Related papers: Probability representation of quantum dynamics usi…
We study quantum maps displaying spectral statistics intermediate between Poisson and Wigner-Dyson. It is shown that they can be simulated on a quantum computer with a small number of gates, and efficiently yield information about fidelity…
We construct a large class of non-Markovian master equations that describe the dynamics of open quantum systems featuring strong memory effects, which relies on a quantum generalization of the concept of classical semi-Markov processes.…
Generalized quantum measurements play a crucial role in quantum mechanics, and symmetric informationally complete positive operator-valued measurements (SIC POVMs) provide a powerful and flexible framework for extracting information from…
By using path integrals, the stochastic process associated to the time evolution of the quantum probability density is formally rewritten in terms of a stochastic differential equation, given by Newton's equation of motion with an…
Random dynamics in isolated quantum systems is of practical use in quantum information and is of theoretical interest in fundamental physics. Despite a large number of theoretical studies, it has not been addressed how random dynamics can…
The tomographic probability distribution is used to decribe the kinetic equations for open quantum systems. Damped oscillator is studied. Purity parameter evolution for different damping regime is considered.
This paper presents a realistic, stochastic, and local model that reproduces nonrelativistic quantum mechanics (QM) results without using its mathematical formulation. The proposed model only uses integer-valued quantities and operations on…
Based on recently derived exact stochastic Liouville-von Neumann equations, several strategies for the efficient simulation of open quantum systems are developed and tested on the spin-boson model. The accuracy and efficiency of these…
The resources required to characterise the dynamics of engineered quantum systems-such as quantum computers and quantum sensors-grow exponentially with system size. Here we adapt techniques from compressive sensing to exponentially reduce…
Discrete stochastic processes (DSP) are instrumental for modelling the dynamics of probabilistic systems and have a wide spectrum of applications in science and engineering. DSPs are usually analyzed via Monte Carlo methods since the number…
We argue that the complex numbers are an irreducible object of quantum probability. This can be seen in the measurements of geometric phases that have no classical probabilistic analogue. Having complex phases as primitive ingredient…
The theory of open quantum systems lays the foundations for a substantial part of modern research in quantum science and engineering. Rooted in the dimensionality of their extended Hilbert spaces, the high computational complexity of…
We show how to efficiently generate pseudo-random states suitable for quantum information processing via cluster-state quantum computation. By reformulating pseudo-random algorithms in the cluster-state picture, we identify a strategy for…
Complex systems are embedded in our everyday experience. Stochastic modelling enables us to understand and predict the behaviour of such systems, cementing its utility across the quantitative sciences. Accurate models of highly…
We present quantum algorithms for sampling from non-logconcave probability distributions in the form of $\pi(x) \propto \exp(-\beta f(x))$. Here, $f$ can be written as a finite sum $f(x):= \frac{1}{N}\sum_{k=1}^N f_k(x)$. Our approach is…
Symmetric informationally complete positive operator-valued measurement (SIC-POVM) is one important class of quantum measurement which is crucial for various quantum information processing tasks. SIC-POVMs have the advantage of providing an…
We develop a fundamental framework for the quantum mechanics of stochastic systems (QMSS), showing that classical discrete stochastic processes emerge naturally as perturbations of the quantum harmonic oscillator (QHO). By constructing…
We demonstrate in this paper that the probabilities for sequential measurements have features very different from those of single-time measurements. First, they cannot be modelled by a classical stochastic process. Second, they are…
An exact and efficient new method to simulate dynamics in dissipative quantum systems is presented. A stochastic Liouville equation, deduced from Feynman and Vernon's path-integral expression of the reduced density matrix, is used to…
The continuous quantum measurement within the probability representation of quantum mechanics is discussed. The partial classical propagator of the symplectic tomogram associated to a particular measurement outcome is introduced, for which…