



01216nas a2200121   4500008004100000245004700041210004600088260001500134520087400149100001901023700001601042856003601058       2015                        eng d00aQuantum Compressed Sensing Using 2-Designs0 aQuantum Compressed Sensing Using 2Designs  c2015/10/293 aWe develop a method for quantum process tomography that combines the efficiency of compressed sensing with the robustness of randomized benchmarking. Our method is robust to state preparation and measurement errors, and it achieves a quadratic speedup over conventional tomography when the unknown process is a generic unitary evolution. 
Our method is based on PhaseLift, a convex programming technique for phase retrieval. We show that this method achieves approximate recovery of almost all signals, using measurements sampled from spherical or unitary 2-designs. This is the first positive result on PhaseLift using 2-designs. We also show that exact recovery of all signals is possible using unitary 4-designs. Previous positive results for PhaseLift required spherical 4-designs, while PhaseLift was known to fail in certain cases when using spherical 2-designs.1 aKimmel, Shelby1 aLiu, Yi-Kai  uhttp://arxiv.org/abs/1510.08887