Dr. Yi-Kai Liu

National Institute of Standards and Technology (NIST)

Seminar: “Phase Retrieval Using Unitary 2-Designs, with Applications to Quantum Process Tomography”

Wednesday, March 1, 2017

11:00 AM

Haus Room, 36-428

Hosted by: Prof. Dirk Englund

Abstract:

We consider a variant of the phase retrieval problem, where vectors are replaced by unitary matrices, i.e., the unknown signal is a unitary matrix U, and the measurements consist of squared inner products |Tr(C*U)|^2 with unitary matrices C that are chosen by the observer. This problem has applications to quantum process tomography, when the unknown process is a unitary operation.

We show that PhaseLift, a convex programming algorithm for phase retrieval, can be adapted to this matrix setting, using measurements that are sampled from unitary 4- and 2-designs. In the case of unitary 4-design measurements, we show that PhaseLift can reconstruct all unitary matrices, using a near-optimal number of measurements. This extends previous work on PhaseLift using spherical 4-designs.

In the case of unitary 2-design measurements, we show that PhaseLift still works pretty well on average: it recovers almost all signals, up to a constant additive error, using a near-optimal number of measurements. These 2-design measurements are convenient for quantum process tomography, as they can be implemented via randomized benchmarking techniques. This is the first positive result on PhaseLift using 2-designs.

(This is joint work with Shelby Kimmel.)

Biography:

Yi-Kai Liu is a computer scientist at the US National Institute of Standards and Technology (NIST), and a Fellow at the Joint Center for Quantum Information and Computer Science (QuICS) at the University of Maryland. He specializes in quantum computation and cryptography. He has worked on the design of tamper-resistant quantum devices, compressed sensing methods for quantum tomography, quantum algorithms based on wavelet transforms, and the computational complexity of quantum chemistry. He received his PhD in computer science at the University of California in San Diego in 2007, and was a postdoctoral researcher at Caltech and UC Berkeley until 2011, when he moved to NIST.