We show how to fully characterize a quantum process in an open quantum system. We particularize the procedure to the case of a universal two-qubit gate in a quantum computer. We illustrate the method with a numerical simulation of a quantum gate in the ion trap quantum computer.PACS Nos. 03.65.Bz, 42.50.Lc, 42.50.Wm Recently there has been a growing interest in "quantum tomography", i.e. in the complete characterization of the state of a quantum system represented by a density operatorρ. Quantum tomography of an unknown quantum state (that can be repeatedly prepared) [1] consists of finding an appropriate sequence of measurements which allows one to determine the complete density operatorρ (for experimental implementations and theoretical schemes in quantum optics see [1]). In this letter we will show how to completely characterize a physical process in an open quantum system. More specifically, suppose that a given quantum dynamics E transforms input states ρ in into output states ρ out , i.e.with E a linear mapping. Our aim is to characterize the process E, given as a "black box", by a sequence of measurements in such a way that it is possible to predict what the output state will be for any input state.The particular problem that we will analyze after developing a general formalism is the characterization of the two-bit universal quantum gate for quantum computing [2]. A quantum computer consists of n two-level atoms with atomic states |0 i , |1 i (i = 1, . . . , n) representing the quantum bits (qubits). States of the quantum computer are n-atom entangled states in the product Hilbert space |ψ ∈ H = i ⊗H 2 (i) with H 2 (i) = {|0 i , |1 i }. Quantum computations correspond to physical processes |ψ out =Û|ψ in where a given input state is mapped to an output state by a unitary transformationÛ. This can be carried out as a sequence of elementary steps (quantum gates) involving operations on a few qubits. It has been shown that any computation can be decomposed into single-bit gates, and a universal two-bit gate which involves an entanglement operation on two qubits [2]. In reality, due to the presence of decoherence and experimental imperfections, these gates (and therefore any computation) will not be ideal. In present experiments related to quantum computing based on both laser cooled trapped ions [3] and atoms in cavities [4], the difficult part is the two-qubit gate, since it requires an interaction between the two two-level systems via an auxiliary system (phonons or photons) which leads to decoherence. In view of this fact, we wish to develop a procedure for characterizing a two-qubit gate, i.e. characterize a physical process E involving entanglement of two qubits 1 and 2 in the state space H 2 (1) ⊗ H 2 (2). Below we will show how to implement this using only product states as inputs, and single qubit measurements on the outputs (assuming that single bit preparations and operations can be performed reliably ). We avoid utilizing any interaction (entanglement) between the qubits which would be require...

We show how to design different couplings between a single ion trapped in a harmonic potential and an environment. The coupling is due to the absorption of a laser photon and subsequent spontaneous emission. The variation of the laser frequencies and intensities allows one to "engineer" the coupling and select the master equation describing the motion of the ion. [S0031-9007(96)01762-0]

Understanding the link between community composition and function is a major challenge in microbial population biology, with implications for the management of natural microbiomes and the design of synthetic consortia. Specifically, it is poorly understood whether community functions can be quantitatively predicted from traits of species in monoculture. Inspired by the study of complex genetic interactions, we have examined how the amylolytic rate of combinatorial assemblages of six starch-degrading soil bacteria depend on the separate functional contributions from each species and their interactions. Filtering our results through the theory of biochemical kinetics, we show that this simple function is additive in the absence of interactions among community members. For about half of the combinatorially assembled consortia, the amylolytic function is dominated by pairwise and higher-order interactions. For the other half, the function is additive despite the presence of strong competitive interactions. We explain the mechanistic basis of these findings and propose a quantitative framework that allows us to separate the effect of behavioral and population dynamics interactions. Our results suggest that the functional robustness of a consortium to pairwise and higher-order interactions critically affects our ability to predict and bottom-up engineer ecosystem function in complex communities.

