Bandwidth Enables Generalization in Quantum Kernel Models
Authors: Abdulkadir Canatar, Evan Peters, Cengiz Pehlevan, Stefan M. Wild, Ruslan Shaydulin
TMLR 2023 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We demonstrate empirically that our theory correctly predicts how varying the bandwidth affects generalization of quantum models on challenging datasets, including those far outside our theoretical assumptions. We evaluate these kernels on binary classification versions of FMNIST (Xiao et al., 2017), KMNIST (Clanuwat et al., 2018), and PLAs Ti CC (The PLAs Ti CC team et al., 2018) datasets... In Table 2, we report the test accuracies with bandwidth parameter c = 1 for the IQP and EVO kernels. |
| Researcher Affiliation | Collaboration | Abdulkadir Canatar EMAIL Center for Computational Neuroscience Flatiron Institute New York, NY 10010, USAEvan Peters EMAIL Department of Physics University of Waterloo Waterloo, Ontario, N2L 3G1, CanadaCengiz Pehlevan EMAIL School of Engineering and Applied Sciences Harvard University Cambridge, MA 0213, USAStefan M. Wild EMAIL Applied Mathematics & Computational Research Division Lawrence Berkeley National Laboratory Berkeley, CA 94720, USARuslan Shaydulin EMAIL Global Technology Applied Research JPMorgan Chase New York, NY 10017, USA |
| Pseudocode | No | The paper describes methods using mathematical equations and text, but does not include any explicitly labeled 'Pseudocode' or 'Algorithm' blocks, nor any structured, code-like procedural steps. |
| Open Source Code | Yes | We use the experimental data provided by Shaydulin & Wild (2021). The code and the data are publicly provided by Shaydulin & Wild (2021) at https://github.com/rsln-s/Importance-of-Kernel-Bandwidth-in-Quantum-Machine-Learning/. |
| Open Datasets | Yes | We evaluate these kernels on binary classification versions of FMNIST (Xiao et al., 2017), KMNIST (Clanuwat et al., 2018), and PLAs Ti CC (The PLAs Ti CC team et al., 2018) datasets with the input data downsized to n = 22 dimensions, which were previously used to evaluate quantum kernel performance in Shaydulin & Wild (2021); Huang et al. (2021); Peters et al. (2021). |
| Dataset Splits | Yes | The datasets were split into 800 training sets and 200 test sets. |
| Hardware Specification | Yes | computing resources provided on Bebop, a high-performance computing cluster operated by the Laboratory Computing Resource Center at Argonne National Laboratory. ... In Fig. E.1, we present the same experiment as Fig. 2 but for different input dimensions n. We find that the optimal bandwidth parameter is c 2/n. Therefore, the optimal scaling of the bandwidth parameter is O(n α) for α = 1 in this special case. |
| Software Dependencies | No | These quantum circuits were simulated in Shaydulin & Wild (2021) using Qiskit (Abraham et al., 2019) software to compute the kernel Gram matrices on the data. The paper mentions 'Qiskit' but does not specify a version number for it or any other software dependency. |
| Experiment Setup | Yes | In Fig. 2C, we perform kernel regression with our toy kernel and confirm that generalization improves with bandwidth up to an optimal value after which it degrades again. ... Regularization with a small ridge parameter λ = 10 10 is applied for numerical stability. ... We perform SVM for binary classification using these kernels with varying bandwidths. In Table 2, we report the test accuracies with bandwidth parameter c = 1 for the IQP and EVO kernels. We also report the test performance with bandwidth parameters c < c optimized by hyperparameter tuning for each kernel using cross validation (see Appendix E). |