Related papers: Markovian Matrix Product Density Operators : Effic…
The von Neumann entropy of various quantum dissipative models is calculated in order to discuss the entanglement properties of these systems. First, integrable quantum dissipative models are discussed, i.e., the quantum Brownian motion and…
An analytical expression for the von Neumann entropy of the Laughlin wave function is obtained for any possible bipartition between the particles described by this wave function, for filling fraction nu=1. Also, for filling fraction nu=1/m,…
The relation between entanglement entropy and the computational difficulty of classically simulating Quantum Mechanics is briefly reviewed. Matrix product states are proven to provide an efficient representation of one-dimensional quantum…
The expression for the density operator of the damped harmonic oscillator is derived from the master equation in the framework of the Lindblad theory for open quantum systems. Then the von Neumann entropy and effective temperature of the…
The inverse problem of 'eigenstates-to-Hamiltonian' is considered for an open chain of $N$ quantum spins in the context of Many-Body-Localization. We first construct the simplest basis of the Hilbert space made of $2^N$ orthonormal…
We present a quantum algorithm for simulating a family of Markovian master equations that can be realized through a probabilistic application of unitary channels and state preparation. Our approach employs a second-order product formula for…
While general quantum many-body systems require exponential resources to be simulated on a classical computer, systems of non-interacting fermions can be simulated exactly using polynomially scaling resources. Such systems may be of…
An exact canonical master equation of the Lindblad form is derived for a central spin interacting uniformly with a sea of completely unpolarized spins. The Kraus operators for the dynamical map are also derived. The non-Markovianity of the…
We present and discuss a general density-matrix description of energy-dissipation and decoherence phenomena in open quantum systems, able to overcome the intrinsic limitations of the conventional Markov approximation. In particular, the…
We discuss fundamental features of the local expression for the entropy production rate of the nonequilibrium quantum dynamics of open systems and its relations to memory effects and the spectrum of the generator of the dynamics. Defining…
Hybrid quantum-classical algorithms are among the most promising systems to implement quantum computing under the Noisy-Intermediate Scale Quantum (NISQ) technology. In this paper, at first, we investigate a quantum dynamics algorithm for…
The evolution of entanglement entropy in quantum circuits composed of Haar-random gates and projective measurements shows versatile behavior, with connections to phase transitions and complexity theory. We reformulate the problem in terms…
We show that the von Neumann's algorithm of reduction (i.e. the algorithm of calculating the density matrix of the observable subsystem from the density matrix of the closed quantum system) corresponds to the special approximation at which…
We develop a general approach for monitoring and controlling evolution of open quantum systems. In contrast to the master equations describing time evolution of density operators, here, we formulate a dynamical equation for the evolution of…
We study a quantum process that can be considered as a quantum analogue for the classical Markov process. We specifically construct a version of these processes for free Fermions. For such free Fermionic processes we calculate the entropy…
A direct numerical algorithm for solving the time-nonlocal non-Markovian master equation in the second Born approximation is introduced and the range of utility of this approximation, and of the Markov approximation, is analyzed for the…
We study the conditions under which Matrix Product States (MPS) or Matrix Product Operators are exact eigenvectors of an extensive local operator, such as a Hamiltonian. By suitably choosing the local operator, this covers a wide range of…
We derive a rigorous, quantum mechanical map of fermionic creation and annihilation operators to continuous Cartesian variables that exactly reproduces the matrix structure of the many-fermion problem. We show how our scheme can be used to…
For a quantum state undergoing unitary Schr\"odinger time evolution, the von Neumann entropy is constant. Yet the second law of thermodynamics, and our experience, show that entropy increases with time. Ingarden introduced the quantum…
The problem of simulating the thermal behavior of quantum systems remains a central open challenge in quantum computing. Unlike well-established quantum algorithms for unitary dynamics, \emph{provably efficient} algorithms for preparing…