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arXiv:2608.23025

A Unified Quantum Neural Network Framework for Hamiltonian Learning and Emulation of Unknown Quantum Systems

Ahmad Salmanogli

quant-phSubmitted Aug 24, 2026• Announced Aug 25, 2026• 0 citations
v1 · Aug 24, 2026v2 · Sep 30, 2026
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Abstract

Accurate identification of unknown quantum systems is essential for quantum computing, sensing, and control because the Hamiltonian governs quantum state evolution. This work proposes a QNN based framework for black box Hamiltonian learning and quantum system emulation using full density matrix trajectory learning. Unlike approaches based only on final states or selected observables, the method exploits the complete temporal evolution of the density matrix under Lindblad dynamics. A synthetic dataset of physically admissible Hamiltonians and dissipation parameters is generated to emulate experimental measurements. The QNN learns a nonlinear mapping from control inputs to a 32-dimensional Hamiltonian coefficient vector, enabling reconstruction and differentiable emulation of the unknown system. Chirped excitation and randomized initial quantum states are incorporated to improve robustness and provide richer dynamical information. Performance is evaluated using trajectory density loss, quantum-state fidelity, and trace distance. Randomized initialization improves state-level reconstruction, increasing fidelity to 0.929 for the single qubit benchmark and 0.787 for the unknown system, while reducing trace distance to 0.124 and 0.316, respectively. In contrast, chirped excitation primarily improves optimization by accelerating convergence and reducing trajectory density loss. Finally, the learned Hamiltonian is mapped onto a physical two qubit bus resonator architecture in the dispersive regime, yielding key circuit parameters including transmon capacitances, Josephson inductances, qubit separation, and bus-resonator length. The framework therefore establishes a data-driven pathway from black box quantum system identification to physical quantum emulation, with potential applications in quantum digital twin modeling.

