Abstract:
The performance of any physical qubit is limited by spurious noises, which makes extremely challenging the goal of building a quantum computer.
To address this challenge, the concept of quantum error correction (QEC) has emerged. QEC consists in using multiple physical qubits to encode information, combined into a single logical qubit with sufficiently low error rates. It has been shown that the use of superconducting Schrödinger cat qubits can significantly improve the QEC thresholds. Cat qubits are driven quantum systems and differ significantly from conventional superconducting qubits, making their study interesting from the fundamental point of view, in addition to their importance for quantum technology.
In this thesis, we conduct an extensive study of errors in cat qubits, with a particular focus on Bogolyubov quasiparticles. These quasiparticles are known to exist in superconducting devices even at the lowest temperatures. Unlike Cooper pairs, Bogolyubov quasiparticles can cause dissipation and degrade the performance of superconducting qubits. They are difficult to mitigate because they are intrinsic to the superconducting circuit. Thus, it is important to quantify their effect on cat qubits.
The thesis covers three related projects. In the first project, I developed perturbation theory for the dissipative cat qubit, which can predict cat qubit lifetimes based on the strength of various noise types. In particular, I calculated the exponentially suppressed bit-flip rate of a cat qubit, and my analytical expressions show good agreement with numerical simulations. In the second project, I investigated the impact of Bogolyubov quasiparticles on cat qubits, including both the driven Kerr and driven-dissipative variations. I derived error rates caused by quasiparticles and found that, due to the driven nature of cat qubits, some error rates differ significantly from those in conventional superconducting qubits. I also examined the potential overheating of quasiparticles due to the drive. In the third project, I studied the pure dephasing rate induced by Bogolyubov quasiparticles. The noise caused by these quasiparticles exhibits long-time correlations, which prevents the determination of the pure dephasing rate using standard approaches perturbative in the coupling strength. By using the low quasiparticle concentration as a small parameter, I determined the pure dephasing rate and showed that the fermionic nature of the quasiparticles bath plays a crucial role.