Qubism: self-similar visualization of many-body wavefunctions

TL;DR

Qubism is a recursive, fractal-like visualization method for quantum many-body wavefunctions that reveals properties like correlations, magnetization, and entanglement through self-similar images.

Contribution

It introduces a novel recursive visualization scheme for quantum states, enabling intuitive analysis of complex many-body wavefunctions.

Findings

Images reflect wavefunction features such as magnetization and correlations

Factorizability is easily identified in the images

Entanglement entropy can be estimated from the visualizations

Abstract

A visualization scheme for quantum many-body wavefunctions is described, which we have termed qubism. Its main property is its recursivity: increasing the number of qubits reflects in an increase in the image resolution. Thus, the plots are typically fractal. As examples, we provide images for the ground states of commonly used Hamiltonians in condensed matter and cold atom physics, such as Heisenberg or ITF. Many features of the wavefunction, such as magnetization, correlations and criticality, can be visualized as properties of the images. In particular, factorizability can be easily spotted, and a way to estimate the entanglement entropy from the image is provided.