Barren Plateau Mitigation in Variational Quantum Eigensolvers via Physics-Informed Quantum Neural Networks
Maldives Maldives Maldives 
Abstract
Barren plateaus severely limit the trainability of Variational Quantum Eigensolvers (VQEs) because exponentially vanishing gradients hinder reliable parameter optimization as circuit depth and system size increase. This study aimed to evaluate whether a physics-informed quantum neural network (PI-QNN) could mitigate gradient suppression while preserving the expressive capacity required for accurate ground-state estimation. A controlled computational experiment compared the PI-QNN with hardware-efficient, symmetry-preserving, and unitary coupled-cluster ansätze across molecular and spin Hamiltonians containing 4–16 qubits. Hamiltonian-informed connectivity, symmetry-preserving gates, conservation penalties, and physics-guided initialization were integrated into the proposed architecture. Gradient variance, convergence behavior, energy error, optimization success, circuit resources, and noise robustness were assessed through repeated ideal and noisy simulations. The PI-QNN exhibited a gradient-variance scaling coefficient of ?0.17, compared with ?0.61 for the hardware-efficient ansatz, indicating substantially slower gradient decay. It achieved an 81.6% optimization success rate, a median energy error of 1.21 × 10?3 Hartree-equivalent units, and faster convergence across the evaluated benchmarks. Ablation and parameter-matched analyses confirmed that the improvement arose from the combined physical constraints rather than parameter reduction alone. These findings demonstrate that physics-informed circuit design offers a principled approach to mitigating barren plateaus, although validation on larger systems and real quantum hardware remains necessary.
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References
Alfonso, D. (2025). Chemical applications of variational quantum eigenvalue-based quantum algorithms: Perspective and survey. Applied Physics Reviews, 12(3). https://doi.org/10.1063/5.0245874
Alvertis, A. M. (2025). Compressing Hamiltonians with ab initio downfolding for simulating strongly-correlated materials on quantum computers. Physical Review Applied, 23(4). https://doi.org/10.1103/PhysRevApplied.23.044028
Barthel, T. (2025). Absence of Barren Plateaus and Scaling of Gradients in the Energy Optimization of Isometric Tensor Network States. Communications in Mathematical Physics, 406(4). https://doi.org/10.1007/s00220-024-05217-x
Battaglia, S. (2024). A general framework for active space embedding methods with applications in quantum computing. Npj Computational Materials, 10(1). https://doi.org/10.1038/s41524-024-01477-2
Bentellis, A. (2023). Benchmarking the Variational Quantum Eigensolver using different quantum hardware. Proceedings 2023 IEEE International Conference on Quantum Computing and Engineering Qce 2023, 1(Query date: 2026-08-07 19:31:40), 518–523. https://doi.org/10.1109/QCE57702.2023.00065
Cao, C. (2024). Accelerated variational quantum eigensolver with joint Bell measurement. Physical Review Research, 6(1). https://doi.org/10.1103/PhysRevResearch.6.013205
Carrascal, G. (2024). Differential evolution VQE for crypto-currency arbitrage. Quantum optimization with many local minima. Digital Signal Processing A Review Journal, 148(Query date: 2026-08-07 19:31:40). https://doi.org/10.1016/j.dsp.2024.104464
Chang, R. Y. (2025). Accelerating Parameter Initialization in Quantum Chemical Simulations via LSTM-FC-VQE. IEEE Access, 13(Query date: 2026-08-07 19:31:40), 189725–189734. https://doi.org/10.1109/ACCESS.2025.3628966
Ciaramelletti, C. (2025). Detecting quasidegenerate ground states in topological models via the variational quantum eigensolver. Physical Review A, 111(2). https://doi.org/10.1103/PhysRevA.111.022437
Denner, M. M. (2023). A hybrid quantum-classical method for electron-phonon systems. Communications Physics, 6(1). https://doi.org/10.1038/s42005-023-01353-3
Dhara, B. (2025). Beamforming optimization via quantum algorithms using Variational Quantum Eigensolver and Quantum Approximate Optimization Algorithm. Iet Quantum Communication, 6(1). https://doi.org/10.1049/qtc2.12120
Fan, Y. (2023). Circuit-Depth Reduction of Unitary-Coupled-Cluster Ansatz by Energy Sorting. Journal of Physical Chemistry Letters, 14(43), 9596–9603. https://doi.org/10.1021/acs.jpclett.3c01804
Grimsley, H. R. (2023). Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. Npj Quantum Information, 9(1). https://doi.org/10.1038/s41534-023-00681-0
