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As Gaussian processes are used to answer increasingly complex questions, analytic solutions become scarcer and scarcer. Monte Carlo methods act as a convenient bridge for connecting intractable mathematical expressions with actionable…
Vecchia's approximate likelihood for Gaussian process parameters depends on how the observations are ordered, which can be viewed as a deficiency because the exact likelihood is permutation-invariant. This article takes the alternative…
A warping operator consists of an invertible axis deformation applied either in the signal domain or in the corresponding Fourier domain. Additionally, a warping transformation is usually required to preserve the signal energy, thus…
The time evolution operator plays a crucial role in the precise computation of chemical experiments on quantum computers and holds immense promise for advancing the fields of physical and computer sciences, with applications spanning…
In this work, we investigate a quasilinear subdiffusion model which involves a fractional derivative of order $\alpha \in (0,1)$ in time and a nonlinear diffusion coefficient. First, using smoothing properties of solution operators for…
The optimal properties for single photons may vary drastically between different quantum technologies. Along with central frequency conversion, control over photonic temporal waveforms will be paramount to the effective coupling of…
Variational autoencoders often assume isotropic Gaussian priors and mean-field posteriors, hence do not exploit structure in scenarios where we may expect similarity or consistency across latent variables. Gaussian process variational…
A quantum unitary gate is realized in this paper by perturbing a free charged particle in a one-dimensional box with a time- and position-varying electric field. The perturbed Hamiltonian is composed of a free particle Hamiltonian plus a…
Koopman operators and transfer operators represent nonlinear dynamics in state space through its induced action on linear spaces of observables and measures, respectively. This framework enables the use of linear operator theory for…
We report on recent work on adaptive timestep control for weakly instationary gas flows [16, 18, 17] carried out within SFB 401, TPA3. The method which we implement and extend is a space-time splitting of adjoint error representations for…
We provide time-evolution operators, gauge transformations and a perturbative treatment for non-Hermitian Hamiltonian systems, which are explicitly time-dependent. We determine various new equivalence pairs for Hermitian and non-Hermitian…
Time-space noncommutativity leads to quantisation of time and energy nonconservation when time is conjugate to a compact spatial direction like a circle. In this context energy is conserved only modulo some fixed unit. Such a possibility…
We formulate gaussian and circular random-matrix models representing a coupled system consisting of an absorbing and an amplifying resonator, which are mutually related by a generalized time-reversal symmetry. Motivated by optical…
We analyze quantum states formed as superpositions of an initial pure product state and its image under local unitary evolution, using two measurement-based measures of superposition size: one based on the optimal quantum binary…
A perturbative treatment of reduced density operators of quantum subsystems is implemented in the same spirit as Fermi Golden Rule for scattering. Analytic expressions for linear entropy (a measure of purity loss, and in some cases of…
Quantum signal processing (QSP) provides a systematic framework for implementing a polynomial transformation of a linear operator, and unifies nearly all known quantum algorithms. In parallel, recent works have developed randomized…
The time operator canonically conjugated to the Hamiltonian of $N$ interacting particles on the line is constructed using SU(1,1) as a dynamical symmetry. This hidden conformal symmetry enables us to make a group theoretic analysis of the…
Parity-time (PT) symmetric quantum theory can broaden the scope of quantum dynamics beyond unitary evolution which may lead to numerous counter-intuitive phenomena, including single-shot discrimination of non-orthogonal states, faster…
In this paper, we prove convergence for contractive time discretisation schemes for semi-linear stochastic evolution equations with irregular Lipschitz nonlinearities, initial values, and additive or multiplicative Gaussian noise on…
Quantum machine learning has shown promise for high-dimensional data analysis, yet many existing approaches rely on linear unitary operations and shared trainable parameters across outputs. These constraints limit expressivity and…