A quantum mechanical model of adaptive mutation

The principle that mutations occur randomly with respect to the direction of evolutionary change has been challenged by the phenomenon of adaptive mutations. There is currently no entirely satisfactory theory to account for how a cell can selectively mutate certain genes in response to environmental signals. However, spontaneous mutations are initiated by quantum events such as the shift of a single proton (hydrogen atom) from one site to an adjacent one. We consider here the wave function describing the quantum state of the genome as being in a coherent linear superposition of states describing both the shifted and unshifted protons. Quantum coherence will be destroyed by the process of decoherence in which the quantum state of the genome becomes correlated (entangled) with its surroundings. Using a very simple model we estimate the decoherence times for protons within DNA and demonstrate that quantum coherence may be maintained for biological time-scales. Interaction of the coherent genome wave function with environments containing utilisable substrate will induce rapid decoherence and thereby destroy the superposition of mutant and non-mutant states. We show that this accelerated rate of decoherence may significantly increase the rate of production of the mutated state.     

Nanofabrication of Gate-defined GaAs/AlGaAs Lateral Quantum Dots

A quantum computer is a computer composed of quantum bits (qubits) that takes advantage of quantum effects, such as superposition of states and entanglement, to solve certain problems exponentially faster than with the best known algorithms on a classical computer. Gate-defined lateral quantum dots on GaAs/AlGaAs are one of many avenues explored for the implementation of a qubit. When properly fabricated, such a device is able to trap a small number of electrons in a certain region of space. The spin states of these electrons can then be used to implement the logical 0 and 1 of the quantum bit. Given the nanometer scale of these quantum dots, cleanroom facilities offering specialized equipment- such as scanning electron microscopes and e-beam evaporators- are required for their fabrication. Great care must be taken throughout the fabrication process to maintain cleanliness of the sample surface and to avoid damaging the fragile gates of the structure. This paper presents the detailed fabrication protocol of gate-defined lateral quantum dots from the wafer to a working device. Characterization methods and representative results are also briefly discussed. Although this paper concentrates on double quantum dots, the fabrication process remains the same for single or triple dots or even arrays of quantum dots. Moreover, the protocol can be adapted to fabricate lateral quantum dots on other substrates, such as Si/SiGe.     

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

Engineering non-classical states of the electromagnetic field is a central quest for quantum optics^1,2. Beyond their fundamental significance, such states are indeed the resources for implementing various protocols, ranging from enhanced metrology to quantum communication and computing. A variety of devices can be used to generate non-classical states, such as single emitters, light-matter interfaces or non-linear systems³. We focus here on the use of a continuous-wave optical parametric oscillator^3,4. This system is based on a non-linear χ² crystal inserted inside an optical cavity and it is now well-known as a very efficient source of non-classical light, such as single-mode or two-mode squeezed vacuum depending on the crystal phase matching. Squeezed vacuum is a Gaussian state as its quadrature distributions follow a Gaussian statistics. However, it has been shown that number of protocols require non-Gaussian states⁵. Generating directly such states is a difficult task and would require strong χ³ non-linearities. Another procedure, probabilistic but heralded, consists in using a measurement-induced non-linearity via a conditional preparation technique operated on Gaussian states. Here, we detail this generation protocol for two non-Gaussian states, the single-photon state and a superposition of coherent states, using two differently phase-matched parametric oscillators as primary resources. This technique enables achievement of a high fidelity with the targeted state and generation of the state in a well-controlled spatiotemporal mode.     

Probing quantum coherence in a biological system by means of DNA amplification

As a result of rapid decoherence, quantum effects in biological systems are usually confined to single electron or hydrogen delocalizations. In principle, molecular interactions at high temperatures can be guided by quantum coherence if embedded in a dynamics preventing decoherence. This was experimentally investigated by analyzing the thermodynamics, kinetics, and quantum mechanics of the primer/template duplex formation during DNA amplification by polymerase chain reaction. The structures of the two oligonucleotide primers used for amplification of a cDNA template were derived either from a repetitive motif or a fractal distribution of nucleotide residues. Contrary to the computer-based calculation of the primer melting temperatures (T(m)) that predicted a higher T(m) for the non-fractal primer due to nearest-neighbor effects, it was found that the T(m) of the non-fractal primer was actually 2 degrees C lower than that of its fractal counterpart. A thermodynamic analysis of the amplification reaction indicated that the primer annealing process followed Bose-Einstein instead of Boltzmann statistics, with an additional binding potential of mu=500 J/mol or 10(-21) J/molecule due to a superposition of binding states within the primer/template duplex. The temporal evolution of the Bose-Einstein state was determined by enzyme kinetic analysis of the association of the primer/template duplex to Taq polymerase. Assuming that collision with the enzyme interrupted the superposition, it was found that the Bose-Einstein state lasted for t(dec)=0.7x10(-12) s, corresponding to the energy dispersion (DeltaE) of quantum coherent states (mu=DeltaE>/=h/t(dec)). A quantum mechanical analysis revealed that the coherent state was stabilized by almost vanishing separation energies between distinct binding states during a temperature-driven shifting of the two DNA strands in the primer/template duplex. The additional binding potential is suggested to arise from a short-lived electron tunneling as the result of overlapping orbitals along the axis of the primer/template duplex. This effect was unique to the fractal primer due to the number of binding states that remained almost constant, irrespective of the size of shifting. It is suggested that fractal structures found in proteins or other macromolecules may facilitate a short-lived quantum coherent superposition of binding states. This may stabilize molecular complexes for rapid sorting of correct-from-false binding, e.g. during folding or association of macromolecules. The experimental model described in this paper provides a low-cost tool for simulating and probing quantum coherence in a biological system.     

