Related papers: Unitary Dilations of Discrete-Time Quantum-Dynamic…
We analyze the asymptotic dynamics of quantum systems resulting from large numbers of iterations of random unitary operations. Although, in general, these quantum operations cannot be diagonalized it is shown that their resulting asymptotic…
Nielsen's geometric approach to quantum circuit complexity provides a Riemannian framework for quantifying the cost of implementing unitary (closed--system) dynamics. For open dynamics, however, the reduced evolution is described by quantum…
It is shown that discrete-time quantum walks can be used to digitize, i.e., to time discretize fermionic models of continuous-time lattice gauge theory. The resulting discrete-time dynamics is thus not only manifestly unitary, but also…
We consider the unitary time evolution of continuous quantum mechanical systems confined to a cavity in contact with a finite bath of variable size. Measures for Markovianity for such finite system-bath configurations are developed in terms…
It is established that both discrete and continuous semigroups of unital quantum channels are eventually mixed unitary. This result is novel even for the subclass of Schur maps and stands in sharp contrast to the resolution of the…
We investigate the possibility of dividing quantum channels into concatenations of other channels, thereby studying the semigroup structure of the set of completely-positive trace-preserving maps. We show the existence of 'indivisible'…
We consider the non-equilibrium behavior of a central spin system where the central spin is periodically reset to its ground state. The quantum mechanical evolution under this effectively dissipative dynamics is described by a discrete-time…
Quantum channels describe subsystem or open system evolution. Using the classical Koopman operator that evolves functions on phase space, 4 classical Koopman channels are identified that are analogs of the 4 possible quantum channels in a…
We use quantum diffusive trajectories to prove that the time evolution of two-qubit entanglement under spontaneous emission can be fully characterized by optimal continuous monitoring. We analytically determine this optimal unraveling and…
Consider a discrete-time quantum walk on the $N$-cycle subject to decoherence both on the coin and the position degrees of freedom. By examining the evolution of the density matrix of the system, we derive some new conclusions about the…
We present an experimental optical implementation of a parallel-in-time discrete model of quantum evolution, based on the entanglement between the quantum system and a finite dimensional quantum clock. The setup is based on a programmable…
We study quantum dynamics of many-qubit systems strongly coupled to a quantized electromagnetic cavity mode, in the presence of decoherence and dissipation for both fermions and cavity photons. The analytic solutions are derived for a broad…
I propose a version of quantum mechanics featuring a discrete and finite number of states that is plausibly a model of the real world. The model is based on standard unitary quantum theory of a closed system with a finite-dimensional…
Quantum simulation has primarily focused on unitary dynamics, while many physical and engineering systems can be modeled by linear ordinary differential equations whose generators include non-Hermitian terms. Recent studies have shown that…
Dual-unitary circuits are a class of locally-interacting quantum many-body systems displaying unitary dynamics also when the roles of space and time are exchanged. These systems have recently emerged as a remarkable framework where certain…
Quantum devices are subject to natural decay. We propose to study these decay processes as the Markovian evolution of quantum channels, which leads us to dynamical semigroups of superchannels. A superchannel is a linear map that maps…
We give a mathematical framework to describe the evolution of an open quantum systems subjected to finitely many interactions with classical apparatuses. The systems in question may be composed of distinct, spatially separated subsystems…
The engineering of new states of matter through Floquet driving has revolutionized the field of condensed matter physics. This technique enables the creation of hybrid topological states and ordered phases that are absent in normal systems.…
We consider the class of quantum stochastic evolutions ($SLH$-models) leading to a quantum dynamical semigroup over a fixed quantum mechanical system (taken to be finite-dimensional). We show that if the semigroup is dissipative, that is,…
We investigate the evolution dynamics of inhomogeneous discrete-time one-dimensional quantum walks displaying long-range correlations in both space and time. The associated quantum coin operators are built to exhibit a random inhomogeneity…