Southwest Quantum Information and Technology

Quantum mixed state compiling and the quantum low-rank approximation problem

Presenting Author: Nic Ezzell, University of Southern California
Contributing Author(s): Elliott M. Ball, Aliza U. Siddiqui, Mark M. Wilde, Andrew T. Sornborger, Patrick J. Coles, Zoë Holmes

We present a variational quantum algorithm (VQA) to compile mixed states which is suitable for near-term hardware. Our algorithm can be viewed as a practical means to solve the quantum low-rank approximation problem which we formally defined and solved as part of a related work. Alternatively, our algorithm is a generalization of previous VQAs that aimed at learning preparation circuits for pure states. We choose to compile a target mixed state using two types of an ansätze; the first is based on learning a purification of the state and the second on representing it as a convex combination of pure states. In both cases, the resources required to store and manipulate the compiled state grow with the rank of the approximation. Thus, by learning a lower rank approximation of the target state, our algorithm provides a means of compressing a state for more efficient processing. As a byproduct of our algorithm, one effectively learns the principal components of the target state, and hence our algorithm further provides a new method for principal component analysis. We investigate the efficacy of our algorithm through extensive numerical implementations, showing that typical random states and thermal states of many body systems may be learnt this way. Finally, we implement our algorithm on real hardware and show how it can be used to study hardware noise-induced states.

Read this article online: https://arxiv.org/abs/2203.00811

(Session 9b : Friday from 4:15 pm - 4:45 pm)