Polynomial neural surrogates for designing photonic quantum experiments

For quantum machine learning, the exact boundary between classical and quantum advantage is still poorly understood. Direct comparison between quantum neural networks (QNNs) and existing classical models, which encompass fundamentally different function classes, often fails to provide broader insight into the difference between the two. Inspired by the techniques of Neural Quantum States and Random Fourier Features, this work introduces Neural Fourier Surrogates (NFS), a stochastic classical neural network architecture for efficiently learning coefficients over the same finite Fourier series support as quantum neural networks. Testing on a selection of tabular benchmark datasets, we find that NFS is an effective classifier architecture broadly competitive with established classical baselines, including a comparable Random Fourier Features model, and possessing comparable performance to data-reuploading QNNs; combined with additional analysis comparing the learned Fourier spectra of QNNs and NFS on synthetic data, these results establish NFS as a natural classical baseline for evaluating QNN performance.

Models of quantum systems faithfully map system parameters to observations, but the inverse problem of parameter inference from measurement data presents a fundamental challenge: computationally intractable likelihoods due to an exponentially large Hilbert space. Here, we introduce simulation-based quantum system inference, a unified, likelihood-free framework that learns parameter posteriors directly from classical simulation data. The central idea is to pair polynomial-cost classical simulators, such as Pauli propagation and tensor networks, with normalizing flows or other neural density estimators for accurate, reusable inference. A single model, trained once, maps any new measurement record to its posterior in one forward pass---turning per-experiment inference into a fixed, up-front cost. We numerically demonstrate the framework's versatility across Pauli noise learning, quantum error mitigation, quantum state tomography, and Hamiltonian learning, with examples involving 81-qubit shallow circuits and 735-parameter inference. In each case, the approach yields accurate estimates of identifiable parameters, while posterior uncertainty provides additional diagnostics of non-identifiability and indicates where further characterization is needed. Our framework reduces data-acquisition requirements in quantum experiments and accelerates parameter inference, providing a practical route to characterizing and improving large-scale quantum systems.

In this work, a quantum architecture search framework for approximate quantum state preparation (QSP) is proposed. QSP is a challenging task, since the search space grows exponentially with the number of qubits, making the identification of the optimal circuit non-trivial. To address this problem, deep reinforcement learning is employed through an agent based on proximal policy optimization. The objective of the agent is to identify the best possible approximation of the target state while simultaneously minimizing the number of gates used. At each step, the agent appends a new gate to the circuit and recomputes the fidelity between the approximated state and the target states. Various experiments have been performed from 2 to 5 qubits. Both predefined states, such as Bell, GHZ, W, and Dicke states, and completely random states are considered. The proposed framework is able to achieve approximation errors of $10^{-14}$.