Matter refers to particles or collection of particles that have mass+volume. These particles can be arranged or behave in different ways, and that is roughly what a "state of matter" is. You know how in solid all the atoms are fixed, but in a gas atoms/molecules are flying about.

There are in fact other forms of matter. In plasma you just have ions (instead of atoms/molecules) just zipping about. In neutron stars, you have pretty much only neutrons collapsed into a packed ball.

You can also make systems at higher levels of abstraction that have some of this matter or particle like behavior. A simple example is "phonons", which are a small packet of vibration (of atoms) that travels inside a solid much like a photon travels through space. I think phonons don't have a "mass", so they are not matter.

Here, they construct a quantum system, some of whose degrees of freedom behave like a matter particle. Qubits are then made from the states of this particle.

People working in solid state is weird. [1]

For example in some cases they have a "gas" of electrons. It's not a normal gas that you can put in a balloon, it only can live inside a solid. If you ignore the atoms in the solid, in some cases the electrons are free enough to think they are a gas. That is similar enough to a normal gas, and then they just call it a gas.

Sometimes the interesting part is a surface between two semiconductors, so they may have a 2D gas. (I'm not sure if this experiment is in 2D or 3D.)

Sometimes the electrons make weird patterns, that are very stable and move around without deformation, and they will call it a quasiparticle, and ignore that it's formed by electrons, and directly think that it's a single entity. And analyze how this quasiparticles apear an disappear and colide with other particles. It's like working on a high level of abstraction, to make the calculations easier. [2]

In particular, if you arrange the electrons very smartly, they create a quasiparticle that is it's own anti-quasipartilce. In particular, this is a Majorana quasiparticle.

This is somewhat related to topological properties of the distribution of the properties of the electrons. Were topological means that is stable under smooth deformations and that helps to make it also stable under thermal noise and other ugly interference. But this is going too far from my area, so my handwaving is not very reliable.

[1] They probably think my area is weird, so we are even :) .

[2] Sometimes the high level abstraction is not an approximation.

See https://en.wikipedia.org/wiki/Topological_order.

For reference topological phases of matter have been observed in other contexts since the mid-1980s. So "entirely new" here is misleading.

We are approaching a full "post truth" society, nothing will be sacred.

through geometry and configuration of materials, you can create quantum effects on a macroscopic scale