• Theoretical Investigations of Superconducting Qubits Under a Subharmonic Drive

Achieving quantum speedup on intermediate-scale quantum processors requires the implementation of high-fidelity gate operations. Quantum gates are typically executed using electromagnetic driving fields tuned to the resonance frequency of the qubit; however, this resonant drive degrades qubit
coherence and leads to the loss of quantum information. Sub-harmonic driving, a new control method proposed in 2023, involves driving the qubit at one third of its resonant frequency. This technique enables decoupling from the resonant decay channel, allowing it to be filtered out.

In this thesis, we analytically investigate the decoherence of a transmon qubit under voltage fluctuations caused by subharmonic driving. We use harmonic analysis techniques commonly used in non-equilibrium statistical mechanics to investigate the effects of a noisy subharmonic Hamiltonian.
 

Our results show that the average infidelity scales inversely with the mean photon number in the infinite photon limit, matching the scaling observed with resonant driving.

While subharmonic driving is not found to improve infidelity scaling, we identify a potential new discovery: vacuum noise at five-thirds of the qubit frequency contributes to the decay rate through a multiphoton process.