Grimsley, H. R. (2025). Challenging excited states from adaptive quantum eigensolvers: Subspace expansions vs. State-averaged strategies. Quantum Science and Technology, 10(2). https://doi.org/10.1088/2058-9565/ad9fa2
Guan, J. (2023). Detecting Violations of Differential Privacy for Quantum Algorithms. Ccs 2023 Proceedings of the 2023 ACM Sigsac Conference on Computer and Communications Security, (Query date: 2026-08-07 19:31:40), 2277–2291. https://doi.org/10.1145/3576915.3623108
Gupta, S. (2023). A Quantum Approach for Stochastic Constrained Binary Optimization. ICASSP IEEE International Conference on Acoustics Speech and Signal Processing Proceedings, 2023(Query date: 2026-08-07 19:31:40). https://doi.org/10.1109/ICASSP49357.2023.10097179
Hagai, M. (2023). Artificial neural network encoding of molecular wavefunctions for quantum computing†. Digital Discovery, 2(3), 634–650. https://doi.org/10.1039/d2dd00093h
Halder, D. (2023). Corrections beyond coupled cluster singles and doubles through selected generalized rank-two operators: Digital quantum simulation of strongly correlated systems. Journal of Chemical Sciences, 135(2). https://doi.org/10.1007/s12039-023-02161-6
Hohenstein, E. G. (2023). Efficient quantum analytic nuclear gradients with double factorization. Journal of Chemical Physics, 158(11). https://doi.org/10.1063/5.0137167
Khamoshi, A. (2023). AGP-based unitary coupled cluster theory for quantum computers. Quantum Science and Technology, 8(1). https://doi.org/10.1088/2058-9565/ac93ae
Khumalo, M. T. (2025). An investigation of IBM quantum computing device performance on combinatorial optimisation problems. Neural Computing and Applications, 37(2), 611–626. https://doi.org/10.1007/s00521-022-07438-4
Le, N. T. (2023). Correlated Reference-Assisted Variational Quantum Eigensolver. Journal of Physical Chemistry A, 127(24), 5222–5230. https://doi.org/10.1021/acs.jpca.3c00993
Li, A. C. Y. (2023). Benchmarking variational quantum eigensolvers for the square-octagon-lattice Kitaev model. Physical Review Research, 5(3). https://doi.org/10.1103/PhysRevResearch.5.033071
Loipersberger, M. (2023). Accurate non-covalent interaction energies on noisy intermediate-scale quantum computers via second-order symmetry-adapted perturbation theory. Chemical Science, 14(13), 3587–3599. https://doi.org/10.1039/d2sc05896k
Marqversen, F. K. (2023). Applications and resource reductions in measurement-based variational quantum eigensolvers. Quantum Science and Technology, 8(4). https://doi.org/10.1088/2058-9565/ace2e6
Michel, A. (2023). Blueprint for a digital-analog variational quantum eigensolver using Rydberg atom arrays. Physical Review A, 107(4). https://doi.org/10.1103/PhysRevA.107.042602
Mineh, L. (2023). Accelerating the variational quantum eigensolver using parallelism. Quantum Science and Technology, 8(3). https://doi.org/10.1088/2058-9565/acd0d2
Mohanty, N. (2023). Analysis of the Vehicle Routing Problem Solved via Hybrid Quantum Algorithms in the Presence of Noisy Channels. IEEE Transactions on Quantum Engineering, 4(Query date: 2026-08-07 19:31:40). https://doi.org/10.1109/TQE.2023.3303989
Mondal, D. (2023). Development of a compact Ansatz via operator commutativity screening: Digital quantum simulation of molecular systems. Journal of Chemical Physics, 159(1). https://doi.org/10.1063/5.0153182
Mondal, D. (2025). Determination of Molecular Symmetry Adapted Eigenroots in the Variational Quantum Eigensolver Framework. International Journal of Quantum Chemistry, 125(7). https://doi.org/10.1002/qua.70029
Mukherjee, A. (2023). Comparative study of adaptive variational quantum eigensolvers for multi-orbital impurity models. Communications Physics, 6(1). https://doi.org/10.1038/s42005-022-01089-6
Nagy, D. (2024). Electric Field Gradient Calculations for Ice VIII and IX Using Polarizable Embedding: A Comparative Study on Classical Computers and Quantum Simulators. Journal of Physical Chemistry A, 128(30), 6305–6315. https://doi.org/10.1021/acs.jpca.4c02697
Okada, K. N. (2023). Classically optimized variational quantum eigensolver with applications to topological phases. Physical Review Research, 5(4). https://doi.org/10.1103/PhysRevResearch.5.043217
Pollard, N. (2025). BenchQC: A Benchmarking Toolkit for Quantum Computation. Journal of Computational Chemistry, 46(21). https://doi.org/10.1002/jcc.70202
Ravi, G. S. (2023). CAFQA: A Classical Simulation Bootstrap for Variational Quantum Algorithms. International Conference on Architectural Support for Programming Languages and Operating Systems ASPLOS, 1(Query date: 2026-08-07 19:31:40), 15–29. https://doi.org/10.1145/3567955.3567958
