Optimal unitary disentanglers for fermionic Gaussian states (and how to use them to play games)

Optimal unitary disentanglers for fermionic Gaussian states (and how to use them to play games)

Seminar author:Raúl Morral Yepes

Event date and time:04/10/2025 02:30:pm

Event location:Seminar Room, GIQ

Event contact:

Unitarily disentangling quantum many-body states is, in general, a complex task. In this talk, I will focus on the problem of finding optimal unitaries to disentangle fermionic Gaussian states (FGS). To address this, I will define a standard form of matchgate circuits capable of generating any FGS, which we denote as the right standard form (RSF). I will then present an algorithm to construct this RSF from the covariance matrix of a given FGS. This construction is provably optimal, meaning that no other matchgate circuit can generate the same FGS with fewer gates. Using this framework, I will introduce algorithms to simulate matchgate circuits and FGS in terms of the RSF. Moreover, this simulation method naturally identifies an optimal disentangling matchgate—namely, the unitary that minimizes the number of gates required to prepare the state. Finally, I will discuss the framework of unitary circuit games, where the competition between random evolution and disentangling evolution can give rise to entanglement phase transitions between volume-law and area-law entanglement.