Quantum matchgate computations and linear threshold gates

Understand

The theory of matchgates is of interest in various areas in physics and computer science.

• Matchgates occur in e.g.
• the study of fermions and spin chains, in the theory of holographic algorithms and in several recent works in quantum computation.
• In this paper we completely characterize the class of boolean functions computable by unitary two-qubit matchgate circuits with some probability of success.