Hybrid Quantum-Classical Neural Networks for Recognizing Quantum Phases

• URL: http://arxiv.org/abs/2606.28201v1
• Date: Fri, 26 Jun 2026 15:49:45 GMT
• Title: Hybrid Quantum-Classical Neural Networks for Recognizing Quantum Phases
• Abstract summary: We introduce and implement a hybrid quantum-classical neural network for quantum phase recognition.<n>We train both components with superconducting quantum hardware in the optimization loop.<n>We experimentally demonstrate a classifier for the quantum phases of surface code lattices with up to 4x4 sites in a magnetic field.
• Score: 27.960775552553272
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Identifying quantum phases of matter is key to understanding strongly correlated materials, but remains a challenging task for both conventional computers and current quantum processors. Here, we introduce and implement a hybrid quantum-classical neural network for quantum phase recognition by combining a hardware-efficient parameterized quantum circuit and a feedforward neural network. We jointly train both components with superconducting quantum hardware in the optimization loop, to experimentally demonstrate a classifier for the quantum phases of surface code lattices with up to 4x4 sites in a magnetic field. To learn nonlocal features of the topological phase, we train the hybrid neural network to distinguish topological ground states of the surface code from a featureless ensemble of product states. This allows the trained classifier to distinguish topological ground states from randomly chosen product states, even when subjected to any single-qubit Pauli error. The classifier reaches accuracies above 85% in single-shot measurements, and above 99% when averaging over ten measurements. We expect hybrid neural networks such as the one presented here to be a promising approach for characterizing quantum states in scenarios where classical methods exhibit an unfavorable scaling of sample complexity.

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