Classical counterparts of shortcuts to adiabaticity in nonlinear dissipative Lagrangian systems

• URL: http://arxiv.org/abs/2604.18439v1
• Date: Mon, 20 Apr 2026 15:56:51 GMT
• Title: Classical counterparts of shortcuts to adiabaticity in nonlinear dissipative Lagrangian systems
• Abstract summary: We show how the same idea can be implemented in classical nonlinear dissipative Lagrangian systems.<n>Using a coupled $r$-$$ manipulator as an illustrative model, we perform inverse engineering on the Euler-Lagrange equations with Rayleigh dissipation.<n>We also compare smooth STA protocols with actuator-bounded time-optimal solutions and with proportional-integral-derivative tracking.
• Score: 3.479150231916641
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Shortcuts to adiabaticity (STA) were first developed in quantum dynamics to realize rapid transformations with suppressed residual excitations. Here we show how the same idea can be implemented in classical nonlinear dissipative Lagrangian systems. Using a coupled $r$-$θ$ manipulator as an illustrative model, we perform inverse engineering on the Euler-Lagrange equations with Rayleigh dissipation by prescribing endpoint-stationary trajectories, obtaining the corresponding force and torque profiles and quantifying how geometric coupling amplifies errors and residual energy. We further compare smooth STA protocols with actuator-bounded time-optimal solutions and with proportional-integral-derivative tracking, which highlights a trade-off among smoothness, speed, and robustness. Finally, we introduce a single-shot correction based on one mid-course measurement to reduce the effect of early deviations while keeping the inputs nearly smooth. These results provide a practical bridge between quantum STA concepts and their classical counterparts.