A precise error bound for quantum phase estimation

Quantum phase estimation is one of the key algorithms in the field of quantum computing, but up until now, only approximate expressions have been derived for the probability of error. We revisit these derivations, and find that by ensuring symmetry in the error definitions, an exact formula can be found. This new approach may also have value in solving other related problems in quantum computing, where an expected error is calculated. Expressions for two special cases of the formula are also developed, in the limit as the number of qubits in the quantum computer approaches infinity and in the limit as the extra added qubits to improve reliability goes to infinity. It is found that this formula is useful in validating computer simulations of the phase estimation procedure and in avoiding the overestimation of the number of qubits required in order to achieve a given reliability. This formula thus brings improved precision in the design of quantum computers.     

A quantum model of exaptation: Incorporating potentiality into evolutionary theory

The phenomenon of preadaptation, or exaptation (wherein a trait that originally evolved to solve one problem is co-opted to solve a new problem) presents a formidable challenge to efforts to describe biological phenomena using a classical (Kolmogorovian) mathematical framework. We develop a quantum framework for exaptation with examples from both biological and cultural evolution. The state of a trait is written as a linear superposition of a set of basis states, or possible forms the trait could evolve into, in a complex Hilbert space. These basis states are represented by mutually orthogonal unit vectors, each weighted by an amplitude term. The choice of possible forms (basis states) depends on the adaptive function of interest (e.g., ability to metabolize lactose or thermoregulate), which plays the role of the observable. Observables are represented by self-adjoint operators on the Hilbert space. The possible forms (basis states) corresponding to this adaptive function (observable) are called eigenstates. The framework incorporates key features of exaptation: potentiality, contextuality, nonseparability, and emergence of new features. However, since it requires that one enumerate all possible contexts, its predictive value is limited, consistent with the assertion that there exists no biological equivalent to “laws of motion” by which we can predict the evolution of the biosphere.     

Quantum Iterative Deepening with an Application to the Halting Problem

Classical models of computation traditionally resort to halting schemes in order to enquire about the state of a computation. In such schemes, a computational process is responsible for signaling an end of a calculation by setting a halt bit, which needs to be systematically checked by an observer. The capacity of quantum computational models to operate on a superposition of states requires an alternative approach. From a quantum perspective, any measurement of an equivalent halt qubit would have the potential to inherently interfere with the computation by provoking a random collapse amongst the states. This issue is exacerbated by undecidable problems such as the Entscheidungsproblem which require universal computational models, e.g. the classical Turing machine, to be able to proceed indefinitely. In this work we present an alternative view of quantum computation based on production system theory in conjunction with Grover''s amplitude amplification scheme that allows for (1) a detection of halt states without interfering with the final result of a computation; (2) the possibility of non-terminating computation and (3) an inherent speedup to occur during computations susceptible of parallelization. We discuss how such a strategy can be employed in order to simulate classical Turing machines.     

Message operators: A new expression of the information

Starting from the synaptic model proposed in a previous paper (Teodorescu, 1976b), based on the idea that, in certain condition, information may be expressed in terms of the constraints in an optimization problem, the concept of an active message is defined. This is a message conveying a certain purpose, which is able to transform an initial orderly state in a new one, subject to some constraints, by choosing the optimal way. Some examples are given to show that active messages play an important role, not only in organisms, but also in communications between individuals and/or groups in social populations. The concept of a message operator, as a mathematical expression of the active message is, then, defined. It is shown that such an operator is, in fact, a pair, having as components a certain transformation and the associate optimization problem involving some information in constraints-form. The transformation is a relationship between the joint moment hypercube, expressing the initial multivariate random process (initial orderly state), and the final orderly state expressed by the joint density hypercube. By solving the optimization problem, the optimized density hypercube (i.e. the new orderly state) is obtained. An example is given to illustrate the procedure. It follows that message operators are able to express, in mathematical form, the transition from a given orderly state (say, a biological population in a quasi-chaotic state) into a new orderly state, with a different degree of orderliness. In such a transition involving three stages i.e. initial orderly state-message-final orderly state, the information is expressed, respectively, in terms of: probabilities-constraints-probabilities. Thus, Shanon's measure of information applies only in the states, since message operators have nothing to do with probabilities. To investigate the particular manner where information is involved in the constraints of the optimization problem, some main properties of the message operators are emphasized and illustrated by an example. Thus, it is shown that message operators are powerfull tools, permitting to investigate some unknown aspects of the information. This leads to a deeper understanding of the communication problems in biological systems as well as to various applications in biology.     

