Related papers: Formalized Quantum Stochastic Processes and Hidden…
The development of emerging technologies in quantum optics demands accurate models that faithfully capture genuine quantum effects. Mature semiclassical approaches reach their limits when confronted with quantized electromagnetic fields,…
Simulating quantum physical processes has been one of the major motivations for quantum information science. Quantum channels, which are completely positive and trace preserving processes, are the standard mathematical language to describe…
In this work, we extend the idea of Quantum Markov chains [S. Gudder. Quantum Markov chains. J. Math. Phys., 49(7), 2008] in order to propose Quantum Hidden Markov Models (QHMMs). For that, we use the notions of Transition Operation…
We study the number of measurements required for quantum process tomography under prior information, such as a promise that the unknown channel is unitary. We introduce the notion of an interactive observable and we show that any unitary…
We present a scalable method for learning local quantum channels using local expectation values measured on a single state -- their steady state. Our method is inspired by the algorithms for learning local Hamiltonians from their ground…
Stochastic models of biochemical reaction networks are widely used to capture intrinsic noise in cellular systems. The typical formulation of these models are based on Markov processes for which there is extensive research on efficient…
Avoided crossings (ACs) are hallmark signatures of mode interaction in quantum and wave systems. Open microcavities whose resonances are naturally described as quasi-normal modes (QNMs) with complex eigenfrequencies offer a convenient…
Quantum mechanical systems exhibit an inherently probabilistic nature upon measurement which excludes in principle the singular direct observability continual case. Quantum theory of time continuous measurements and quantum prediction…
This manuscript aims to illustrate a quantum-classical dissipative theory (suited to be converted to effective algorithms for numerical simulations) within the long-term project of studying molecular processes in the brain. Other…
We study dynamics and thermodynamics of ion channels, considered as effective 1D Coulomb systems. The long range nature of the inter-ion interactions comes about due to the dielectric constants mismatch between the water and lipids,…
Aggregated Markov models provide a flexible framework for stochastic dynamics that develops on multiple timescales. For example, Markov models for ion channels often consist of multiple open and closed state to account for "slow" and "fast"…
Stochastic gradient MCMC (SG-MCMC) algorithms have proven useful in scaling Bayesian inference to large datasets under an assumption of i.i.d data. We instead develop an SG-MCMC algorithm to learn the parameters of hidden Markov models…
We derive the classical Hamilton-Jacobi equation from first principles as the natural description for smooth stochastic processes when one neglects stochastic velocity fluctuations. The Schr\"{o}dinger equation is shown to be the natural…
Neuronal cells present periodic trains of localized voltage spikes involving a large amount of different ionic channels. A relevant question is whether this is a cooperative effect or it could also be an intrinsic property of individual…
Single neuron models have a long tradition in computational neuroscience. Detailed biophysical models such as the Hodgkin-Huxley model as well as simplified neuron models such as the class of integrate-and-fire models relate the input…
Stochastic transitions between discrete microscopic states play an important role in many physical and biological systems. Often, these transitions lead to fluctuations on a macroscopic scale. A classic example from neuroscience is the…
Logical hidden Markov models (LOHMMs) upgrade traditional hidden Markov models to deal with sequences of structured symbols in the form of logical atoms, rather than flat characters. This note formally introduces LOHMMs and presents…
A linear open quantum system consisting of a harmonic oscillator linearly coupled to an infinite set of independent harmonic oscillators is considered; these oscillators have a general spectral density function and are initially in a…
Any physical process can be represented as a quantum channel mapping an initial state to a final state. Hence it can be characterized from the point of view of communication theory, i.e., in terms of its ability to transfer information.…
We present a channel-constrained Markovian quantum diffusion (CCMQD) model that prepares quantum states by rigorously framing the generative process within the dynamics of open quantum systems. Our model interprets the forward diffusion…