48 research outputs found
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 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 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
specified by a generator . This algorithm requires only
single qubit and CNOT gates and approximates the channel up to chosen accuracy . 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