Title: Subharmonic control and measurement of superconducting qubits

Abstract: Superconducting circuits are a leading platform for quantum information processing because of their flexibility as engineered quantum systems. Parametric controls provide an effective and flexible approach for manipulating superconducting circuits. In parametric control, appropriate choices of drive frequency, amplitude, and phase activate nonlinear Hamiltonian terms that turn on selected interactions and control them dynamically. In designing a SNAIL-mediated four-qubit quantum module, this work demonstrates parametrically activated single- and two-qubit control. However, design tradeoffs appear when stronger coupling and faster gates are pursued. To push parametric control further, this thesis uses transmons to explore subharmonic driving, subharmonic measurement, and a general strong-drive limit that applies not only to transmons but also to other superconducting circuits.

Subharmonic single-qubit control is demonstrated using a drive near one third of the qubit transition frequency, where the Josephson nonlinearity converts three drive photons into one excitation of the computational transition. This frequency separation allows the control line to be filtered strongly at the qubit frequency while still passing the lower-frequency control tone. With phase tracking, chirped modulation, transfer-function correction, and leakage-aware pulse tuning, this protocol realizes single-qubit gates with a best fidelity above 99.9% and π and π/2 gate times of 50.9ns and 37.4ns, respectively. I then extend the same idea to measurement by using an alternate subharmonic drive to generate a resonator field through the transmon nonlinearity. The resulting dispersive readout achieved a best measurement fidelity of 95.0%, and the model indicates that improved lifetime, frequency planning, and readout parameters can push the protocol toward much higher fidelity.

The second part of the dissertation studies the strong-drive threshold that limits parametric control. In experiments on strongly driven circuits, the driven mode population spreads into many highly excited transmon levels above a critical drive amplitude, causing the intended coherent response to disappear. I identify this breakdown as a speed limit for parametric interactions. By comparing simulations with experimental characterization, the model successfully predicts this threshold in driven transmons. This threshold model provides a tool for estimating the limits of parametrically driven systems and designing new devices that can further improve parametric control