we present the findings from a comprehensive experimental study comparing 6 different POVM constructions and 4 different state estimators, using as our testbed the d = 16 dimensional hyperfine manifold in the 6S1/2 electronic ground state of the 133Cs atom. Our results show a clear trade-off between efficiency and robustness to experimental error, with mutually unbiased bases achieving the best compromise in our system and reaching a QST fidelity of ~98% in d = 16. We have further used a minimal set of intelligently chosen probe states to implement QPT, testing the scheme on randomly chosen unitary processes in Hilbert spaces of varying dimension, and reaching a QPT fidelity of ~90% in d = 16.

(Session 13 : Saturday from 4:15 pm - 4:45 pm)