NVQLS introduces the first hybrid quantum-classical unsupervised operator learning method for parametric PDEs via Legendre-Galerkin weak form, sign ambiguity resolution, and neural embedding.
Variational quantum linear solver
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The Projector Variational Ansatz (PVA) is a new VQE ansatz that can match ISQ-QSP or ADAPT-VQE structures and converges with shallower circuits than standard ADAPT-VQE in experiments.
Continuous-variable photonic platform with 20,000-mode cluster state simulates advection transport equation, achieving relative errors of 0.8% and 0.92% on first- and second-order moments via homodyne readout.
Hybrid VQLS pipeline with Carleman linearization recovers high-fidelity solutions to the weakly nonlinear Duffing equation on IBM and Xanadu hardware using symmetry-grouped measurements and optimized ansatzes.
Hybrid variational quantum algorithm solves the advection-diffusion equation on small systems using current noisy IBM quantum hardware, with claimed logarithmic scaling in vector space dimension.
citing papers explorer
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Neural Quantum Spectral Operator Learning for Solving Partial Differential Equations
NVQLS introduces the first hybrid quantum-classical unsupervised operator learning method for parametric PDEs via Legendre-Galerkin weak form, sign ambiguity resolution, and neural embedding.
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Projector Quantum Variational Ansatz
The Projector Variational Ansatz (PVA) is a new VQE ansatz that can match ISQ-QSP or ADAPT-VQE structures and converges with shallower circuits than standard ADAPT-VQE in experiments.
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Analog photonic simulator for large-scale transport
Continuous-variable photonic platform with 20,000-mode cluster state simulates advection transport equation, achieving relative errors of 0.8% and 0.92% on first- and second-order moments via homodyne readout.
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Measurement-Efficient Variational Quantum Linear Solver for Carleman-Linearized Nonlinear Dynamics
Hybrid VQLS pipeline with Carleman linearization recovers high-fidelity solutions to the weakly nonlinear Duffing equation on IBM and Xanadu hardware using symmetry-grouped measurements and optimized ansatzes.
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Variational Quantum Solutions to the Advection-Diffusion Equation for Applications in Fluid Dynamics
Hybrid variational quantum algorithm solves the advection-diffusion equation on small systems using current noisy IBM quantum hardware, with claimed logarithmic scaling in vector space dimension.