Tutorial: bosonic qubit calibration

Tune up a bosonic qubit with Presto

Bosonic qubits take advantage of the large Hilbert space of linear resonators to store quantum information in a hardware-efficient way. Similarly to tuning up a qubit, a few characterization measurements are frequently performed on bosonic modes. We use the pulsed mode in this tutorial to characterize a system of two linear modes that are dispersively coupled to the same fixed-frequency transmon qubit. We use the name memory for the high-quality-factor bosonic mode, and readout resonator for the over-coupled mode used to probe the state of the transmon qubit. You can view the complete source code of the example scripts in the presto-measure repository. Here’s a list of the examples in this tutorial with a brief description, click on the headers to view the related page.

Memory spectroscopy

pulsed – Measure the rough estimate of the memory frequency.

Displacement calibration

pulsed – Calibrate the amplitude of the memory drive. Extract the amplitude of displacement that corresponds to the amplitude of the pulse in FS Presto units. Fit the dispersive shift \(\chi\) between the memory and the qubit.

Relaxation time \(T_1\) of the bosonic mode (coherent state decay)

pulsed – Measure the energy-relaxation time \(T_1\) of the bosonic mode. Initiate the memory in a coherent state \(|\alpha\rangle\).

Ramsey \(T_2^*\) of the bosonic mode

pulsed – Measure Ramsey like oscillations of the memory mode by changing the delay between two displacement pulses with amplitudes \(\alpha\) and \(-\alpha\). Fit detuning of memory drive frequency from the memory frequency, and the coherence time \(T_2^*\).