Table 1 Truth table of the selection rule for the two-tone readout.

From: Transmon qubit readout fidelity at the threshold for quantum error correction without a quantum-limited amplifier

Primary Result

Secondary Result

Before Readout

Initial State

\(\left\vert 0\right\rangle\)

\(\left\vert 0\right\rangle\)

\(\left\vert 0\right\rangle\)

\(\left\vert 0\right\rangle\)

\(\left\vert \overline{0}\right\rangle\)

\(\left\vert 1\right\rangle\)

\(\left\vert 3\right\rangle\)

\(\left\vert 1\right\rangle\)

\(\left\vert \overline{0}\right\rangle\)

\(\left\vert \tilde{2}\right\rangle\)

\(\left\vert 1\right\rangle\)

\(\left\vert 2\right\rangle\)

\(\left\vert 0\right\rangle\)

\(\left\vert \overline{0}\right\rangle\)

Overlap Error

\(\left\vert \overline{0}\right\rangle\)

\(\left\vert 0\right\rangle\)

Overlap Error

 
  1. The first two columns are the discrimination results from the two readout tones, respectively. There is a unique initial state if the results agree with each other. Otherwise, the shots where the two readout results disagree will be counted towards overlap error and discarded.