We introduce a model for random chain complexes over finite field. The randomness in our complex comes from choosing the entries matrices that represent boundary maps uniformly \(\mathbb {F}_q\), conditioned on ensuring composition of consecutive is zero map. then investigate combinatorial and homological properties this complex.

In this general article, we map the one-dimensional transverse field quantum Ising model of ferromagnetism to Kitaev’s p-wave superconductor, which has application in fault-tolerant topological computing. Kitaev chain is an example a new class critical phenomena—the phase transition. Mapping Pauli’s spin operators spinless fermionic creation and annihilation by inverse Jordan-Wigner transformat...