Related papers: Score Reversal Is Not Free for Quantum Diffusion M…
We address the characterization of classical fractional random noise via quantum probes. In particular, we focus on estimation and discrimination problems involving the fractal dimension of the trajectories of a system subject to fractional…
We present an optimal control-based strategy to enhance the estimation of impulse-like disturbances in continuously monitored linear classical and quantum systems by exploiting non-equilibrium states. Using optimal estimation techniques for…
Score-based generative models (SGMs) are powerful tools to sample from complex data distributions. Their underlying idea is to (i) run a forward process for time $T_1$ by adding noise to the data, (ii) estimate its score function, and (iii)…
Realistic multi-qubit noise processes often result in error mechanisms that are not captured by the probabilistic, Markovian error models commonly employed in circuit-level analyses of quantum fault-tolerance. By working within an…
Speech enhancement is a critical component of many user-oriented audio applications, yet current systems still suffer from distorted and unnatural outputs. While generative models have shown strong potential in speech synthesis, they are…
The inverse problem of backward diffusion is known to be ill-posed and highly unstable. Backward diffusion processes appear naturally in image enhancement and deblurring applications. It is therefore greatly desirable to establish a…
The true dynamical randomness is obtained as a natural fundamental property of deterministic quantum systems. It provides quantum chaos passing to the classical dynamical chaos under the ordinary semiclassical transition, which extends the…
It is well known that the problem of computing the feedback capacity of a stationary Gaussian channel can be recast as an infinite-dimensional optimization problem; moreover, necessary and sufficient conditions for the optimality of a…
An important issue in developing quantum technology is that quantum states are so sensitive to noise. We propose a protocol that introduces reverse dynamics, in order to precisely control quantum systems against noise described by the…
The covariance for clean data given a noisy observation is an important quantity in many training-free guided generation methods for diffusion models. Current methods require heavy test-time computation, altering the standard diffusion…
Quantum fluctuations, through quantum corrections, have the potential to lead to irreversibility in quantum field theory. We consider the virtual ``charge" distribution generated by quantum corrections in the leading log, short range…
We study the distribution of maxima (Extreme Value Statistics) for sequences of observables computed along orbits generated by random transformations. The underlying, deterministic, dynamical system can be regular or chaotic. In the former…
Dynamical decoupling as a quantum control strategy aims at suppressing quantum decoherence adopting the popular philosophy that the disorder in the unitary evolution of the open quantum system caused by environmental noises should be…
An ordinary differential equation perturbed by a null-recurrent diffusion will be considered in the case where the averaging type perturbation is strong only when a fast motion is close to the origin. The normal deviations of these…
Standard jump-diffusion models assume independence between jumps and diffusion components. We develop a multi-type jump-diffusion model where jump occurrence and magnitude depend on contemporaneous diffusion movements. Unlike previous…
In this paper, the optimal control for discrete-time systems driven by fractional noises is studied. A stochastic maximum principle is obtained by introducing a backward stochastic difference equation contains both fractional noises and the…
Diffusion models have attracted a lot of attention in recent years. These models view speech generation as a continuous-time process. For efficient training, this process is typically restricted to additive Gaussian noising, which is…
The dynamics of quantum phase transitions are inevitably accompanied by the formation of defects when crossing a quantum critical point. For a generic class of quantum critical systems, we solve the problem of minimizing the production of…
Dephasing decoherence induced by interaction of one qubit with a quantum bath can be simulated classically by random unitary evolution without the need for a bath and this random unitary evolution is equivalent to the quantum case. For a…
Stochastic maximum principle of nonlinear controlled forward-backward systems, where the set of strict (classical) controls need not be convex and the diffusion coefficient depends explicitly on the variable control, is an open problem…