Quantum Computation with Gottesman-Kitaev-Preskill Codes: Logical Gates, Measurements, and Analysis Techniques

Abstract

The Gottesman-Kitaev-Preskill (GKP) error-correcting code uses one or more bosonic modes to encode a finite-dimensional logical space, allowing a low-error logical qubit to be encoded in a small number of resonators. In this thesis, I propose new methods to implement logical gates and measurements with GKP codes and analyse their performance. The logical gate scheme uses the single-qubit Clifford frame to greatly reduce the number of gates needed to implement an algorithm without increasing the hardware requirements. The logical measurement scheme uses one ancilla mode to achieve a 0.1% logical error rate over a measurement time of 630 ns when the measurement efficiency is as low as 75%. Finally, I provide a subsystem decomposition which can be used to analyse GKP codes efficiently even as the Fock space distribution of the codestates goes to infinity.