Quantum Error Correction with the GKP Code and Concatenation with Stabilizer Codes

Abstract

Gottesman, Kitaev and Preskill have proposed a scheme to encode a qubit in a harmonic oscillator, which is called the GKP code. It is designed to be resistant to small shift errors contained in momentum and position quadratures. Thus there's some intrinsic fault tolerance of the GKP code. In this thesis,we propose a method to utilize all the information contained in the continuous shifts, not just simply map a GKP-encoded qubit to a normal qubit. This method enables us to do maximum-likelihood decisions and thus increase fault-tolerance of the GKP code. This thesis shows that the continuous nature of the GKP code is quite useful for quantum error correction.

arXiv comment50 pages, Master Thesis, RWTH-Aachen, Germany

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• Quantum Error Correction with the Toric-GKP Code
• Equivalence of approximate Gottesman-Kitaev-Preskill codes
• Measurement-free preparation of grid states
• Finite Rate QLDPC-GKP Coding Scheme that Surpasses the CSS Hamming Bound
• Twirling and Hamiltonian Engineering via Dynamical Decoupling for GKP Quantum Computing
• Quantum error correction with higher Gottesman-Kitaev-Preskill codes: minimal measurements and linear optics
• Quantum error correction with the color-Gottesman-Kitaev-Preskill code
• Characterizing the performance of continuous-variable Gaussian quantum gates
• Coherent manipulation of graph states composed of finite-energy Gottesman-Kitaev-Preskill-encoded qubits
• Concatenation Schemes for Topological Fault-tolerant Quantum Error Correction
• Wigner distribution on a double cylinder phase space for studying quantum error correction protocol
• Quantum Computation and Communication in Bosonic Systems