Related papers: Quantum filtering for systems driven by fermion fi…
This paper provides an introduction to quantum filtering theory. An introduction to quantum probability theory is given, focusing on the spectral theorem and the conditional expectation as a least squares estimate, and culminating in the…
In this thesis we study continuously observed open quantum systems from the point of view of quantum filtering theory. The conditioned state of the open system obeys a non-commutative or quantum analogue of the Kushner-Stratonovich equation…
Both in classical and quantum stochastic control theory a major role is played by the filtering equation, which recursively updates the information state of the system under observation. Unfortunately, the theory is plagued by…
Using Gardiner and Collet's input-output model and the concept of cascade system, we determine the filtering equation for a quantum system driven by chosen non-classical states of light. The quantum system and electromagnetic field are…
A comprehensive input-output theory is developed for Fermionic input fields. Quantum stochastic differential equations are developed in both the Ito and Stratonovich forms. The major technical issue is the development of a formalism which…
Quantum systems have an exponentially large degree of freedom in the number of particles and hence provide a rich dynamics that could not be simulated on conventional computers. Quantum reservoir computing is an approach to use such a…
Fermions are fundamental particles which obey seemingly bizarre quantum-mechanical principles, yet constitute all the ordinary matter that we inhabit. As such, their study is heavily motivated from both fundamental and practical incentives.…
Quantum cluster approaches offer new perspectives to study the complexities of macroscopic correlated fermion systems. These approaches can be understood as generalized mean-field theories. Quantum cluster approaches are non-perturbative…
The purpose of this paper is to determine quantum master and filter equations for systems coupled to fields in certain non-classical continuous-mode states. Specifically, we consider two types of field states (i) single photon states, and…
We stress the notion of statistical experiment, which is mandatory for quantum mechanics, and recall Ludwig's foundation of quantum mechanics, which provides the most general framework to deal with statistical experiments giving evidence…
Fuelled by increasing computer power and algorithmic advances, machine learning techniques have become powerful tools for finding patterns in data. Since quantum systems produce counter-intuitive patterns believed not to be efficiently…
A filtering problem for a class of quantum systems disturbed by a classical stochastic process is investigated in this paper. The classical disturbance process, which is assumed to be described by a linear stochastic differential equation,…
This review summarizes recent developments in the study of fermionic quantum criticality, focusing on new progress in numerical methodologies, especially quantum Monte Carlo methods, and insights that emerged from recently large-scale…
In this paper, the Pontryagin-type maximum principle for optimal control of quantum stochastic systems in fermion fields is obtained. These systems have gained significant prominence in numerous quantum applications ranging from physical…
In this paper, we derive the stochastic master equations for quantum systems driven by a single-photon input state which is contaminated by quantum vacuum noise. To improve estimation performance, quantum filters based on multiple-channel…
Quantum computers are expected to become a powerful tool for studying physical quantum systems. Consequently, a number of quantum algorithms for studying the physical properties of such systems have been developed. While qubit-based quantum…
We give a tutorial exposition of the analogue of the filtering equation for quantum systems focusing on the quantum probabilistic framework and developing the ideas from the classical theory. Quantum covariances and conditional expectations…
Machine learning algorithms learn a desired input-output relation from examples in order to interpret new inputs. This is important for tasks such as image and speech recognition or strategy optimisation, with growing applications in the IT…
Fluctuation Theorems are central in stochastic thermodynamics, as they allow for quantifying the irreversibility of single trajectories. Although they have been experimentally checked in the classical regime, a practical demonstration in…
The concurrent rise of artificial intelligence and quantum information poses opportunity for creating interdisciplinary technologies like quantum neural networks. Quantum reservoir processing, introduced here, is a platform for quantum…