Time evolution of nonlinear dynamics on a quantum processor

• URL: http://arxiv.org/abs/2608.13041v1
• Date: Thu, 13 Aug 2026 10:07:19 GMT
• Title: Time evolution of nonlinear dynamics on a quantum processor
• Abstract summary: We experimentally realize the time evolution of nonlinear fluid dynamics on a quantum processor.<n>Our results constitute to our knowledge the first experimental realization of nonlinear time propagation on a quantum processor.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: From fluid flow and transport to collective dynamics, numerical simulation of nonlinear partial differential equations underpins modern scientific computing. Extending this capability to quantum computers remains a longstanding challenge because nonlinear and non-Hermitian evolution is fundamentally incompatible with conventional Hamiltonian-based quantum simulation. Here we experimentally realize the time evolution of nonlinear fluid dynamics on a quantum processor using a hybrid variational framework for the viscous and inviscid Burgers equations. Our approach directly encodes the nonlinear dynamics into a variational optimization procedure, avoiding the enlarged linear embeddings and truncation overhead associated with Carleman linearization-based quantum algorithms. We further demonstrate convection-dominated dynamics corresponding to Reynolds numbers of order $10^2$. We encode the governing evolution into parametrized quantum circuits and iteratively reconstruct the time-dependent field through quantum-classical optimization. By introducing a zero-noise extrapolation method without additional circuit-folding overhead, we accurately execute deep error-circuits with entangling-gate counts beyond those typical of Hadamard test circuits. We accurately reconstruct the time evolution across multiple timesteps despite hardware noise and finite device coherence. Our results constitute, to our knowledge, the first experimental realization of nonlinear time propagation on a quantum processor, extending quantum simulation beyond predominantly linear settings and establishing a route toward quantum computation for nonlinear continuum dynamics.

Related papers

• Quantum simulation of real-world nonlinear dynamics via Koopman method [8.214716873336412]
  We propose the quantum Koopman method, a data-driven framework that embeds nonlinear dynamics into a learned linear representation.<n>This method learns Koopman observables from trajectory data, projects the lifted dynamics onto a finite-dimensional subspace, and decomposes the corresponding non-unitary propagator into parallel spectral channels.<n>We utilize the Koopman method on a superconducting processor to simulate three distinct nonlinear systems.
  arXiv  Detail & Related papers  (2026-07-08T12:27:12Z)
• Quantum-Accelerated Solution of Nonlinear Equations from Variational Principles [0.0]
  We introduce a novel algorithm tailored for fault-tolerant quantum computers (FTQCs)<n>Our approach recasts the static nonlinear problem as a time-evolution process, enabling an effective linearization amenable to quantum acceleration.<n>This work paves the way toward leveraging fault-tolerant quantum computing for complex nonlinear systems across physics and engineering disciplines.
  arXiv  Detail & Related papers  (2025-08-25T02:19:17Z)
• A time-marching quantum algorithm for simulation of the nonlinear Lorenz dynamics [0.0]
  We develop a quantum algorithm that implements the time evolution of a second order time-discretized version of the Lorenz model.<n> Notably, we showcase that it accurately captures the structural characteristics of the Lorenz system.
  arXiv  Detail & Related papers  (2025-06-26T15:08:00Z)
• Simulating Time Dependent and Nonlinear Classical Oscillators through Nonlinear Schrödingerization [0.5729426778193399]
  We present quantum algorithms for simulating the dynamics of a broad class of classical oscillator systems.<n>Our work extends the applicability of quantum algorithms to simulate the dynamics of non-conservative and nonlinear classical systems.
  arXiv  Detail & Related papers  (2025-05-22T17:48:42Z)
• Enhanced quantum frequency estimation by nonlinear scrambling [41.94295877935867]
  We show that dynamically encoding an unknown frequency in a nonlinear quantum electromagnetic field can significantly improve frequency estimation.<n>We quantify this effect using the Wigner-Yanase skew information, which measures the degree of noncommutativity in the Hamiltonian structure.
  arXiv  Detail & Related papers  (2025-03-03T19:00:01Z)
• Quantum lattice Boltzmann method for simulating nonlinear fluid dynamics [12.270811823319576]
  We introduce a novel ensemble description of lattice gas for simulating nonlinear fluid dynamics on a quantum computer.<n>We propose a quantum lattice Boltzmann method that relies on linear operations with medium dimensionality.
  arXiv  Detail & Related papers  (2025-02-23T13:25:35Z)
• Nonlinear dynamics as a ground-state solution on quantum computers [39.58317527488534]
  We present variational quantum algorithms (VQAs) that encode both space and time in qubit registers. The spacetime encoding enables us to obtain the entire time evolution from a single ground-state computation.
  arXiv  Detail & Related papers  (2024-03-25T14:06:18Z)
• Ab-initio variational wave functions for the time-dependent many-electron Schrödinger equation [41.94295877935867]
  We introduce a variational approach for fermionic time-dependent wave functions, surpassing mean-field approximations. We use time-dependent Jastrow factors and backflow transformations, which are enhanced through neural networks parameterizations. The results showcase the ability of our variational approach to accurately capture the time evolution, providing insight into the quantum dynamics of interacting electronic systems.
  arXiv  Detail & Related papers  (2024-03-12T09:37:22Z)
• Simulating the Mott transition on a noisy digital quantum computer via Cartan-based fast-forwarding circuits [62.73367618671969]
  Dynamical mean-field theory (DMFT) maps the local Green's function of the Hubbard model to that of the Anderson impurity model. Quantum and hybrid quantum-classical algorithms have been proposed to efficiently solve impurity models. This work presents the first computation of the Mott phase transition using noisy digital quantum hardware.
  arXiv  Detail & Related papers  (2021-12-10T17:32:15Z)
• Quantum algorithms for quantum dynamics: A performance study on the spin-boson model [68.8204255655161]
  Quantum algorithms for quantum dynamics simulations are traditionally based on implementing a Trotter-approximation of the time-evolution operator. variational quantum algorithms have become an indispensable alternative, enabling small-scale simulations on present-day hardware. We show that, despite providing a clear reduction of quantum gate cost, the variational method in its current implementation is unlikely to lead to a quantum advantage.
  arXiv  Detail & Related papers  (2021-08-09T18:00:05Z)
• Designing Kerr Interactions for Quantum Information Processing via Counterrotating Terms of Asymmetric Josephson-Junction Loops [68.8204255655161]
  static cavity nonlinearities typically limit the performance of bosonic quantum error-correcting codes. Treating the nonlinearity as a perturbation, we derive effective Hamiltonians using the Schrieffer-Wolff transformation. Results show that a cubic interaction allows to increase the effective rates of both linear and nonlinear operations.
  arXiv  Detail & Related papers  (2021-07-14T15:11:05Z)
• Variational Quantum Optimization with Multi-Basis Encodings [62.72309460291971]
  We introduce a new variational quantum algorithm that benefits from two innovations: multi-basis graph complexity and nonlinear activation functions. Our results in increased optimization performance, two increase in effective landscapes and a reduction in measurement progress.
  arXiv  Detail & Related papers  (2021-06-24T20:16:02Z)
• Fixed Depth Hamiltonian Simulation via Cartan Decomposition [59.20417091220753]
  We present a constructive algorithm for generating quantum circuits with time-independent depth. We highlight our algorithm for special classes of models, including Anderson localization in one dimensional transverse field XY model. In addition to providing exact circuits for a broad set of spin and fermionic models, our algorithm provides broad analytic and numerical insight into optimal Hamiltonian simulations.
  arXiv  Detail & Related papers  (2021-04-01T19:06:00Z)

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.