Quantum simulation of electron Coulomb interactions

¹ Beijing Computational Science Research Center - Beijing 100094, China
² Center for Quantum Science and Engineering and Department of Physics, Stevens Institute of Technology Hoboken, NJ 07030, USA
³ Department of Physical Chemistry, The University of the Basque Country UPV/EHU 48080 Bilbao, Spain
⁴ IKERBASQUE, Basque Foundation for Science - 48013 Bilbao, Spain
⁵ Department of Physics and Astronomy, University of Tennessee - Knoxville, TN 37996, USA
⁶ Department of Physics and State Key Laboratory of Modern Optical Instrumentation, Zhejiang University Hangzhou 310027, China

^(a) lianaowu@gmail.com (corresponding author)

Received: 15 April 2020
Accepted: 16 April 2020

Abstract

We review a strategy to use an ion-based analog quantum simulator to study the many-body electron-electron Coulomb interaction of an electron gas. This is made possible by an exact unitary dilatation mapping, which allows an experimentally challenging system to be replaced by an alternative one that may be experimentally more accessible. We show the feasibility of this simulation strategy mathematically. As a bonus, the dilatation transformation does not even need to be physically implemented when only the system spectrum is needed, in which case the simulation induces no experimental complexity overhead. This proposal is dimension-agnostic, and could be generalized as a simulation strategy between systems involving terms with different position or momentum dependence.