Geometric phases in generalized radical Floquet dynamics
- URL: http://arxiv.org/abs/2312.04500v1
- Date: Thu, 7 Dec 2023 18:21:38 GMT
- Title: Geometric phases in generalized radical Floquet dynamics
- Authors: Brenden Roberts, Sagar Vijay, Arpit Dua
- Abstract summary: We show that the Pancharatnam phase is a natural invariant for a wide class of quantum many-body dynamics involving measurements.
We specifically investigate how a non-trivial Pancharatnam phase arises in the trajectories of Floquet quantum error-correcting codes.
- Score: 0.5755004576310334
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: The Pancharatnam phase is a generalization of the Berry phase that applies to
discrete sequences of quantum states. Here, we show that the Pancharatnam phase
is a natural invariant for a wide class of quantum many-body dynamics involving
measurements. We specifically investigate how a non-trivial Pancharatnam phase
arises in the trajectories of Floquet quantum error-correcting codes and show
that this phase can be extracted in a "computationally-assisted" interferometry
protocol, involving additional post-processing based on the measurement record
that defines a given quantum many-body trajectory. This Pancharatnam phase can
also be directly related to the Berry phase accrued by continuous unitary
evolution within a gapped phase. For the $\mathbb Z_2$ Floquet code of Hastings
and Haah, we show that the associated family of unitary evolutions is the
radical chiral Floquet phase. We demonstrate this correspondence explicitly by
studying an exactly-solvable model of interacting spins.
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