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The IBM Quantum services website lists calibration statistics for their devices, including the (sx) error rate per qubit, which is listed as a single number. One can also manually calibrate a device using the ampcal_1Q_circuits and anglecal_1Q_circuits functions in Ignis, but doing so results in two different numbers for the sx amplitude error and angle error. What is the relationship between these two errors and the number listed on the website?

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For information, the reported errors for single and 2 qubit gates for each backend are measured using randomized benchmarking (look at the qiskit textbook https://qiskit.org/textbook/ch-quantum-hardware/randomized-benchmarking.html)

Another good source of information is available in the community tutorials notebooks https://github.com/qiskit-community/qiskit-community-tutorials/tree/master/ignis
You'll find in the "gate_errors.ipynb" notebook the different sequences to amplify possible errors such as amplitude and phase errors)

These IGNIS routines (ampcal_1Q_circuits and anglecal_1Q_circuits) you mention, are rather for measuring specific errors such as an amplitude error or phase error and they are typically run to calibrate the pulses....
Generaly the different pulses instructions for gates can be retrieved from the command definition schedule map. See below:

properties = backend.properties()
defaults = backend.defaults()
default_inst_map = defaults.instruction_schedule_map
backend.defaults().instruction_schedule_map.get('sx',qubits=[0]).instructions

This gives you the drag pulse name and instruction executed for a "sx" gate

Play(Drag(duration=160, amp=(0.08500674523685206+0.0012428209077864267j), sigma=40, beta=-0.7194390183174101, name='X90p_d0'), DriveChannel(0), name='X90p_d0')),)

In summary, the Random Benchmark incorporates all sources of error into one number that is given as "error" value for each gate in the backend properties.

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