Towards fault-tolerant quantum error correction with the surface-GKP code

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dc.contributor.authorJaeken, Thomas
dc.contributor.departmentChalmers tekniska högskola / Institutionen för mikroteknologi och nanovetenskap (MC2)sv
dc.contributor.departmentChalmers University of Technology / Department of Microtechnology and Nanoscience (MC2)en
dc.contributor.examinerFerrini, Giulia
dc.contributor.supervisorHillmann, Timo
dc.contributor.supervisorSorée, Bart
dc.date.accessioned2024-12-04T08:20:53Z
dc.date.available2024-12-04T08:20:53Z
dc.date.issued2024
dc.date.submitted
dc.description.abstractQuantum 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.
dc.identifier.coursecodeMCCX04
dc.identifier.urihttp://hdl.handle.net/20.500.12380/309018
dc.language.isoeng
dc.setspec.uppsokPhysicsChemistryMaths
dc.subjectQuantum error correction, GKP, surface code, continuous variable quantum computing, stabilizer code, Fault-tolerance threshold, Gottesman-Kitaev-Preskill
dc.titleTowards fault-tolerant quantum error correction with the surface-GKP code
dc.type.degreeExamensarbete för masterexamensv
dc.type.degreeMaster's Thesisen
dc.type.uppsokH
local.programmeNanotechnology (MPNAT), MSc
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