Effect of alternating G loads on the activities of a human operator wearing a protective helmet

Specific types of operator activity make it necessary to wear a helmet protecting the head against various physical factors. Wearing a heavy helmet for a long time may affect the quality of operator activity when the operator is exposed to alternating G loads. Studies have been performed using a dynamic model of a vehicle subjected to considerable alternating G loads. Crash test dummies have been used to test a system protecting the cervical region of the spinal column. The effects of accelerations, vibrations, and the time of wearing helmets with different weights on the functional state and operator performance have been studied. Data on the effects of helmet weight on some physiological, psychological, and biomechanical reactions of human operators are reported. Some relationships have been found that have practical implications for the functional improvement of the operator component of vehicle operation.     

Dispersion population models discrete in time and continuous in space

We analyze a discrete-time model of populations that grow and disperse in separate phases. The growth phase is a nonlinear process that allows for the effects of local crowding. The dispersion phase is a linear process that distributes the population throughout its spatial habitat. Our study quantifies the issues of survival and extinction, the existence and stability of nontrivial steady states, and the comparison of various dispersion strategies. Our results show that all of these issues are tied to the global nature of various model parameters. The extreme strategies of staying-in place and going-everywhere-uniformly are compared numerically to diffusion strategies in various contexts. We approach the mathematical analysis of our model from a functional analysis and an operator theory point of view. We use recent results from the theory of positive operators in Banach lattices.     

Indispensable role of quantum theory in the brain dynamics

Recently, Tegmark pointed out that the superposition of ion states involved in the superposition of firing and resting states of a neuron quickly decohere. It undoubtedly indicates that neural networks cannot work as quantum computers, or computers taking advantage of coherent states. Does it also mean that the brain can be modeled as a neural network obeying classical physics? Here we show that it does not mean that the brain can be modeled as a neural network obeying classical physics. A brand new perspective in research of neural networks from quantum theoretical aspect is presented.     

Derivation of a Floquet Formalism within a Natural Framework

Many biological systems experience a periodic environment. Floquet theory is a mathematical tool to deal with such time periodic systems. It is not often applied in biology, because linkage between the mathematics and the biology is not available. To create this linkage, we derive the Floquet theory for natural systems. We construct a framework, where the rotation of the Earth is causing the periodicity. Within this framework the angular momentum operator is introduced to describe the Earth’s rotation. The Fourier operators and the Fourier states are defined to link the rotation to the biological system. Using these operators, the biological system can be transformed into a rotating frame in which the environment becomes static. In this rotating frame the Floquet solution can be derived. Two examples demonstrate how to apply this natural framework.     

Quantum Entanglement and Spin Control in Silicon Nanocrystal

Selective coherence control and electrically mediated exchange coupling of single electron spin between triplet and singlet states using numerically derived optimal control of proton pulses is demonstrated. We obtained spatial confinement below size of the Bohr radius for proton spin chain FWHM. Precise manipulation of individual spins and polarization of electron spin states are analyzed via proton induced emission and controlled population of energy shells in pure ²⁹Si nanocrystal. Entangled quantum states of channeled proton trajectories are mapped in transverse and angular phase space of ²⁹Si axial channel alignment in order to avoid transversal excitations. Proton density and proton energy as impact parameter functions are characterized in single particle density matrix via discretization of diagonal and nearest off-diagonal elements. We combined high field and low densities (1 MeV/92 nm) to create inseparable quantum state by superimposing the hyperpolarizationed proton spin chain with electron spin of ²⁹Si. Quantum discretization of density of states (DOS) was performed by the Monte Carlo simulation method using numerical solutions of proton equations of motion. Distribution of gaussian coherent states is obtained by continuous modulation of individual spin phase and amplitude. Obtained results allow precise engineering and faithful mapping of spin states. This would provide the effective quantum key distribution (QKD) and transmission of quantum information over remote distances between quantum memory centers for scalable quantum communication network. Furthermore, obtained results give insights in application of channeled protons subatomic microscopy as a complete versatile scanning-probe system capable of both quantum engineering of charged particle states and characterization of quantum states below diffraction limit linear and in-depth resolution.PACS numbers: 03.65.Ud, 03.67.Bg, 61.85.+p, 67.30.hj     

