High-fidelity quantum gate learning via physics-informed neural networks
Abstract
We propose a physics-informed neural network (PINN) approach for high-fidelity quantum gate learning in both one- and two-qubit systems. We train a PINN using the time-dependent Schrödinger equation, where smooth control fields with fixed boundary conditions are obtained by minimizing a loss function that considers model dynamics, gate error, physical constraints, regularization terms, and multiple initial conditions. Training considers pairs of mutually unbiased bases, while independent validation combines Haar-random input states with the average gate fidelity. Unitary simulations yield an average gate infidelity of 8.49×10−8 for Hadamard and values between 3.39×10−7 and 4.96×10−6 for controlled-NOT under XX, YY, and ZZ interactions. We examine how the learned control fields depend on the coupling, training configuration, and available local fields, including five exchange-type dipolar scenarios. We test the learned control fields under the Lindblad master equation with dephasing and amplitude damping, theoretically reproducing the expected first-order fidelity loss in the weak-dissipation regime. Finally, boundary-adapted Chebyshev expansions represent 139 learned controls with a minimum common count of K∗=24 coefficients per control for all eleven family-averaged mean squared errors to fall below 10−6. Separately, square-pulse and Strang propagation at K=30 preserve all 31 continuous polynomial references within infidelity 10−5 at N=128 and all larger tested resolutions, under both sampling rules. These results connect multi-state gate synthesis, control-resource characterization, and compact square-pulse playback.
Related
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BibTeX
@misc{fabra2026highfidelity,
title = {{High-fidelity quantum gate learning via physics-informed neural networks}},
author = {Luis Fabra and Cristian E. Susa and Alcides Montoya and Ariel Norambuena},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.03851},
eprint = {2611.03851},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.03851},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - High-fidelity quantum gate learning via physics-informed neural networks
AU - Luis Fabra
AU - Cristian E. Susa
AU - Alcides Montoya
AU - Ariel Norambuena
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.03851
UR - https://arxiv.org/abs/2611.03851
AB - We propose a physics-informed neural network (PINN) approach for high-fidelity quantum gate learning in both one- and two-qubit systems. We train a PINN using the time-dependent Schrödinger equation, where smooth control fields with fixed boundary conditions are obtained by minimizing a loss function that considers model dynamics, gate error, physical constraints, regularization terms, and multiple initial conditions. Training considers pairs of mutually unbiased bases, while independent validation combines Haar-random input states with the average gate fidelity. Unitary simulations yield an average gate infidelity of 8.49×10^−8 for Hadamard and values between 3.39×10^−7 and 4.96×10^−6 for controlled-NOT under XX, YY, and ZZ interactions. We examine how the learned control fields depend on the coupling, training configuration, and available local fields, including five exchange-type dipolar scenarios. We test the learned control fields under the Lindblad master equation with dephasing and amplitude damping, theoretically reproducing the expected first-order fidelity loss in the weak-dissipation regime. Finally, boundary-adapted Chebyshev expansions represent 139 learned controls with a minimum common count of K_∗=24 coefficients per control for all eleven family-averaged mean squared errors to fall below 10^−6. Separately, square-pulse and Strang propagation at K=30 preserve all 31 continuous polynomial references within infidelity 10^−5 at N=128 and all larger tested resolutions, under both sampling rules. These results connect multi-state gate synthesis, control-resource characterization, and compact square-pulse playback.
ER -