We introduce a measurement-induced quantum neural network (MINN), an adaptive monitored-circuit architecture in which mid-circuit measurement outcomes determine the entangling gates in subsequent layers. In contrast to standard monitored circuits where sites and gates are sampled randomly, the gates are parametrized and variational, producing correlated history-dependent dynamics and injecting nonlinearity through measurement back-action. A generic MINN is not expected to be efficiently classically simulable. To demonstrate feasibility, we study a matchgate MINN that admits exact fermionic simulation and can be trained with gradient estimators. We apply the architecture to continuous optimization, image classification, and ground-state search in the Sherrington-Kirkpatrick spin glass, finding effective training and performance over a broad range of monitoring rates.
We introduce Quantum Port-Hamiltonian Neural Networks (Q-pHNNs), parameterised quantum circuits that learn classical dynamics in a structure-preserving manner. The framework rests on the Isomorphic Hamiltonian Mapping (IHM): the skew-symmetric interconnection matrix
J corresponds to unitary gate evolution, and the positive-semidefinite dissipation matrix
R to Measurement-Induced NonLinearity (MINL), realised by mid-circuit measurement with classical feedforward. Conservation and passivity are then enforced by construction rather than by penalty terms, and dissipation becomes an intrinsically quantum effect: energy leaves through the act of measurement. We instantiate the IHM in three architectures: a Quantum HNN that extracts Hamilton's equations via the Parameter-Shift Rule; a Q-pHNN that dissipates through MINL; and a topology-entangled Quantum Graph Neural Network lifting both channels to
N-node coupled-phasor networks. In simulation, where every model here was trained, we obtain
1.35% relative energy drift under a symplectic integrator,
100% energy monotonicity for the single-oscillator MINL circuit, and
92--
98% phase-space energy decay across ring, star and chain networks at
N∈{3,6,9}. On an IBM Heron processor the trained energy surface and its parameter-shift gradients reproduce their simulated values, with an error budget dominated by readout rather than gate infidelity; the dissipative channel executes natively, but its decay is not separable from measurement back-action at these depths.
Quantum neural networks promise to extend the power of machine learning into the quantum domain, with potential applications ranging from automatic recognition of quantum states to the control of quantum devices. However, their physical implementation and training remain challenging. In particular, the backpropagation algorithm that underpins the efficiency of classical neural networks cannot generally be applied to large quantum systems, as nonlinear quantum dynamics are not efficiently simulable. Instead, variational quantum circuits typically rely on parameter-shift rules or sampling-based gradient estimation. Here we propose a bosonic quantum neural network based on parametrically coupled Gaussian modes. Although the underlying quantum dynamics are linear, nonlinear output features are generated through Fock-basis measurements. Because Gaussian evolution can be efficiently simulated in the Heisenberg representation, the system admits gradient-based optimization by differentiating a classical model of the dynamics, while the forward evolution itself could be implemented on quantum hardware. This hybrid approach enables end-to-end training of physically meaningful parameters without requiring gradient extraction from the experimental device. Such architectures are naturally compatible with circuit quantum electrodynamics platforms featuring tunable parametric couplers, as well as integrated photonic systems with engineered χ(2) or χ(3) nonlinearities. Our results demonstrate that linear bosonic networks combined with nonlinear measurement provide a scalable and trainable route toward experimentally realizable quantum neural networks.
Quantum neural networks promise to extend the power of machine learning into the quantum domain, with potential applications ranging from automatic recognition of quantum states to the control of quantum devices. However, their physical implementation and training remain challenging. In particular, the backpropagation algorithm that underpins the efficiency of classical neural networks cannot generally be applied to large quantum systems, as nonlinear quantum dynamics are not efficiently simulable. Instead, variational quantum circuits typically rely on parameter-shift rules or sampling-based gradient estimation. Here we propose a bosonic quantum neural network based on parametrically coupled Gaussian modes. Although the underlying quantum dynamics are linear, nonlinear output features are generated through Fock-basis measurements. Because Gaussian evolution can be efficiently simulated in the Heisenberg representation, the system admits gradient-based optimization by differentiating a classical model of the dynamics, while the forward evolution itself could be implemented on quantum hardware. This hybrid approach enables end-to-end training of physically meaningful parameters without requiring gradient extraction from the experimental device. Such architectures are naturally compatible with circuit quantum electrodynamics platforms featuring tunable parametric couplers, as well as integrated photonic systems with engineered
χ(2) or
χ(3) nonlinearities. Our results demonstrate that linear bosonic networks combined with nonlinear measurement provide a scalable and trainable route toward experimentally realizable quantum neural networks.
Quantum neural networks generalize classical artificial neural networks into the quantum domain. They are formulated as parameterized quantum circuits which are optimized by measuring and minimizing a suitably chosen loss function. The core challenge in understanding, implementing and ultimately using quantum neural networks is that they represent many-body systems with an exponentially large Hilbert space, in combination with a large parameter search space. Moreover, noise -- which is inherent to any quantum measurement -- sets practical limits for the estimation of training loss. Here, we study physics-informed large-scale quantum neural networks that are trained through a finite number of noisy loss function measurements. We show that this architecture permits the construction of nontrivial decision boundaries that enable the classification of quantum states through measuring an order parameter. Our approach can directly process quantum data that is output from quantum simulators and computers and is well suited for implementation on current hardware. Moreover, owed to a close link between the neural network dynamics and the evolution of Markovian open many-body quantum systems, one may expect a certain robustness to noise, which is ubiquitous in the current NISQ era.
We implement a quantum neural network on trapped-ion and IBM superconducting quantum computers for Modified National Institute of Standards image classification. Feedforward is realized through qubit rotations conditioned on measurement outcomes from previous layers. The network is trained classically, while inference is performed experimentally on quantum hardware. A tunable interpolation parameter connects the classical and quantum regimes. Moderate values improve classification performance by introducing measurement uncertainty. For borderline images misclassified classically but correctly identified quantum mechanically, we observe strong deviations from idealized simulations due to physical noise, consistent with fluctuations between nearby minima in the classification landscape. We further benchmark noise by inserting additional single- and two-qubit gate pairs into the circuits. Our results motivate more complex quantum neural networks on noisy intermediate-scale quantum devices and suggest a possible route toward classically nonsimulable architectures.
This paper investigates the feasibility of leveraging quantum entanglement to facilitate self-organizing feature discovery within neural networks. Traditional neural networks rely on gradient-based optimization to learn feature representations, often requiring substantial computational resources and careful hyperparameter tuning. We propose a novel quantum neural network (QNN) architecture designed to exploit the inherent correlations provided by quantum entanglement. The core idea is that dynamic entanglement between qubits will intrinsically adapt the network's weights, leading to the emergence of richer, more relevant feature representations directly from the data. Specifically, we outline a network structure incorporating controlled quantum gates and measurement operations to induce entanglement. The theoretical framework demonstrates how this entanglement can evolve to capture underlying data correlations, effectively performing unsupervised feature learning. We detail the mathematical formulation of the network's dynamics, emphasizing the role of entanglement entropy as a key indicator of feature discovery. While experimental validation is not included in this theoretical exploration, this work lays the groundwork for future investigations into the potential of quantum neural networks for efficient and adaptive feature extraction. The key concepts involve the construction of a QNN with entangled qubits, the evolution of entanglement under data input, and the quantification of feature discovery through entanglement entropy.