Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in [1].
QuanONet: Quantum Neural Operator with Application to Differential Equation
Authors: Ruocheng Wang, Zhuo Xia, Ge Yan, Junchi Yan
ICML 2025 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We evaluate Quan ONet and TF-Quan ONet on a range of benchmark problems: three ordinary differential equation (ODE) and one partial differential equation (PDE) problem: ... We use 5 runs with different training/test data sampling and network initialization to compute the mean error and the standard deviation (SD), as presented in Table 1. |
| Researcher Affiliation | Academia | 1School of Artificial Intelligence & School of Computer Science & Zhiyuan College, SJTU. Correspondence to: Junchi Yan <EMAIL>. |
| Pseudocode | No | The paper describes methods and architectures but does not include any explicitly labeled pseudocode or algorithm blocks. Figure 2 shows a schematic architecture, not pseudocode. |
| Open Source Code | No | The paper does not provide a direct link to source code or an explicit statement about the release of source code for the Quan ONet methodology. It mentions using 'Mind Spore' and 'Deep Xde' frameworks, but this refers to third-party tools, not their own implementation. |
| Open Datasets | No | We generate the dataset by using the mean-zero Gaussian random field with the form: u G(0, kl(x1, x2)) where the covariance kernel kl(x1, x2) = e x1 x2 2/2l2 is the radial-basis function (RBF) kernel with a length-scale parameter l > 0 to sample input function u. We solve the ODE systems by Runge-Kutta (4, 5) and PDEs by a second-order finite difference method. |
| Dataset Splits | Yes | Table 2. Default parameters for each problem Case u space Sensors # Training # Testing # Batch Size ODE Anti-deriv operator GRF(l = 0.2) 100 10000 100000 100 Homogeneous operator GRF(l = 0.2) 100 10000 100000 100 Nonlinear ODE GRF(l = 0.2) 100 10000 100000 100 PDE D-R system GRF(l = 0.2) 100 100000 1000000 100 |
| Hardware Specification | Yes | All the numerical simulations are performed on a machine with 190GB memory, one physical CPU with 32 cores AMD Ryzen Threadripper 3970X CPU, and 5 GPUs (NV Ge Force RTX 3090). |
| Software Dependencies | No | We implement a Python quantum simulator without noise to simulate QNNs Based on Mind Spore (Xu et al., 2024) framework, and designing classical neural networks using Deep Xde (Lu et al., 2020) framework. ... By leveraging Qiskit s compilation optimization techniques and using standard noise mitigation... |
| Experiment Setup | Yes | We scale the various QNNs to ensure that they have close number of parameters (1200 for ODE and 2400 for PDE) and use the Adam optimizer (Kingma, 2014) with learning rate 0.0001. The details are shown in the Appendix A. The number of qubits of all QNNs is 5, and the Hamiltonian is H = P5 i=1 σ(i) z . Detailed configuration is given in Table 2, Table 3 and Table 4. |