Roca-Jerat, S. (2023). Circuit Complexity through phase transitions: Consequences in quantum state preparation. Scipost Physics, 15(5). https://doi.org/10.21468/SciPostPhys.15.5.186
Sakurai, R. (2024). Comparative study on compact quantum circuits of hybrid quantum-classical algorithms for quantum impurity models. Physical Review Research, 6(2). https://doi.org/10.1103/PhysRevResearch.6.023110
Sayginel, H. (2024). A fault-tolerant variational quantum algorithm with limited T-depth. Quantum Science and Technology, 9(1). https://doi.org/10.1088/2058-9565/ad0571
Schroeder, A. (2024). Deterministic Ansätze for the measurement-based variational quantum eigensolver. New Journal of Physics, 26(6). https://doi.org/10.1088/1367-2630/ad51e5
Scriva, G. (2024). Challenges of variational quantum optimization with measurement shot noise. Physical Review A, 109(3). https://doi.org/10.1103/PhysRevA.109.032408
Sennane, W. (2023). Calculating the ground-state energy of benzene under spatial deformations with noisy quantum computing. Physical Review A, 107(1). https://doi.org/10.1103/PhysRevA.107.012416
Shkolnikov, V. O. (2023). Avoiding symmetry roadblocks and minimizing the measurement overhead of adaptive variational quantum eigensolvers. Quantum, 7(Query date: 2026-08-07 19:31:40). https://doi.org/10.22331/q-2023-06-12-1040
Simmons, J. (2023). Computing vibrational spectra using a new collocation method with a pruned basis and more points than basis functions: Avoiding quadrature. Journal of Chemical Physics, 158(14). https://doi.org/10.1063/5.0146703
Sivakumar, A. (2024). A computational study and analysis of Variational Quantum Eigensolver over multiple parameters for molecules and ions. EPJ Quantum Technology, 11(1). https://doi.org/10.1140/epjqt/s40507-024-00280-8
Skogh, M. (2023). Accelerating variational quantum eigensolver convergence using parameter transfer. Electronic Structure, 5(3). https://doi.org/10.1088/2516-1075/ace86d
Stokes, J. (2023). Continuous-variable neural network quantum states and the quantum rotor model. Quantum Machine Intelligence, 5(1). https://doi.org/10.1007/s42484-023-00100-9
Sun, R. Y. (2023). Efficient variational quantum circuit structure for correlated topological phases. Physical Review B, 108(7). https://doi.org/10.1103/PhysRevB.108.075127
Tsukayama, D. (2025). Enhancing computational accuracy with parallel parameter optimization in variational quantum eigensolver. Aip Advances, 15(1). https://doi.org/10.1063/5.0236028
Uttarkar, A. (2024). A comparative insight into peptide folding with quantum CVaR-VQE algorithm, MD simulations and structural alphabet analysis. Quantum Information Processing, 23(2). https://doi.org/10.1007/s11128-024-04261-9
Volpe, D. (2024). A Predictive Approach for Selecting the Best Quantum Solver for an Optimization Problem. Proceedings IEEE Quantum Week 2024 Qce 2024, 1(Query date: 2026-08-07 19:31:40), 1014–1025. https://doi.org/10.1109/QCE60285.2024.00121
Vu, T. H. (2025). Benchmarking Variants of the Adam Optimizer for Quantum Machine Learning Applications. IEEE Open Journal of the Computer Society, 6(Query date: 2026-08-07 19:31:40), 1146–1154. https://doi.org/10.1109/OJCS.2025.3586953
Weaving, T. (2025). Contextual subspace variational quantum eigensolver calculation of the dissociation curve of molecular nitrogen on a superconducting quantum computer. Npj Quantum Information, 11(1). https://doi.org/10.1038/s41534-024-00952-4
Xu, G. (2023). Concurrent quantum eigensolver for multiple low-energy eigenstates. Physical Review A, 107(5). https://doi.org/10.1103/PhysRevA.107.052423
Yoffe, D. (2025). A qubit-efficient variational selected configuration-interaction method. Quantum Science and Technology, 10(1). https://doi.org/10.1088/2058-9565/ad7d32
Zaytsev, V. A. (2024). Calculation of the moscovium ground-state energy by quantum algorithms. International Journal of Quantum Chemistry, 124(1). https://doi.org/10.1002/qua.27232
Zhang, H. K. (2024). Absence of Barren Plateaus in Finite Local-Depth Circuits with Long-Range Entanglement. Physical Review Letters, 132(15). https://doi.org/10.1103/PhysRevLett.132.150603
Zhang, J. (2023). DISQ: Dynamic Iteration Skipping for Variational Quantum Algorithms. Proceedings 2023 IEEE International Conference on Quantum Computing and Engineering Qce 2023, 1(Query date: 2026-08-07 19:31:40), 1062–1073. https://doi.org/10.1109/QCE57702.2023.00120
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Copyright (c) 2026 Mariyam Asma, Mohamed Naseer, Aminath Nafeeza
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