Thema der Dissertation:
The fabulous world of GKP codes
The fabulous world of GKP codes
Abstract: Quantum error correction is an essential ingredient in the development of quan- tum technologies. Its core subject is to investigate ways to embed quantum Hilbert spaces into a physical system such that this subspace is robust against small imperfections in the physical systems. This task is exceedingly complex: for one, this is due to the vast diversity of possible physical systems with dif- ferent inherent structure to use. For another, every different physical setting also comes with different types of dominant imperfections that need to be protected against. Bred by the complexity of this technological ambition, research on quantum error correction has developed into a large field of research that ranges from questions about the engineering of small systems with a single pho- ton to the creation of macroscopic topological phases of matter and models of complex emergent physics.
A quintessential tool in quantum error correction is the stabilizer formalism, which tames complicated quantum systems by enforcing symmetries. A Gottesman-Kitaev-Preskill (GKP) code is a stabilizer code that creates a logical subspace within the infinite dimensional Hilbert space of a collection of quantum harmonic oscillators by endowing it with translational symmetries. While practical approaches to GKP codes consider the infinitude of the Hilbert space, as well as the infinitude of the translational symmetry group as obstacles for implementation, in theory these are precisely the features that make the theory of GKP codes particularly rich, well behaved and well-connected to fascinating topics in mathematics.
In this talk I will present our research from he past years, which accumulates to a unified geometric picture of the GKP code:
I’ll discuss the its physical basis and show how the tools of lattice theory yield a rich coding theory for this class of codes, and how the understanding of the underlying mathematical structure allows for a geometric theory of fault tolerance for these codes. I will explain how the understanding of lattice theory helps to design concrete GKP codes, and how their decoding problem relates to generically hard lattice problems. Equipped with these tools, we outline how a post-quantum crypto system can be used to derive GKP codes with beneficial parameter guarantees, and how to flip the picture to use these GKP codes in designing quantum cryptographic protocols.
Finally, I will discuss how GKP codes can be implemented in physical systems by explaining a Floquet-engineering approach.
A quintessential tool in quantum error correction is the stabilizer formalism, which tames complicated quantum systems by enforcing symmetries. A Gottesman-Kitaev-Preskill (GKP) code is a stabilizer code that creates a logical subspace within the infinite dimensional Hilbert space of a collection of quantum harmonic oscillators by endowing it with translational symmetries. While practical approaches to GKP codes consider the infinitude of the Hilbert space, as well as the infinitude of the translational symmetry group as obstacles for implementation, in theory these are precisely the features that make the theory of GKP codes particularly rich, well behaved and well-connected to fascinating topics in mathematics.
In this talk I will present our research from he past years, which accumulates to a unified geometric picture of the GKP code:
I’ll discuss the its physical basis and show how the tools of lattice theory yield a rich coding theory for this class of codes, and how the understanding of the underlying mathematical structure allows for a geometric theory of fault tolerance for these codes. I will explain how the understanding of lattice theory helps to design concrete GKP codes, and how their decoding problem relates to generically hard lattice problems. Equipped with these tools, we outline how a post-quantum crypto system can be used to derive GKP codes with beneficial parameter guarantees, and how to flip the picture to use these GKP codes in designing quantum cryptographic protocols.
Finally, I will discuss how GKP codes can be implemented in physical systems by explaining a Floquet-engineering approach.
Zeit & Ort
29.11.2024 | 09:30
FB Sitzungsraum (1.1.16)
Fachbereich Physik, Arnimallee 14, 14195 Berlin