A fantastic article by Natalie Wolchover at Quanta magazine: What Is a Particle? An overview of current physics theories about elementary particles.
The properties of these particles and fields appeared to follow numerical patterns. By extending these patterns, physicists were able to predict the existence of more particles.
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Fundamental particles are objects that essentially stay the same when acted on by a certain group. Namely, particles are representations of the Poincaré group: the group of 10 ways of moving around in the space-time continuum. […] The Standard Model of particle physics […] is often said to represent the symmetry group SU(3) × SU(2) × U(1), consisting of all combinations of the symmetry operations in the three subgroups. …
Algebraic operations on the qubits “behave just like rotations acting on the particles,” Van Raamsdonk said. “You realize there’s this picture being encoded by this nongravitational quantum system. And somehow in that code, if you can decode it, it’s telling you that there are particles in some other space.”