Optimal Haar random fermionic linear optics circuits

Understand

Sampling unitary Fermionic Linear Optics (FLO), or matchgate circuits, has become a fundamental tool in quantum information.

• Such capability enables a large number of applications ranging from randomized benchmarking of continuous gate sets, to fermionic classical shadows.
• In this work, we introduce optimal algorithms to sample over the non-particle-preserving (active) and particle-preserving (passive) FLO Haar measures.
• In particular, we provide appropriate distributions for the gates of $n$-qubit parametrized circuits which produce random active and passive FLO.