Machine Learning for Discriminating Quantum Measurement Trajectories and Improving Readout

Current methods for classifying measurement trajectories in superconducting qubit systems produce fidelities systematically lower than those predicted by experimental parameters. Here, we place current classification methods within the framework of machine learning (ML) algorithms and improve on them by investigating more sophisticated ML approaches. We find that nonlinear algorithms and clustering methods produce significantly higher assignment fidelities that help close the gap to the fidelity possible under ideal noise conditions. Clustering methods group trajectories into natural subsets within the data, which allows for the diagnosis of systematic errors. We find large clusters in the data associated with $T_1$ processes and show these are the main source of discrepancy between our experimental and ideal fidelities. These error diagnosis techniques help provide a path forward to improve qubit measurements.

Figure 1

Circuit diagram of the single-qubit setup. See text for details.

Figure 2

Measured output of $I$ and $Q$ quadratures for state $|0⟩$ single-shot trajectory.

Figure 3

Mean trajectories and single shots for $|0⟩$ (blue) and $|1⟩$ (red) preparations. The $|0⟩$ ($|1⟩$) single-shot trajectory [blue (red) dotted line] has arrows pointing up (down) and to the left (right). The mean trajectories of $|0⟩$ (blue solid line) and $|1⟩$ (red solid line) have steady states of $\sim$ ($-0.07$, $-0.02$) and ($-0.01$, $-0.07$).

Figure 4

Subclasses found from $k$-means algorithm. $C_0$ and $C_1$ have three subclasses, the trajectory representing each subclass is the mean over all subclass trajectories. Subclasses of $C_0$ (purple dashed-dotted line, blue solid line, light blue dotted line) initially move up and left. Subclasses of $C_1$ (red dashed line, green solid line, dark red dotted line) initially move down and right. The $T_1$ subclass (green solid line) of $C_1$ initially moves down and right but abruptly changes its path up and left. Legend numbers are subclass sizes.

Figure 5

$I$ and $Q$ quadratures for $T_1$ subclass mean trajectory.

Figure 6

Varying measurement time.