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Accurate identification of unknown quantum systems is essential for quantum computing, sensing, and control because the Hamiltonian governs quantum state evolution. This work proposes a QNN based framework for black box Hamiltonian learning and quantum system emulation using full density matrix trajectory learning. Unlike approaches based only on final states or selected observables, the method exploits the complete temporal evolution of the density matrix under Lindblad dynamics. A synthetic dataset of physically admissible Hamiltonians and dissipation parameters is generated to emulate experimental measurements. The QNN learns a nonlinear mapping from control inputs to a 32-dimensional Hamiltonian coefficient vector, enabling reconstruction and differentiable emulation of the unknown system. Chirped excitation and randomized initial quantum states are incorporated to improve robustness and provide richer dynamical information. Performance is evaluated using trajectory density loss, quantum-state fidelity, and trace distance. Randomized initialization improves state-level reconstruction, increasing fidelity to 0.929 for the single qubit benchmark and 0.787 for the unknown system, while reducing trace distance to 0.124 and 0.316, respectively. In contrast, chirped excitation primarily improves optimization by accelerating convergence and reducing trajectory density loss. Finally, the learned Hamiltonian is mapped onto a physical two qubit bus resonator architecture in the dispersive regime, yielding key circuit parameters including transmon capacitances, Josephson inductances, qubit separation, and bus-resonator length. The framework therefore establishes a data-driven pathway from black box quantum system identification to physical quantum emulation, with potential applications in quantum digital twin modeling.
Characterizing the memory properties of the environment has become critical for the high-fidelity control of qubits and other advanced quantum systems. However, current non-Markovian tomography techniques are either limited to discrete superoperators, or they employ machine learning methods, neither of which provide physical insight into the dynamics of the quantum system. To circumvent this limitation, we design learning architectures that explicitly encode physical constraints like the properties of completely-positive trace-preserving maps in a differential form. This method preserves the versatility of the machine learning approach without sacrificing the efficiency and fidelity of traditional parameter estimation methods. Our approach provides the physical interpretability that machine learning and opaque superoperators lack. Moreover, it is aware of the underlying continuous dynamics typically disregarded by superoperator-based tomography. This paradigm paves the way to noise-aware optimal quantum control and opens a path to exploiting the bath as a control and error mitigation resource.
Learning the unknown interactions that govern a quantum system is crucial for quantum information processing, device benchmarking, and quantum sensing. The problem, known as Hamiltonian learning, is well understood under the assumption that interactions are local, but this assumption may not hold for arbitrary Hamiltonians. Previous methods all require high-order inverse polynomial dependency with precision, unable to surpass the standard quantum limit and reach the gold-standard Heisenberg-limited scaling. Whether Heisenberg-limited Hamiltonian learning is possible without prior assumptions about the interaction structures, a challenge we term , remains an open question. In this work, we present a quantum algorithm to learn arbitrary sparse Hamiltonians without any structure constraints using only black-box queries of the system’s real-time evolution and minimal digital controls to attain Heisenberg-limited scaling in estimation error. Our method is also resilient to state-preparation-and-measurement errors, enhancing its practical feasibility. We numerically demonstrate our ansatz-free protocol for learning physical Hamiltonians and validating analog quantum simulations, benchmarking our performance against the state-of-the-art Heisenberg-limited learning approach. Moreover, we establish a fundamental trade-off between total evolution time and quantum control on learning arbitrary interactions, revealing the intrinsic interplay between controllability and total evolution-time complexity for any learning algorithm. These results pave the way for further exploration into Heisenberg-limited Hamiltonian learning in complex quantum systems under minimal assumptions, potentially enabling new benchmarking and verification protocols.
Sparse identification of nonlinear dynamics (SINDy) is a data-driven framework for estimating classical nonlinear dynamical systems from time-series data. In this approach, system dynamics is represented as a linear combination of a predefined set of basis functions, and the corresponding coefficients are sparsely estimated from observed time-series data. In this study, we propose sparse identification of quantum Hamiltonian dynamics (SIQHDy), a SINDy-inspired quantum circuit learning framework for estimating quantum Hamiltonian dynamics from time-series data of quantum measurement outcomes. In SIQHDy, the unitary evolution of a quantum Hamiltonian system is expressed as a product of basis quantum circuits, and the corresponding circuit parameters are estimated through sparsity-promoting optimization. We numerically demonstrate that SIQHDy accurately reconstructs the dynamics of single-, three-, and five-spin systems, and exhibits robustness to measurement noise in the three-spin case. Furthermore, we propose an extension of SIQHDy for scenarios with limited accessible observables and evaluate its performance in identifying two-spin systems and in network-structure identification for five-spin systems.
Quantum systems in near-term devices operate in noisy, open-system regimes where decoherence and control imperfections are unavoidable. This study presents a physics-informed neural-network framework for modelling, noiseaware simulation, and residual-based control of open quantum systems, validated against a closed-form Lindblad solution for a driven, amplitude-damped qubit rather than a numerical reference. Across three random seeds, the trained network reproduces population and coherence dynamics with a mean RMSE of 0.00060 and a standard deviation of 0.00054. The mixed-state fidelity exceeds 0.999999 over the evaluation trajectory, while the squared Bloch-vector norm remains within the physical bound for the main modelling benchmark. Removing the Fourier-feature input encoding produces a 70-fold degradation in RMSE, confirming a strong representational benefit for the oscillatory dynamics. Direct comparison against fourth-order Runge-Kutta integration shows the classical solver to be approximately five orders of magnitude faster and two orders more accurate at this scale; the value of the proposed framework for a single qubit therefore lies in data-free, physics-constrained modelling rather than computational speed. A residual-based state-transfer control demonstration and a control-effort sweep further reveal a clear fidelity-versus-energy trade-off and a marked reduction in seed-to-seed variation as regularisation increases. These results support physics-constrained learning as a faithful approach to singlequbit open-system modelling and control, while motivating further validation on multi-qubit systems before broader scalability claims are made.
Abstract Sparse identification of nonlinear dynamics (SINDy) is a data-driven framework for estimating classical nonlinear dynamical systems from time-series data. In this approach, system dynamics is represented as a linear combination of a predefined set of basis functions, and the corresponding coefficients are sparsely estimated from observed time-series data. In this study, we propose sparse identification of quantum Hamiltonian dynamics (SIQHDy), a SINDy-inspired quantum circuit learning framework for estimating quantum Hamiltonian dynamics from time-series data of quantum measurement outcomes. In SIQHDy, the unitary evolution of a quantum Hamiltonian system is expressed as a product of basis quantum circuits, and the corresponding circuit parameters are estimated through sparsity-promoting optimization. We numerically demonstrate that SIQHDy accurately reconstructs the dynamics of single-, three-, and five-spin systems, and exhibits robustness to measurement noise in the three-spin case. Furthermore, we propose an extension of SIQHDy for scenarios with limited accessible observables and evaluate its performance in identifying three-spin systems and in network-structure identification for five-spin systems.
Characterizing the dynamics of open quantum systems at the level of microscopic interactions and error mechanisms is essential for calibrating quantum hardware, designing robust simulation protocols, and developing tailored error-correction methods. Under Markovian noise/dissipation, a natural characterization approach is to identify the full Lindbladian generator that gives rise to both coherent (Hamiltonian) and dissipative dynamics. Prior protocols for learning Lindbladians from dynamical data assumed pre-specified interaction structure, which can be restrictive when the relevant noise channels or control imperfections are not known in advance. In this paper, we present a sample-efficient protocol for learning sparse Lindbladians without assuming any a priori structure. Our protocol is ancilla-free, uses only product-state preparations and Pauli-basis measurements, admits provably stable coefficient reconstruction, and achieves near-optimal time resolution, making it compatible with near-term experimental capabilities. Together, this provides a systematic route to scalable characterization of open-system quantum dynamics, especially in settings where the error mechanisms of interest are unknown.