The Computational Power of Non-interacting Particles

Understand

Shortened abstract: In this thesis, I study two restricted models of quantum computing related to free identical particles.

• Free fermions correspond to a set of two-qubit gates known as matchgates.
• Matchgates are classically simulable when acting on nearest neighbors on a path, but universal for quantum computing when acting on distant qubits or when SWAP gates are available.
• I generalize these results in two ways.