Wave-function Networks: Probe and understand quantum many-body systems via network and complexity theory

Introduction

WaveNets aims to establish a novel theoretical paradigm for understanding quantum systems, centred on a network interpretation of many-body wave-functions.

Motivation

Ongoing experimental progress motivates the need for a new theoretical approach. In the field of quantum simulation and quantum computing, probing capabilities have reached unprecedented levels, with the ability to collect thousands of wave function snapshots with impressive accuracy.

However, most of our theoretical understanding of such settings still relies on and relates to few-body observables. This has created a clear gap between experimental capabilities and theoretical tools and concepts available to understand physical phenomena.

Overall Goal

The overall goal of WaveNets is to bridge this gap by introducing a mathematical framework to describe wave-function snapshots based on network theory — wave function networks — that will enable a completely new set of tools to address open problems in the field of quantum matter.

Main Objectives

WaveNets' main objectives are:

1. To demonstrate that wave function snapshots of correlated systems are described by scale-free networks, and classify the robustness of quantum simulators according to such.
2. To formulate methods for quantifying the Kolmogorov complexity of many-body systems, and propose an information-theory-based characterization of topological matter and confinement in gauge theories.
3. To propose scalable methods for measuring entanglement in quantum simulators and computers, as well as for their validation.

Expected Outcomes

Achieving these objectives will:

• Provide unique insights into the information structure of quantum matter.
• Enable methods of probing and controlling matter of direct experimental relevance thanks to the intrinsic scalability of network-type descriptions.
• Establish a new, interdisciplinary bridge between quantum science, and network and data mining theory, that makes possible knowledge transfer between two mature, yet poorly connected disciplines.