Dynamics of Epidemiological Models

We study the SIS and SIRI epidemic models discussing different approaches to compute the thresholds that determine the appearance of an epidemic disease. The stochastic SIS model is a well known mathematical model, studied in several contexts. Here, we present recursively derivations of the dynamic equations for all the moments and we derive the stationary states of the state variables using the moment closure method. We observe that the steady states give a good approximation of the quasi-stationary states of the SIS model. We present the relation between the SIS stochastic model and the contact process introducing creation and annihilation operators. For the spatial stochastic epidemic reinfection model SIRI, where susceptibles S can become infected I, then recover and remain only partial immune against reinfection R, we present the phase transition lines using the mean field and the pair approximation for the moments. We use a scaling argument that allow us to determine analytically an explicit formula for the phase transition lines in pair approximation.     

生物光子发射的半经典理论

生物光子发射（ＰＥ）方法是揭示生命活动的一种非损伤方法。由于机理不清,仅获有限的认同。根据Ｄｉｃｋｅ近似,顾樵曾经提出ＰＥ的全量子理论。然而,Ｄｉｃｋｅ近似不适合生物系统。本文在不引入Ｄｉｃｋｅ近似的前提下,利用量子化学和半径典辐射理论研究了ＰＥ的全同粒子模型。结果表明,全同粒子会成相干态,其中超辐射态的光子发射几率是粒子数的平方和三次方的线性函数。本文结论成功地解了细胞分裂和细胞癌变等生命活动的ＰＥ现象和外界因素对ＰＥ现象的影响。     

Temporal coding: the relevance of classical activity, its relation to pattern frequency bands, and a remark on recoding of excitatory drive into phase shifts

We consider an oscillatory network model that is obtained as complex-valued generalization of the classical Cohen-Grossberg-Hopfield (CGH) model. Apart from a synchronizing mechanism, a stronger and/or more coherent input to a unit in the network implies a higher phase velocity of this unit. This constitutes the desynchronizing mechanism, referred to as acceleration. The units' activity of the classical model translates into the amplitudes of the phase model oscillators. This allows to associate classical and temporal coding with amplitude and phase dynamics, respectively. We discuss how the two dynamics act together to achieve the unambiguous pattern recognition that avoids the superposition problem. With respect to coherence, dominating patterns may take coherent states also if only a subset of its units is on-state. The competition for coherence, introduced by acceleration, realizes a kind of feature counting that identifies the dominating pattern as the pattern with the most on-state units. This dominating but possibly only partially active pattern may take a coherent state with a frequency level that is related to the number of on-state units. We also speculate on neurophysiological findings, related to observed phase differences between optimally and suboptimally activated neurons, that may indicate the presence of acceleration.     

DNA supercoiling promotes formation of a bent repression loop in lac DNA

Titration experiments on supercoiled lac DNA show that one repressor tetramer can bind simultaneously to the primary lac operator and to the very weak lac pseudo-operator, located 93 base-pairs apart. The formation of this complex is accompanied by the appearance of an extreme hypersensitive site in a five base-pair sequence located approximately midway between the operators. This remote sequence is hypersensitive to attack by two different chemical probes, dimethyl sulfate and potassium permanganate, the latter of which is a new probe for distorted DNA. We interpret these results in terms of a complex in which lac repressor holds two remote operators together in a DNA loop. The formation of this bent DNA loop requires negative DNA supercoiling. In vivo, both lac operators bind repressor even though the presence of multiple operator copies has forced the two operators to compete for a limited amount of repressor. This suggests that the operator and pseudo-operator have similar affinities for repressor in vivo. Such similar affinities were observed in vitro only when DNA supercoiling forced formation of a repression loop.     

Long-lived charge-separated states in bacterial reaction centers isolated from Rhodobacter sphaeroides

We studied the accumulation of long-lived charge-separated states in reaction centers isolated from Rhodobacter sphaeroides, using continuous illumination, or trains of single-turnover flashes. We found that under both conditions a long-lived state was produced with a quantum yield of about 1%. This long-lived species resembles the normal P(+)Q(-) state in all respects, but has a lifetime of several minutes. Under continuous illumination the long-lived state can be accumulated, leading to close to full conversion of the reaction centers into this state. The lifetime of this accumulated state varies from a few minutes up to more than 20 min, and depends on the illumination history. Surprisingly, the lifetime and quantum yield do not depend on the presence of the secondary quinone, Q(B). Under oxygen-free conditions the accumulation was reversible, no changes in the normal recombination times were observed due to the intense illumination. The long-lived state is responsible for most of the dark adaptation and hysteresis effects observed in room temperature experiments. A simple method for quinone extraction and reconstitution was developed.