Related papers: General fixed points of quasi-local frustration-fr…
We investigate whether a generic multipartite pure state can be the unique asymptotic steady state of locality-constrained purely dissipative Markovian dynamics. In the simplest tripartite setting, we show that the problem is equivalent to…
We provide a solution to the problem of determining whether a target pure state can be asymptotically prepared using dissipative Markovian dynamics under fixed locality constraints. Beside recovering existing results for a large class of…
We characterize and construct time-independent Markovian dynamics that drive a finite-dimensional multipartite quantum system into a target (pure) entangled steady state, subject to physical locality constraints. In situations where the…
Open quantum systems evolving according to discrete-time dynamics are capable, unlike continuous-time counterparts, to converge to a stable equilibrium in finite time with zero error. We consider dissipative quantum circuits consisting of…
Preparation of pure states on networks of quantum systems by controlled dissipative dynamics offers important advantages with respect to circuit-based schemes. Unlike in continuous-time scenarios, when discrete-time dynamics are considered,…
Statistical mechanics assumes that a quantum many-body system at low temperature can be effectively described by its Gibbs state. However, many complex quantum systems exist only as metastable states of dissipative open system dynamics,…
We consider finite-dimensional Markovian open quantum systems, and characterize the extent to which time-independent Hamiltonian control may allow to stabilize a target quantum state or subspace and optimize the resulting convergence speed.…
We propose a general framework for investigating a large class of stabilization problems in Markovian quantum systems. Building on the notions of invariant and attractive quantum subsystem, we characterize attractive subspaces by exploring…
The unavoidable interaction of quantum systems with their environment usually results in the loss of desired quantum resources. Suitably chosen system Hamiltonians, however, can, to some extent, counteract such detrimental decay, giving…
We provide a systematic framework for constructing generic models of nonequilibrium quantum dynamics with a target stationary (mixed) state. Our framework identifies (almost) all combinations of Hamiltonian and dissipative dynamics that…
Statistical equilibrium configurations are important in the physics of macroscopic systems with a large number of constituent degrees of freedom. They are expected to be crucial also in discrete quantum gravity, where dynamical spacetime…
Based on recent work on the asymptotic behavior of controlled quantum Markovian dynamics, we show that any generic quantum state can be stabilized by devising constructively a simple Lindblad-GKS generator that can achieve global asymptotic…
We study the stability with respect to a broad class of perturbations of gapped ground state phases of quantum spin systems defined by frustration-free Hamiltonians. The core result of this work is a proof using the…
We prove stability of the spectral gap for gapped, frustration-free Hamiltonians under general, quasi-local perturbations. We present a necessary and sufficient condition for stability, which we call "Local Topological Quantum Order" and…
Steady-state manifolds of open quantum systems, such as decoherence-free subspaces and noiseless subsystems, are of great practical importance to the end of quantum information processing. Yet, it is a difficult problem to find steady-state…
Based on the environment induced semigroup approach to the quantum measurement process, we show that a certain class of these semigroups, referred to as contractive uniformly $k$-Lipschitzian semigroups, exhibit a fixed point property. With…
In this paper we study the semi-global (approximate) state feedback stabilization of an infinite dimensional quantum stochastic system towards a target state. A discrete-time Markov chain on an infinite-dimensional Hilbert space is used to…
The Markov property entails the conditional independence structure inherent in Gibbs distributions for general classical Hamiltonians, a feature that plays a crucial role in inference, mixing time analysis, and algorithm design. However,…
A broad range of quantum optimisation problems can be phrased as the question whether a specific system has a ground state at zero energy, i.e.\ whether its Hamiltonian is frustration free. Frustration-free Hamiltonians, in turn, play a…
In order to successfully explore quantum systems which are perturbations of simple models, it is essential to understand the complexity of perturbation bounds. We must ask ourselves: How quantum many-body systems can be artificially…