Hybrid Reduction Techniques with Covariate Shift Optimization in High-Dimensional Track Geometry

In discussions of track geometry, track safety takes precedence over other requirements because its shortfall often leads to unrecoverable loss. Track geometry is unanimously positioned as the index for safety evaluation—corrective or predictive—to predict the rightful maintenance regime based on track conditions. A recent study has shown that track defect probability thresholds can best be explored using a hybrid index. Hence, a dimension reduction technique that combines both safety components and geometry quality is needed. It is observed that dimensional space representation of track parameters without prior covariate shift evaluation could affect the overall distribution as the underlying discrepancies could pose a problem for the accuracy of the prediction. In this study, the authors applied a covariate shift framework to track geometry parameters before applying the dimension reduction techniques. Whilst both principal component analysis (PCA) and t-distributed stochastic neighbour embedding (TSNE) are viable techniques that express the probability distribution of parameters based on correlation in their embedded space and inclination to maximize the variance, shift distribution evaluation should be considered. In conclusion, we demonstrate that our framework can detect and evaluate a covariate shift likelihood in a high-dimensional track geometry defect problem.

Leakage detection for a transmon-based surface code

Leakage outside of the qubit computational subspace, present in many leading experimental platforms, constitutes a threatening error for quantum error correction (QEC) for qubits. We develop a leakage-detection scheme via Hidden Markov models (HMMs) for transmon-based implementations of the surface code. By performing realistic density-matrix simulations of the distance-3 surface code (Surface-17), we observe that leakage is sharply projected and leads to an increase in the surface-code defect probability of neighboring stabilizers. Together with the analog readout of the ancilla qubits, this increase enables the accurate detection of the time and location of leakage. We restore the logical error rate below the memory break-even point by post-selecting out leakage, discarding less than half of the data for the given noise parameters. Leakage detection via HMMs opens the prospect for near-term QEC demonstrations, targeted leakage reduction and leakage-aware decoding and is applicable to other experimental platforms.