Source-linked AI summary
Machine learning for discriminating quantum measurement trajectories and improving readout
Easwar Magesan, Jay M. Gambetta, A. D. Córcoles, Jerry M. Chow
TL;DR
Current trajectory-classification methods in superconducting-qubit measurements yield assignment fidelities below the ideal-noise achievable value. The paper applies machine-learning classifiers and clustering to improve readout and diagnose errors; non-linear classification improves fidelity, while T1 events account for a substantial part of the remaining discrepancy.
Problem
Existing trajectory-classification methods in the studied superconducting-qubit system produce assignment fidelities below the achievable value under ideal noise conditions.
Source: pp. 1–2Method
The paper applies machine-learning classification and clustering to measurement trajectories to improve assignment and identify naturally occurring error-related subsets.
Source: p. 1Results
Non-linear SVMs raised assignment fidelity from 0.9586 to 0.9821, and replacing the T1 cluster with typical trajectories raised it from 0.9821 to 0.9945.
Source: p. 4Takeaways & Limitations
Clustering identifies heating and T1 effects in the trajectories, and the T1 cluster is a significant source of the fidelity gap in this experiment.
Source: p. 4The remaining discrepancy may be due to effects such as heating and state-preparation errors.
Source: p. 5
Abstract
from arXiv · showhide
High-fidelity measurements are important for the physical implementation of quantum information protocols. Current methods for classifying measurement trajectories in superconducting qubit systems produce fidelities that are systematically lower than those predicted by experimental parameters. Here, we place current classification methods within the framework of machine learning algorithms and improve on them by investigating more sophisticated ML approaches. We find that non-linear algorithms and clustering methods produce significantly higher assignment fidelities that help close the gap to the fidelity achievable under ideal noise conditions. Clustering methods group trajectories into natural subsets within the data, which allows for the diagnosis of specific systematic errors. We find large clusters in the data associated with relaxation processes and show these are the main source of discrepancy between our experimental and achievable fidelities. These error diagnosis techniques help provide a concrete path forward to improve qubit measurements.
Measurement and linear amplification in circuit
In dispersive circuit QED, the resonator output encodes the qubit state as a coherent trajectory, enabling a quantum non-demolition measurement. The section describes how amplification and quadrature selection shape the measured signal-to-noise ratio.
Measurement and linear amplification in circuit
- The resonator frequency depends on the qubit state, so its output provides a quantum non-demolition measurement through distinct coherent-state trajectories.The output field is amplified before measurement; the amplifier bandwidth is assumed constant and larger than the signal bandwidth.Source: Measurement and linear amplification… · p. 5
- The measured qubit has transition frequency 5.415 GHz, readout-resonator frequency 6.693 GHz, energy-relaxation time 29 µs, and coherence time 22 µs.The measured dispersive shift is −2.8 MHz and resonator linewidth is 1210 kHz.Source: Measurement and linear amplification… · p. 5
- The experiment uses a linear phase-preserving amplifier, with efficiency ηl = 2/(1 + 2A) and noise figure f = 1 + 2A.For a quantum-limited amplifier, the noise figure is 2.Source: Measurement and linear amplification… · pp. 5–6
- Measuring the information-bearing quadrature I(t) = Re[c(t)e^−iθ] yields an instantaneous signal-to-noise ratio, while a phase-sensitive amplifier can improve effective SNR by a factor of two.The single-quadrature measurement efficiency is half the efficiency of a linear phase-preserving amplifier.Source: Measurement and linear amplification… · p. 6
Filtering protocol for ideal noise and the achievable
The section describes how filtered trajectories are summarized by their separation and how an ideal-noise model sets an achievable fidelity. The measured distributions depart from that ideal, so fitted distributions are used to estimate the idealized parameters.
Filtering protocol for ideal noise and the achievable
- The achievable fidelity Fach assumes symmetric, diagonal Gaussian noise, but the measured class distributions show significant non-Gaussian statistics.The distributions are fitted with double Gaussians of equal variance to estimate the means and standard deviation expected under ideal noise; Fig. 4 shows the projected data and fits.Source: fidelity · pp. 6–7, Figure 4 · p. 7
- The fitted variance var(S) is 0.6758 ± 0.0109, giving separation R = 55.56 ± 1.02.The fitted class means are ⟨S0⟩ = −0.2149 ± 0.0149 and ⟨S1⟩ = 2.750 ± 0.0161.Source: fidelity · p. 7
- The filtered trajectories are characterized by separation R, which in the time-independent limit is related to signal-to-noise by SNRI = R/4.R is used as a standard measure of separation in machine learning.Source: fidelity · pp. 6–7
SVM’s and k-means clustering
The section introduces soft-margin SVM classification and k-means clustering for trajectory analysis. It explains the clustering objective and its sensitivity to initialization, and illustrates heating and relaxation subclasses found in the data.
SVM’s and k-means clustering
- Soft-margin SVM adds slack variables for misclassification and a mislabelling-cost term to the quadratic program, with constraints y(i)(wT x(i) + b) ≥ 1 − ξi.Ten-fold cross-validation on the training set gives misclassification error 0.0163, agreeing with assignment fidelity Fa = 0.9825.Source: SVM’s and k-means clustering · p. 7
- K-means partitions trajectories into k sets to minimize within-set distance to each mean, but is guaranteed to converge only to a local minimum.Initialization can affect meaningful solutions; averaging subclass means over many runs helps make the algorithm more reproducible and stable.Source: SVM’s and k-means clustering · p. 7
- With k = 7, k-means identifies a heating subclass of C0, while four C1 subclasses include two T1 groups and two groups of typical |1⟩ trajectories.The heating subclass is shown in Fig. 5 and the C1 subclasses in Fig. 6.Source: SVM’s and k-means clustering · p. 7, Figure 5 · p. 8, Figure 6 · p. 8