Related papers

• Universal Optimization and Tighter Fidelity Bounds for Approximate Quantum Error Correction [5.2107604548805915]
  Approximate quantum error correction (AQEC) dictates the performance of discrete- and continuous-variable quantum error correction codes.<n>Finding the optimal recovery channel to maximize entanglement fidelity via standard semidefinite programming is computationally bottlenecked by the exponentially growing number of Kraus operators.<n>We establish an efficient framework by leveraging the duality between recovery and environment decoupling.
  arXiv  Detail & Related papers  (2026-07-27T18:18:58Z)
• Stochastic Counterdiabatic Driving via Biorthogonal Liouvillian Eigenmodes [42.668742604089324]
  Escorted free energy simulations address the non-adiabatic lag by engineering control fields $mathbfu$ that eliminate the lag.<n>We construct a complementary numerical framework based on gauge-type transforms instead of generalized coordinate transforms.<n>We show that the counterdiabatic condition is satisfied to machine precision, with the non-adiabatic lag suppressed by roughly twelve orders of magnitude.
  arXiv  Detail & Related papers  (2026-07-27T13:08:14Z)
• Circuit Depth Reduction of One-Ancilla Quantum Differential Equation Solver via Extrapolation [1.0742675209112622]
  A recent one-ancilla quantum differential equation solver provides a hardware-friendly and locality-preserving approach.<n>We reduce the maximum single-run circuit depth to $O(mathrmpolylog (1/)$ without adding quantum ancillae or sacrificing locality.<n> Numerical experiments on the Hatano-Nelson model (ODE) and the convection-diffusion equation (PDE) demonstrate the effectiveness of the approach.
  arXiv  Detail & Related papers  (2026-07-08T13:20:43Z)
• Learned Lagrangian Models of PDEs via Euler-Lagrange Residual Minimization [6.069579199180933]
  We present the first method to directly use a learned continuous Lagrangian to forecast the dynamics of systems governed by partial differential equations.<n>We develop an optimization-based integrator that minimizes the squared Euler-Lagrange residual.<n>We validate our approach on a learned representation of a double pendulum, a one-dimensional wave equation, and a two-dimensional wave equation.
  arXiv  Detail & Related papers  (2026-05-08T02:43:11Z)
• Plug-and-Play Diffusion Meets ADMM: Dual-Variable Coupling for Robust Medical Image Reconstruction [45.25461515976432]
  Plug-and-Play diffusion prior (DP) frameworks have emerged as a powerful paradigm for imaging reconstruction.<n>We present a novel approach to resolving bias-hallucination trade-off, achieving state-of-the-art gradients with significantly accelerated convergence.
  arXiv  Detail & Related papers  (2026-02-26T16:58:43Z)
• Structure-Preserving Physics-Informed Neural Network for the Korteweg--de Vries (KdV) Equation [0.0]
  This paper introduces a emphstructure-preserving PINN framework for the nonlinear Korteweg--de Vries (KdV) equation.<n>The proposed method embeds the conservation of mass and Hamiltonian energy directly into the loss function.<n>We successfully reproduces hallmark behaviors of KdV dynamics while maintaining conserved invariants.
  arXiv  Detail & Related papers  (2025-11-01T06:07:24Z)
• PhysicsCorrect: A Training-Free Approach for Stable Neural PDE Simulations [4.7903561901859355]
  We present PhysicsCorrect, a training-free correction framework that enforces PDE consistency at each prediction step.<n>Our key innovation is an efficient caching strategy that precomputes the Jacobian and its pseudoinverse during an offline warm-up phase.<n>Across three representative PDE systems, PhysicsCorrect reduces prediction errors by up to 100x while adding negligible inference time.
  arXiv  Detail & Related papers  (2025-07-03T01:22:57Z)
• Quantum channel for modeling spin-motion dephasing in Rydberg chains [44.99833362998488]
  We introduce a quantum channel to model the dissipative dynamics resulting from the coupling between spin and motional degrees of freedom in chains of neutral atoms with Rydberg interactions.<n>We benchmark the accuracy of our approach against exact diagonalization for small systems, identifying its regime of validity and the onset of perturbative breakdown.<n>We then apply the quantum channel to compute fidelity loss during transport of single-spin excitations across extended Rydberg chains in intractable regimes via exact diagonalization.
  arXiv  Detail & Related papers  (2025-06-30T17:37:38Z)
• On Disentangled Training for Nonlinear Transform in Learned Image Compression [59.66885464492666]
  Learned image compression (LIC) has demonstrated superior rate-distortion (R-D) performance compared to traditional codecs.<n>Existing LIC methods overlook the slow convergence caused by compacting energy in learning nonlinear transforms.<n>We propose a linear auxiliary transform (AuxT) to disentangle energy compaction in training nonlinear transforms.
  arXiv  Detail & Related papers  (2025-01-23T15:32:06Z)
• An N-Point Linear Solver for Line and Motion Estimation with Event Cameras [45.67822962085412]
  Event cameras respond primarily to edges--formed by strong gradients--that are well-suited for motion estimation. Recent work has shown that events generated by single lines satisfy a novel constraint which describes a manifold in space-time volume. We show that, with suitable line parametrization, this system of constraints is actually linear in the unknowns.
  arXiv  Detail & Related papers  (2024-04-01T00:47:02Z)
• The Limiting Dynamics of SGD: Modified Loss, Phase Space Oscillations, and Anomalous Diffusion [29.489737359897312]
  We study the limiting dynamics of deep neural networks trained with gradient descent (SGD) We show that the key ingredient driving these dynamics is not the original training loss, but rather the combination of a modified loss, which implicitly regularizes the velocity and probability currents, which cause oscillations in phase space.
  arXiv  Detail & Related papers  (2021-07-19T20:18:57Z)
• Fast and differentiable simulation of driven quantum systems [58.720142291102135]
  We introduce a semi-analytic method based on the Dyson expansion that allows us to time-evolve driven quantum systems much faster than standard numerical methods. We show results of the optimization of a two-qubit gate using transmon qubits in the circuit QED architecture.
  arXiv  Detail & Related papers  (2020-12-16T21:43:38Z)
• Assessment of weak-coupling approximations on a driven two-level system under dissipation [58.720142291102135]
  We study a driven qubit through the numerically exact and non-perturbative method known as the Liouville-von equation with dissipation. We propose a metric that may be used in experiments to map the regime of validity of the Lindblad equation in predicting the steady state of the driven qubit.
  arXiv  Detail & Related papers  (2020-11-11T22:45:57Z)
• Fast Gravitational Approach for Rigid Point Set Registration with Ordinary Differential Equations [79.71184760864507]
  This article introduces a new physics-based method for rigid point set alignment called Fast Gravitational Approach (FGA) In FGA, the source and target point sets are interpreted as rigid particle swarms with masses interacting in a globally multiply-linked manner while moving in a simulated gravitational force field. We show that the new method class has characteristics not found in previous alignment methods.
  arXiv  Detail & Related papers  (2020-09-28T15:05:39Z)
• Dissipative Rabi model in the dispersive regime [0.0]
  We present results on the dispersive regime of the dissipative Rabi model without taking the rotating wave approximation of the underlying Hamiltonian. Results additionally predict new types of drive induced qubit dissipation and dephasing, not present in previous theories.
  arXiv  Detail & Related papers  (2020-04-06T09:45:24Z)
• Shortcuts to adiabaticity for an interacting Bose-Einstein condensate via exact solutions of the generalized Ermakov equation [3.8580539160777625]
  Shortcuts to adiabatic expansion of the effectively one-dimensional Bose-Einstein condensate (BEC) loaded in the harmonic-oscillator (HO) trap is investigated. Results are reported for the minimal transfer time, excitation energy, and stability for the shortcut-to-adiabaticity protocols.
  arXiv  Detail & Related papers  (2020-02-10T10:16:26Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.