Qubism - plotting quantum states

### What is Qubism?

It is a technique to generate pictorial representations of quantum many-body states, developed by researchers at UC3M, ICFO and IFT (UAM/CSIC). The plots provide a visual characterization of many properties, such as magnetization, criticality or entanglement.

The original paper:

• J. Rodriguez-Laguna, P. Migdał, M. Ibanez Berganza, M. Lewenstein, G. Sierra,
Qubism: self-similar visualization of many-body wavefunctions,
New J. Phys. 14 053028 (2012), arXiv:1112.3560

A poster:

### The idea

Scientists tend to be very visual people. We love to understand through pictures. About one year ago, we had one of those ideas which remind you why it’s so fun to be a theoretical physicist… Simple and deep. The idea was about how to represent quantum many-body wavefunctions in pictures. Speaking very coarsely, the high complexity of the wavefunction maps into fractality of the final image.

So, more slowly. A bit can take only two values: 0 and 1. A qubit is a quantum bit, which can be in any linear combination of 0 and 1, like Schrödinger’s cat, which we denote by $|0\rangle$ and $|1\rangle$. In other terms: a qubit is represented by two complex numbers: $|\psi\rangle=\alpha |0\rangle+\beta |1\rangle$. If you have two qubits, the basic states are four: 00, 01, 10 and 11, so we get $|\psi\rangle=\alpha_{00} |00\rangle + \alpha_{01} |01\rangle +\alpha_{10} |10\rangle+\alpha_{11} |11\rangle$.

If you add one qubit, the number of parameters doubles. For N qubits, you need 2N parameters in order to specify completely the state. The task of representing those values in a picture in a meaningful way seems hopeless… Our idea is to start with a square and divide it in four quadrants. Each quadrant will be filled with a color associated with the corresponding parameter.

### Qubistic plots by others

(If you made one, just e-mail us.)