Characterization and tomography of a hidden qubit

We implement work published in ref [1]. The device used in this paper has three elements: A superconducting qubit connected to a control line and a readout resonator, a second transmon which is not connected to such lines and is therefore hidden and a tunable coupling element, controlling the interaction of these two qubits.

In the paper, it is explained how single qubit roations (on the visible qubit) alongside two qubit operations enabled by the coupler allow to effectively perform any rotation on the hidden qubit as well. To prove this ability, full tomography of several processes is performed. We implement this procedure using QUA in this script. The operations, initialization steps and tomography operation set are defined in dictionaries in the configuration file.

The code for this procedure is quite succinctly implemented with just a few for loops:

with for_(var=N, init=0, cond=N < N_shots, update=N + 1):

for process in processes.keys(): # 1/4

for input_state in state_prep.keys(): # 16

for readout_operator in tomography_set.keys(): # 15

align("RR", "control", "TC")

for pulse in state_prep[input_state]:

play_pulse(pulse)

for pulse in processes[process]:

play_pulse(pulse)

for op in tomography_set[readout_operator]:

if op != "readout":

play_pulse(op)

else:

align("RR", "control", "TC")

measure_and_reset_state("RR", I, Q, state_c, state_h, stream_c, stream_h)

[1] Pechal, M., Salis, G., Ganzhorn, M., Egger, D. J., Werninghaus, M., & Filipp, S. (2020). Characterization and tomography of a hidden qubit. ArXiv, 1–14.