Open Quantum Walks: a short introduction

The concept of open quantum walks (OQW), quantum walks exclusively driven by the interaction with the external environment, is reviewed. OQWs are formulated as discrete completely positive maps on graphs. The basic properties of OQWs are summarised and new examples of OQWs on $\mathbb{Z}$ and their simulation by means of quantum trajectories are presented.Comment: 10 pages, 5 figures; contribution to 6th International Workshop DICE2012, 17-21 September 2012, Castiglioncello (Tuscany), Ital

The quest for a Quantum Neural Network

With the overwhelming success in the field of quantum information in the last decades, the "quest" for a Quantum Neural Network (QNN) model began in order to combine quantum computing with the striking properties of neural computing. This article presents a systematic approach to QNN research, which so far consists of a conglomeration of ideas and proposals. It outlines the challenge of combining the nonlinear, dissipative dynamics of neural computing and the linear, unitary dynamics of quantum computing. It establishes requirements for a meaningful QNN and reviews existing literature against these requirements. It is found that none of the proposals for a potential QNN model fully exploits both the advantages of quantum physics and computing in neural networks. An outlook on possible ways forward is given, emphasizing the idea of Open Quantum Neural Networks based on dissipative quantum computing.Comment: Review of Quantum Neural Networks research; 21 pages, 5 figs, 71 Ref

Open Quantum Walks on Graphs

Open quantum walks (OQW) are formulated as quantum Markov chains on graphs. It is shown that OQWs are a very useful tool for the formulation of dissipative quantum computing algorithms and for dissipative quantum state preparation. In particular, single qubit gates and the CNOT-gate are implemented as OQWs on fully connected graphs. Also, dissipative quantum state preparation of arbitrary single qubit states and of all two-qubit Bell-states is demonstrated. Finally, the discrete time version of dissipative quantum computing is shown to be more efficient if formulated in the language of OQWs.Comment: 13 pages, 5 figure

Dynamics and non-equilibrium steady state in a system of coupled harmonic oscillators

A system of two coupled oscillators, each of them coupled to an independent reservoir, is analysed. The analytical solution of the non-rotating wave master equation is obtained in the high-temperature and weak coupling limits. No thermal entanglement is found in the high-temperature limit. In the weak coupling limit the system converges to an entangled non-equilibrium steady state. A critical temperature for the appearance of quantum correlations is found.Comment: 25 pages, 8 figure

Initial correlation in a system of a spin coupled to a spin bath through an intermediate spin

The strong system-bath correlation is a typical initial condition in many condensed matter and some quantum optical systems. Here, the dynamics of a spin interacting with a spin bath through an intermediate spin are studied. Initial correlations between the spin and the intermediate spin are taken into account. The exact analytical expression for the evolution operator of the spin is found. Furthermore, correlated projection superoperator techniques are applied to the model and a time-convolutionless master equation to second order is derived. It is shown that the time-convolutionless master equation to second order reproduces the exact dynamics for time-scales of the order 1/{\gamma}, where {\gamma} is the coupling of the central spin to the intermediate spin. It is found that there is a strong dependence on the initial system-bath correlations in the dynamics of the reduced system, which cannot be neglected.Comment: 10 pages, 9 figures. arXiv admin note: text overlap with arXiv:0708.0410 by other author

Dissipative preparation of large W states in Optical Cavities

Two novel schemes are proposed for the dissipative preparation of large W states, of the order of ten qubits, within the context of Cavity QED. By utilizing properties of the irreducible representations of su(3), we are able to construct protocols in which it is possible to restrict the open system dynamics to a fully symmetric irreducible subspace of the total Hilbert space, and hence obtain analytic solutions for effective ground state dynamics of arbitrary sized ensembles of $\Lambda$ atoms within an optical cavity. In the proposed schemes, the natural decay processes of spontaneous emission and photon loss are no longer undesirable, but essential to the required dynamics. All aspects of the proposed schemes relevant to implementation in currently available optical cavities are explored, especially with respect to increasing system size.Comment: 21 page, 14 figures

Nonequilibrium thermal entanglement for simple qubit systems

The dynamics of simple qubit systems in a chain configuration coupled at both ends to separate bosonic baths at different temperatures is studied. An exact analytical solution of the master equation in the Born-Markov approximation for the reduced density matrix of the qubit system is constructed. The unique non-equilibrium stationary state for the long time behavior of the reduced density matrix in obtained. Dynamical and steady state properties of the concurrence between the first and the last spin are studied.Comment: Proceedings of Quantum optics V conference, Cozumel, Mexico (2010

Simulation of single-qubit open quantum systems

A quantum algorithm is presented for the simulation of arbitrary Markovian dynamics of a qubit, described by a semigroup of single qubit quantum channels $\{T_t\}$ specified by a generator $\mathcal{L}$. This algorithm requires only $\mathcal{O}\big((||\mathcal{L}||_{(1\rightarrow 1)} t)^{3/2}/\epsilon^{1/2} \big)$ single qubit and CNOT gates and approximates the channel $T_t = e^{t\mathcal{L}}$ up to chosen accuracy $\epsilon$. Inspired by developments in Hamiltonian simulation, a decomposition and recombination technique is utilised which allows for the exploitation of recently developed methods for the approximation of arbitrary single-qubit channels. In particular, as a result of these methods the algorithm requires only a single ancilla qubit, the minimal possible dilation for a non-unitary single-qubit quantum channel.Comment: Revised version. Restricted recombination method to first order Suzuki-Lie-Trotter integrators, and added discussion concerning issues with application of higher order integrators within the open quantum systems settin

Nonequilibrium thermal entanglement for three-spin chain

The dynamics of a chain of three spins coupled at both ends to separate bosonic baths at different temperatures is studied. An exact analytical so- lution of the master equation in the Born-Markov approximation for the reduced density matrix of the chain is constructed. It is shown that for long times the reduced density matrix converges to the non-equilibrium steady- state. Dynamical and steady state properties of the concurrence between the first and the last spin are studied.Comment: 19 pages, 4 figure

Energetic and entropic effects of bath-induced coherences

The unavoidable interaction of a quantum system with its surrounding (bath) is not always detrimental for quantum properties. For instance, under some specific conditions (that we identify as indistinguishability), a many-body system can gain internal coherences thanks to the interaction with its bath. The most famous consequence of this phenomenon is superradiance. Beyond that, the thermodynamic effects on the system of these bath-induced coherences have been mostly unexplored. We show here, for a simple and common system (a pair of two-level systems), that the energetic and entropic impacts can indeed be dramatic and diverse, including amplification of the action of the bath but also its mitigation. Our results can be tested experimentally. They suggest that bath-induced coherences can be harnessed to enhance thermodynamic tasks, opening up interesting perspectives for thermal machines, quantum battery charging, natural or artificial energy harvesting systems, and state preparation and protection.Comment: 9 pages of main text, 5 pages of appendix, 9 figure