Towards fault-tolerant quantum error correction with the surface-GKP code
Typ
Examensarbete för masterexamen
Master's Thesis
Master's Thesis
Program
Nanotechnology (MPNAT), MSc
Publicerad
2024
Författare
Jaeken, Thomas
Modellbyggare
Tidskriftstitel
ISSN
Volymtitel
Utgivare
Sammanfattning
Quantum computers have been predicted to be of great importance in the future.
However, realization of this technology comes with many challenges. The fragile nature of quantum phenomena necessitates the development of fault-tolerant
computation. The need for robust error correction schemes is evident. One of
the most promising efforts at this time is the surface code. Recently, it became
apparent that the surface code can synergize with the Gottesman-Kitaev-Preskill
(GKP) code. This thesis explores that concatenated code within a circuit-level
noise model approximating reality as close as possible, through classical Monte
Carlo simulations relying on the state-twirling approximation and relates. We reproduce the results of ref. [1, Noh and Chamberland, Phys. Rev. A 101, 012316
(2020)] and expand on them.
We simulate the concatenated code in different experimental setups within the
parameter space of the noise model and expose relations between the results.
This leads to, among others, an analogy of error-flow with current in electrical
circuits. This behavior is not directly recognized in analogous simulations of the
discrete surface code and was not reported previously. It corroborates the recent
theory by ref. [2, Conrad et al., Quantum 6, 648 (2022)] that the concatenation
of GKP codes with stabilizer codes are a particular case of general multi-mode
GKP codes. From individual simulations of the threshold for each noise source
in the model, we learn that two-qubit gate noise is the most critical, while measurement noise is the most tolerable. Finally, we investigate the threshold of the
concatenated code, σ*gkp as a function of the measurement efficiency and confirm
the concern that this is a critical issue for practical realizations. The result of this
work is a better understanding of the effect that different kinds of noise have on
the logical error rate and can potentially support experimental implementations in
the future.
Beskrivning
Ämne/nyckelord
Quantum error correction, GKP, surface code, continuous variable quantum computing, stabilizer code, Fault-tolerance threshold, Gottesman-Kitaev-Preskill