Five Starter Pieces: Quantum Information Science via Semi-definite Programs

TL;DR

This paper introduces five fundamental quantum information problems formulated as semi-definite programs, providing accessible explanations and computational tools for researchers from operations research, computer science, physics, and electrical engineering.

Contribution

It offers a self-contained, accessible introduction to key QIS problems via SDPs, bridging gaps between disciplines and facilitating computational study.

Findings

Provides background and computational solutions for five QIS problems

Recreates known solutions in Jupyter notebooks for practical understanding

Aims to foster interdisciplinary research and advances in QIS

Abstract

As the title indicates, this chapter presents a brief, self-contained introduction to five fundamental problems in Quantum Information Science (QIS) that are especially well-suited to be formulated as Semi-definite Programs (SDP). We have in mind two audiences. The primary audience comprises of Operations Research (and Computer Science) graduate students who have familiarity with SDPs, but have found it daunting to become even minimally conversant with pre-requisites of QIS. The second audience consists of Physicists (and Electrical Engineers) already knowledgeable with modeling of QIS via SDP but interested in computational tools that are applicable more generally. For both audiences, we strive for rapid access to the unfamiliar material. For the first, we provide just enough required background material (from Quantum Mechanics, treated via matrices, and mapping them in Dirac notation) and simultaneously for the second audience we recreate, computationally in Jupyter notebooks, known closed-form solutions. We hope you will enjoy this introduction and gain understanding of the marvelous connection between SDP and QIS by self-study, or as a short seminar course. Ultimately, we hope this disciplinary outreach will fuel advances in QIS through their fruitful study via SDPs.