Zotero Catalogue

Quantum noise fundamentally limits the utility of near-term quantum devices, making error mitigation essential for practical quantum computation. While traditional quantum error correction codes require substantial qubit overhead and complex syndrome decoding, we propose a machine learning approach that directly reconstructs clean quantum states from noisy density matrices without additional qubits. We formulate quantum noise reduction as a supervised learning problem using a convolutional neural network (CNN) autoencoder architecture with a novel fidelity-aware composite loss function. Our method is trained and evaluated on a comprehensive synthetic dataset of 10,000 density matrices derived from random 5-qubit quantum circuits, encompassing five noise types (depolarizing, amplitude damping, phase damping, bit-flip, and mixed noise) across four intensity levels (0.05-0.20). The CNN successfully reconstructs quantum states across all noise conditions, achieving an average fidelity improvement from 0.298 to 0.774 (Δ = 0.476). Notably, the model demonstrates superior performance on complex mixed noise scenarios and higher noise intensities, with mixed noise showing the highest corrected fidelity (0.807) and improvement (0.567). The approach effectively preserves both diagonal elements (populations) and off-diagonal elements (quantum coherences), making it suitable for entanglement-dependent quantum algorithms. While phase damping presents fundamental information-theoretic limitations, our results suggest that CNN-based density matrix reconstruction offers a promising, resource-efficient alternative to traditional quantum error correction for NISQ-era devices. This data-driven approach could enable practical quantum advantage with fewer physical qubits than conventional error correction schemes require.

Neural networks are a central technique in machine learning. Recent years have seen a wave of interest in applying neural networks to physical systems for which the governing dynamics are known and expressed through differential equations. Two fundamental challenges facing the development of neural networks in physics applications is their lack of interpretability and their physics-agnostic design. The focus of the present work is to embed physical constraints into the structure of the neural network to address the second fundamental challenge. By constraining tunable parameters (such as weights and biases) and adding special layers to the network, the desired constraints are guaranteed to be satisfied without the need for explicit regularization terms. This is demonstrated on upervised and unsupervised networks for two basic symmetries: even/odd symmetry of a function and energy conservation. In the supervised case, the network with embedded constraints is shown to perform well on regression problems while simultaneously obeying the desired constraints whereas a traditional network fits the data but violates the underlying constraints. Finally, a new unsupervised neural network is proposed that guarantees energy conservation through an embedded symplectic structure. The symplectic neural network is used to solve a system of energy-conserving differential equations and out-performs an unsupervised, non-symplectic neural network.