The widely used theoretical methods include MD **method** based on molecular mechanics (Huang et al., 2012) **quantum** **mechanical** **method** (Wang et al., 2012) and other high delity computational model based on rst principles (Ellabaan et al., 2012) The **method** used to study lipid bilayer systems usually is equilibrium MD **method** using atomistic (Heine et al., 2007) or coarse grain model (Yuan et al., 2009) This **method** depends largely on the **simulation** time and the initial conguration. The **simulation** time is limited to tens to hundreds of nanoseconds for most biological system, so equilibrium MD cannot be used to explore portions of the energy landscape separated by high barriers from the initial minimum (Hamelberg and McCammon, 2004). To overcome this defect of equilibrium MD, a number of approaches have been introduced: replica exchange, umbrella sampling, accelerated MD (aMD), and so on.

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In this research, we successfully apply the uncoupled winding number formulation of path integral Monte Carlo theory to the torsional degrees of freedom in the molecules ethane, n-butane, n-octane, and enkephalin. This torsional PIMC technique offers a significant reduction in computational cost for systems in which vibrational degrees of freedom may be safely neglected. Employment of the PIMC m ethod is simplified by the observation th a t contributions to calculated properties will be negligible for winding numbers greater than zero. For a simple ethane model potential, the PIMC result recovers the exact internal energy value obtained with a variational technique. For n-butane, n-octane, and enkephalin, the PIMC converged to the **quantum** me chanical limit with only two or three Trotter beads. All studied molecules exhibited significant **quantum** **mechanical** contributions to their internal energy expectation values according to the PIMC technique.

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As discussed earlier, the key difficulty in predicting the behavior of materials beginning from the full equations of **quantum** mechanics is the fiendishly complicated many-body wavefunction. In the Kohn-Sham **method** we skirt the many-body wavefunction and all of the difficulty it entails by making an audacious assumption. We assume that a system of non-interacting particles exists which gives the same ground state density as the fully interacting system of electrons present in our material. A priori, we have no reason to be confident that such a non-interacting system exists. Nevertheless, in practice, this assumption has proven successful beyond anyone’s reasonable expectation. The success of this approximation in practice may be gauged from the fact that the original paper by Kohn and Sham [87] laying out the **method** based on this assumption is the most cited Physical Review paper of all time [88]. It is even more amazing that the number of citations this paper receives has been growing every year for over forty years [88].

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Following a suggestion by Dr. Halpern, v/e view the Casimir problem (for the sphere) as one of **quantum** field theory. The fields considered are a quantized photon field and an external field (one whose values in all space-time points can be governed by macroscopic devices and is thus a given quantity) given in the local limit by the sphere. By such a consideration, one obtains an expression for the zero- point energy, which is of some interest as a source of

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In popular science, **quantum** mechanics is seen mainly as a source of non-intuitive, “spooky” phe- nomena that we can exploit to produce new technologies. Lasers, transistors, and scanning tunneling microscopes are all touted as applications of **quantum** mechanics. Superconductors are commonly found in MRI magnets and SQUID magnetometers, and have been used in maglev train prototypes. **Quantum** key distribution systems that use either **quantum** indeterminacy or entanglement to se- curely share keys between multiple parties are already available from several companies. **Quantum** computers, which rely on superposition and entanglement to perform calculations at faster speeds than their classical counterparts, are seen as the technology of the future.

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A characteristic point is that not only in classical physics, but also in **quantum** theory, we follow the scale of time of (1) and (2) which is typical for everyday life. According to this scale the events labelled by time do not repeat themselves. Our aim is, in the first step, to point out that an application of such scale in the **quantum** theory is not really justified. To this purpose a time analysis of the **quantum**-**mechanical** perturbation problem within the formalism introduced by Schrödinger will be carried out.

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junction between presynaptic and postsynaptic membranes, which is suggested as a source for generation of sustainable hyperexcitation of nerve ending (pain signal). Therefore, the activation of RNa + /Ca 2+ exchange-induced hydration of nerve ending and dehydration of endplate are suggested as a primary **quantum** **mechanical** sensitive mechanism generating pain signals. To check this suggestion, the comparative study of the effects of 40 Ca 2+ (cold) and 45 Ca 2+ (radioactive) containing physiological solution (PS) intraperitoneal injections on thermal pain thresholds and brain and heart tissues hydration as well as the 45 Ca 2+ uptake by these tissues in different experimental conductions were performed.

