We consider ensembles of two level atoms interacting with the field in one mode resonator; such ensembles are homogeneous, if the force of interaction is the same for all atoms. We represent the results of numerical simulation of the following effects: relaxation of atomic excitation for one atom, dephasing assisted transport of energy along the chain of optical cavities (DAT), optical conductivity of a network of cavities, quantum bottleneck, thermal attractors for two atomic systems and ensemble Rabi oscillation for a hundred of atoms and dark states. The last effect required the supercomputer simulation on Lomonosov-2. DAT and quantum bottleneck play the peculiar role in biology (FMO light harvesting complex in green sulfur bacteria), dark states are significant for quantum computations. This elucidates the special role of dark states in such ensembles and the power of finite dimension models of QED, which allow inclusion of dipole-dipole interaction and nonlinearity that makes such models very powerful.
We propose quantum protection circuit (quantum lock), based on dark states of ensembles of two-level atoms in optical cavity. The secret key is the splitting of atoms into pairs, and publicly accessible part of the lock is the tensor product of EPR singlets, corresponding to the given splitting. To open the lock one must move synchronously pairs of atoms from the correct splitting to the other cavity; the lock will open if atoms do not emit photons. This scheme has perfect secrecy: it is impossible to hack it, even with effective solutions of any classical computational problems, in contrast to the RSA scheme. The method of obtaining dark states through Stark shift of atomic excitation energy is also proposed. This scheme makes possible to create secret keys of a few tens of atoms that is sufficient for the most practical applications.
We describe computer methods of simulation of Tavis-Cummings based quantum models, and apply those methods to specific tasks, conductivity measurements of atomic excitations in short chains of optical cavities with two-level atoms, C-Sign optical model, and dark states. For the conductivity measurements, we reproduce the dephasing assisted transport and quantum bottleneck effects and show their relation, and study the "which way?" problem. For the C-Sign optical model, we use the model to find optimal parameters of the system to minimize the error. For dark states, we study their collapse due to dephasing noise.
An ensemble of identical two level atoms in dark state neither adsorbs nor emits photons due to destructive interference. Dark states have numerous applications. It can be used for the source of energy for nano-devices; the space of dark states is decoherence free and can serve as the carrier for the fault tolerant quantum computations, etc. Since a dark state does not interact with the electromagnetic field it is an eigenstate of Tavis-Cummings Hamiltonian and the preparation of such states requires the exit from this model. We show how to prepare a dark state by the photon pumping and drain from the optical cavity with two atoms, one from which has Stark or Zeeman splitting of energy levels. This splitting is removed before photon drain from the cavity. The dark state yield after one such cycle has the order of energy level splitting. We show the scheme of the experiment, in which such cycles repeat until the dark state is produced with high probability and the results of its computer simulation. The structure of dark states is briefly discussed.
We consider qubit modification of Jaynes-Cummings-Hubbard model with phonon environment and relaxation for exciton transport in Fenna{Matthews{Olson light-harvesting complex. We establish the view of interference picture for the subspace spanned by states of W-type (one exciton), and more general form of exciting states. We find numerically the dependence of exciton conductivity from dephasing coefficients in the case when excitations are transmitted via photons.1
We describe an approach to quantum computer inspired by the information processing at the molecular level in living cells. It is based on the separation of a small ensemble of qubits inside the living system (e.g., a bacterial cell), such that coherent quantum states of this ensemble remain practically unchanged for a long time. We use the notion of a quantum kernel to describe such an ensemble. Quantum kernel is not strictly connected with certain particles; it permanently exchanges atoms and molecules with the environment, which makes quantum kernel a virtual notion. There are many reasons to expect that the state of quantum kernel of a living system can be treated as the stationary state of some Hamiltonian. While the quantum kernel is responsible for the stability of dynamics at the time scale of cellular life, at the longer inter-generation time scale it can change, varying smoothly in the course of biological evolution. To the first level of approximation, quantum kernel can be described in the framework of qubit modification of Jaynes-Cummings-Hubbard model, in which the relaxation corresponds to the exchange of matter between quantum kernel and the rest of the cell and is represented as Lindblad super-operators.
We give the universal scheme of quantum computations on ions of metals in Paul
traps and estimate the capacity of this computational model taking into account
the uncertainty conditions.
We represent the economy method of separation of the entangled states of GHZ and W types which arise
in the process of association of a single molecule. It makes possible to separate these types of quantum states
in the simulation of real processes like the association of molecular ion of hydrogen by means of existing
computers with the strictly limited memory. Numerical realization of this method is in process; we represent
the semiclassical part of it, that is based on Landau-Ziner description of the association of molecules. Results
of statistical processing of the row of numerical experiments are shown.
Algorithmic approach to quantum theory is considered. It is based on the supposition that every evolution of many particle system can be simulated by classical algorithms of polynomial complexity. This hypothesis agrees with all known experiments but it presumes the principle cut-off of quantum formalism because it excludes a scalable quantum computer. Algorithmic approach describes quantum evolution uniformly, without separation of measurements from the unitary dynamics; it is shown how Bohrn rule for quantum probability follows from the basic principles of this approach. The radical difference of algorithmic approach from the standard and its perspectives are discussed.
We study the problem of the most economical representation of entangled states in the classical simulations. The idea is to reduce the general form of entanglement to the bipartite entanglement which has the short representation through Schmidt expansion. The problem of such reduction is stated exactly and discussed. The example is given which shows that if we allow the linear transformation (not only unitary), the general form of entanglement cannot be described in terms of bipartite entanglement. We also study the entanglement dynamics of 2 and 3 level atoms interacting randomly and find interesting dependence of the number of its excited levels.
The method of collective behavior is based on the representation of real quantum particle by the swarm of classical particles which have all properties of the initial particle but have classical states like coordinates and impulse. Simulation with swarms can be more flexible and powerful than analytical methods because it preserves the methodology of classical description of dynamics. The method of collective behavior is illustrated on the diffusion Monte Carlo way of calculating stationary states of electrons.
Nowadays the task of molecular modeling plays the important role in many branches of science and engineering. But the existing models do not take quantum effects into account because of known calculating issues. The main difficulty in modeling of the evolution of multi particle quantum states by solving the Schroedinger equation consists iii exponential growth of required time and memory with the corresponding increase of entangled particles. The approach to this problem considered in works [3 4] consists in applying Feynman path integrals instead of solving Schroedinger equation. In terms of the "amplitude quanta" method based on this approach the wave function of a particle is calculated as a sum of the large amount of a.q. that probably will allow the linear growth of required memory with the corresponding increase of entangled particles. This approach also allows to the easy transition from the classical description of a particle to the quantum and back. The given work is devoted to the development of the quantum state evolution model based on the a. q. method in one and two-dimensional cases.
We study a realistic quantum computational model with the permanent interaction of diagonal type between qubits. Its universality was proven in quant-ph/0202030. We propose two types of control over computations: random and periodical NOTs. The slowdown of computations in comparison with the abstract model is estimated. It is shown how fermionic computations can be implemented in the framework of this model.
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