Southwest Quantum Information and Technology

Fermionic partial tomography via classical shadows

Presenting Author: Andrew Zhao, University of New Mexico CQuIC
Contributing Author(s): Nicholas C. Rubin, Akimasa Miyake

We propose a tomographic protocol for estimating any k-body reduced density matrix (k-RDM) of a fermionic state, a ubiquitous step in near-term quantum algorithms for simulating many-body physics, chemistry, and materials. Our approach extends the framework of classical shadows, a randomized approach to learning a collection of quantum-state properties, to the fermionic setting. Our sampling protocol employs randomized measurements generated by a discrete group of fermionic Gaussian unitaries, implementable with linear-depth circuits, to achieve near-optimal scaling in the number of repeated state preparations required of fermionic RDM tomography. We also numerically demonstrate that our protocol offers a substantial improvement in constant overheads over prior state-of-the-art for estimating 2-, 3-, and 4-RDMs.

Read this article online: https://arxiv.org/abs/2010.16094

(Session 5 : Thursday from 12:00pm-2:00 pm)