Time-series based quantum state discrimination

TL;DR

This work targets readout fidelity in superconducting qubits, where $T_1$ decay and measurement noise degrade performance. It introduces a time-series approach that applies an LSTM to raw readout traces, supplemented by bandpass filtering and path-based feature engineering, to preserve temporal correlations lost in conventional integration. Across eight fixed-frequency transmons, the LSTM-based method consistently outperforms Gaussian Mixture Model baselines, with the largest gains near cluster boundaries and robustness across qubit coherence times. The result is a practical, hardware-feasible enhancement to qubit readout that can improve error correction and real-time feedback, with potential extensions to multi-qubit readout and FPGA deployment.

Abstract

Accurate quantum state readout is crucial for error correction and algorithms, but measurement errors are detrimental. Readout fidelity is typically limited by a poor signal-to-noise ratio (SNR) and energy relaxation ($T_1$ decay), a significant problem for superconducting qubits. While most approaches classify results using clustering algorithms on integrated readout signals, these methods cannot distinguish a qubit that was initially in the ground state from one that decayed to it during measurement. We instead propose using machine learning (ML) on the raw, non-integrated analog signal. We apply time-series classification models, such as a long short-term memory (LSTM) network, to the full data trajectory. We find that our LSTM model, combined with filtering and feature engineering, consistently outperforms clustering. The largest improvements come from reclassifying points in the boundary regions between clusters. These points correspond to atypical measurement records, likely due to transient or noisy features lost during data integration. By retaining temporal information, sequence-aware models like LSTMs can better discriminate these trajectories, whereas clustering methods based on integrated values are more prone to misclassification.

Figures (5)

• Figure 1: Bloch sphere representation.
• Figure 2: Control and readout schematic.
• Figure 3: Fourier spectra of the readout signal before and after bandpass filtering. The raw signal (left) exhibits broadband noise across the spectrum, while the filtered signal (right) isolates a sharp peak at the aliased readout frequency, significantly reducing off-resonant noise contributions.
• Figure 4: Comparison of qubit state trajectories in the I-Q plane under different preprocessing methods. Raw trajectories (left) contain irregular fluctuations and overlapping regions between states. Path-transformed trajectories (middle) smooth out short-timescale noise and highlight longer-term dynamics, leading to clearer separation between states. Filtered trajectories (right) suppress high-frequency noise, further improving cluster structure and discriminability.
• Figure 5: Comparison of LSTM and GMM classification performance in the I-Q plane. (A) Cluster distributions of the three prepared states ($\ket{0}$, $\ket{1}$, $\ket{2}$), showing the overlap regions where misclassifications are most likely. (B) Points highlighted in color indicate cases correctly classified by the LSTM but misclassified by the GMM. These improvements are concentrated near cluster boundaries, where transient fluctuations and relaxation effects create ambiguity. (C) Points highlighted in color represent cases misclassified by the LSTM but correctly classified by the GMM, which are comparatively fewer. Overall, the LSTM provides more robust classification in boundary regions by leveraging temporal information from the full readout trace.