Comment by abdullahkhalids

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.