Akshunna Shaurya Dogra

There has been a wave of interest in applying machine learning to study dynamical systems. We present a Hamiltonian neural network that solves the differential equations that govern dynamical systems. This is an equation-driven machine learning method where the optimization process of the network depends solely on the predicted functions without using any ground truth data. The model learns solutions that satisfy, up to an arbitrarily small error, Hamilton's equations and, therefore, conserve the Hamiltonian invariants. The choice of an appropriate activation function drastically improves the predictability of the network. Moreover, an error analysis is derived and states that the numerical errors depend on the overall network performance. The Hamiltonian network is then employed to solve the equations for the nonlinear oscillator and the chaotic Hénon-Heiles dynamical system. In both systems, a symplectic Euler integrator requires two orders more evaluation points than the Hamiltonian network to achieve the same order of the numerical error in the predicted phase space trajectories.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Technologies that rely on quantum bits (qubits) require long coherence times and high-fidelity operations¹. Superconducting qubits are one of the leading platforms for achieving these objectives^2,3. However, the coherence of superconducting qubits is affected by the breaking of Cooper pairs of electrons^4,5,6. The experimentally observed density of the broken Cooper pairs, referred to as quasiparticles, is orders of magnitude higher than the value predicted at equilibrium by the Bardeen–Cooper–Schrieffer theory of superconductivity^7,8,9. Previous work^10,11,12 has shown that infrared photons considerably increase the quasiparticle density, yet even in the best-isolated systems, it remains much higher¹⁰ than expected, suggesting that another generation mechanism exists¹³. Here we provide evidence that ionizing radiation from environmental radioactive materials and cosmic rays contributes to this observed difference. The effect of ionizing radiation leads to an elevated quasiparticle density, which we predict would ultimately limit the coherence times of superconducting qubits of the type measured here to milliseconds. We further demonstrate that radiation shielding reduces the flux of ionizing radiation and thereby increases the energy-relaxation time. Albeit a small effect for today’s qubits, reducing or mitigating the impact of ionizing radiation will be critical for realizing fault-tolerant superconducting quantum computers.

In pipes and channels, the onset of turbulence is initially dominated by localized transients, which lead to sustained turbulence through their collective dynamics. In the present work, we study numerically the localized turbulence in pipe flow and elucidate a state space structure that gives rise to transient chaos. Starting from the basin boundary separating laminar and turbulent flow, we identify transverse homoclinic orbits, the presence of which necessitates a homoclinic tangle and chaos. A direct consequence of the homoclinic tangle is the fractal nature of the laminar-turbulent boundary, which was conjectured in various earlier studies. By mapping the transverse intersections between the stable and unstable manifold of a periodic orbit, we identify the gateways that promote an escape from turbulence.