It is now recognized that molecular circuits with positive feedback can induce two different gene expression states (bistability) under the very same cellular conditions. Whether, and how, cells make use of the coexistence of a larger number of stable states (multistability) is however largely unknown. Here, we first examine how autoregulation, a common attribute of genetic master regulators, facilitates multistability in two-component circuits. A systematic exploration of these modules' parameter space reveals two classes of molecular switches, involving transitions in bistable (progression switches) or multistable (decision switches) regimes. We demonstrate the potential of decision switches for multifaceted stimulus processing, including strength, duration, and flexible discrimination. These tasks enhance response specificity, help to store short-term memories of recent signaling events, stabilize transient gene expression, and enable stochastic fate commitment. The relevance of these circuits is further supported by biological data, because we find them in numerous developmental scenarios. Indeed, many of the presented information-processing features of decision switches could ultimately demonstrate a more flexible control of epigenetic differentiation.

Genetic oscillators based on the interaction of a small set of molecular components have been shown to be involved in the regulation of the cell cycle, the circadian rhythms, or the response of several signaling pathways. Uncovering the functional properties of such oscillators then becomes important for the understanding of these cellular processes and for the characterization of fundamental properties of more complex clocks. Here, we show how the dynamics of a minimal two-component oscillator is drastically affected by its genetic implementation. We consider a repressor and activator element combined in a simple logical motif. While activation is always exerted at the transcriptional level, repression is alternatively operating at the transcriptional (Design I) or post-translational (Design II) level. These designs display differences on basic oscillatory features and on their behavior with respect to molecular noise or entrainment by periodic signals. In particular, Design I induces oscillations with large activator amplitudes and arbitrarily small frequencies, and acts as an “integrator” of external stimuli, while Design II shows emergence of oscillations with finite, and less variable, frequencies and smaller amplitudes, and detects better frequency-encoded signals (“resonator”). Similar types of stimulus response are observed in neurons, and thus this work enables us to connect very different biological contexts. These dynamical principles are relevant for the characterization of the physiological roles of simple oscillator motifs, the understanding of core machineries of complex clocks, and the bio-engineering of synthetic oscillatory circuits.

Cell competition is a short-range cell-cell interaction leading to the proliferation of winner cells at the expense of losers, although either cell type shows normal growth in homotypic environments. Drosophila Myc (dMyc; Dm -FlyBase) is a potent inducer of cell competition in wing epithelia, but its role in the ovary germline stem cell niche is unknown. Here, we show that germline stem cells (GSCs) with relative lower levels of dMyc are replaced by GSCs with higher levels of dMyc. By contrast, dMyc-overexpressing GSCs outcompete wild-type stem cells without affecting total stem cell numbers. We also provide evidence for a naturally occurring cell competition border formed by high dMyc-expressing stem cells and low dMyc-expressing progeny, which may facilitate the concentration of the niche-provided self-renewal factor BMP/Dpp in metabolically active high dMyc stem cells. Genetic manipulations that impose uniform dMyc levels across the germline produce an extended Dpp signaling domain and cause uncoordinated differentiation events. We propose that dMyc-induced competition plays a dual role in regulating optimal stem cell pools and sharp differentiation boundaries, but is potentially harmful in the case of emerging dmyc duplications that facilitate niche occupancy by pre-cancerous stem cells. Moreover, competitive interactions among stem cells may be relevant for the successful application of stem cell therapies in humans.

The interaction of a trapped ion with a laser beam in the strong excitation regime is analyzed. In this regime, a variety of non-classical states of motion can be prepared either by using laser pulses of well defined area, or by an adiabatic passage scheme based on the variation of the laser frequency. We show how these states can be used to investigate fundamental properties of quantum mechanics. We also study possible applications of this system to build an ion interferometer.

Background: Why do some groups of physically linked genes stay linked over long evolutionary periods? Although several factors are associated with the formation of gene clusters in eukaryotic genomes, the particular contribution of each feature to clustering maintenance remains unclear.