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Decay of a measured qubit under repeated readout

Run. ibm_fez, 11 October 2026, three jobs (IBM job IDs in the data file); ibm_fez ran 14 jobs that day, and the other 11 are a three-box probe-strength sweep. A qubit prepared in 1 is read out 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96 or 128 times; untouched qubits nearby run a Ramsey sequence; an idle arm of 40 µs sits in the same jobs.

What holds

• The measured qubit’s population after k readouts follows a three-parameter stretched exponential in every job (χ²/dof 0.72 / 1.38 / 1.32), exponent 0.823 ± 0.012 (spread of three jobs).
• The untouched qubits’ Ramsey coherence follows a stretched exponential with exponent 1.381 ± 0.074 (a different quantity, so the two exponents are not compared as one effect).
• Population 0.965 after one readout; 0.067 after 128 (job 1). It crosses 1/2 after 25.5, 22.6 and 23.9 readouts in the three jobs.
• At equal elapsed time, 24 readouts (39.8 µs) leave 0.517 / 0.481 / 0.498; 40 µs of idle leaves 0.661 / 0.623 / 0.647.

The script also prints a stored “measured” length of one ibm_kingston readout (2.323 µs on 4 October, 2.402 on 6 October, against 2.180 stated). That figure comes from the earlier fitted-rate method, which converts the untouched qubits’ extra phase into time and so includes the readout kick (October campaign); it does not measure how long the readout lasts. The reading that tests duration is the extra-time bound of the 21 October control run, at most 1 % on kingston.

Run it

Download the script and the files in data/ into one folder (data in data/), then python3 verify_cost.py. Standard library only; it prints each figure beside the recomputed value. The compact data were cut from the raw results; the raw files and the reduction scripts are available on request.

Files: verify_cost.py · data/fez_measurement_series_20261011.json · data/kingston_spectators_20261004_06.json

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