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subtle [26]. For simple analogy, in life’s perspective, we can consider chemistry (DNA, RNA and Proteins) and consciousness as these two aspects. Now the question is how the interplay between these two aspects takes place? We might consider this as Chalmers [37] calls the ‘hard problem of consciousness’ and information at the subtle level may help to understand the observed phenomena [26]. ‘Informare’- the Latin root for the word information, means to form, fashion, or bring a certain shape or order into something [38]. More simply, information is a difference that makes a difference [39]. Feynman suggested that all points in the space can process incoming information and outputting novel information just like a computer [40]. But living system differs from the **mechanical** systems as it compensates the ever increasing entropy by continually drawing negative entropy from its environment and prevents the state of maximum entropy to be alived [35]. If information arises from matter and energy, as regarded in reductionist approach, thermodynamics doesn’t support its harmonic interplay in a living non-equilibrium steady state. So information should have its definition outside the realm of matter and energy and obviously there is evidence in support of the proposition that information is non-material and helps to maintain the non-equilibrium steady state [41]. It is not possible to separate any informational aspect from causal relations of matter and energy if the effects of a system are completely derivable from the outside causes. Information is produced by a system when effects become system dependent that means when the system is self-organizing at any level [42]. And there has been several evidences claiming living system as an information processor [5]. Thus we can say that an autopoietic living system utilizes information to maintain the holarchy that simultaneously ranges from classical to **quantum** or physical to metaphysical paradigm. So we define living system as consciousness driven information processor which is autopoietic by nature. And no secular geometry at present can outline this complex hierarchy of, how an invisibly small egg grows into an entire human being?

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Our appeal to photon counting as a way of thinking about **quantum** jumps for the hitting problem raises another interesting question related to the use of measurements in **quantum** walks. This is related to our allusion to other unravellings made earlier in Sec. 1.1. In general, an unravelling is a specific decomposition of the master equation into stochastic trajectories such that the ensemble average of them recovers the dynamics of the master equation. Two classes of unravellings have special significance in **quantum** optics—the jump unravellings used in our paper, and the so-called diffusive unravellings—because they turn out to have concrete interpretations in terms of **quantum** optical measurements (as already seen with the jump unravellings in our work) [13]. Canonical examples of **quantum**-optical measurements that give rise to (or essentially realise) diffusive unravellings are the homodyne and heterodyne detection schemes [57, 58]. Since we are defining the graph of a continuous-time open **quantum** walk by a master equation, and we know that a master equation can be unravelled in different ways, one might wonder if another type of unravelling can be used to study a hitting problem. Given that diffusive unravellings form the second major class of unravellings in **quantum** optics we might then ask if they can be used for the hitting problem in this paper. The short answer is that there is not much motivation to do so because they are unhelpful for solving hitting problems with discrete-state **quantum** walks. To understand this we recall that in our **quantum**-jump approach we imagined the incoherent transitions in the graph gave off photons which were measured by photodetectors. Using a diffusive unravelling is equivalent to superimposing the stream of photons coming from an incoherent transition with a local-oscillator field (a laser in a coherent state) on a beam splitter before it is detected by the photodetector. In this case the photodetector actually measures a quadrature of the stream of photons determined by the phase of the local oscillator. A diffusive unravelling thus gives us information about a continuous variable that does not directly reveal to us if the walker has reached a prescribed state or not. To get around this one can then try to introduce the fidelity between ρ f (here taken to be a parameter) and the walker’s state to define when ρ f is reached

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Hafezi, a post-doc at JQI, we started to develop the theory for periodic arrays of optomechanical systems, to see if arrays of these structure could be made to act as a **quantum** memory, as atoms had roughly a decade ago. Darrick and Mohammed, who were from Misha Lukin’s group, and had been intimately involved in atom cloud theory and experiments, approached the problem form that view. I was more familiar with work in the integrated optics setting, and Coupled Resonator Optical Waveguide (CROW) work by Amnon Yariv’s group at Caltech. Interestingly, a complete picture required a synthesis of both approaches, which ended up being an excellent educational opportunity for me, thanks to Darrick’s caring a careful tutelage. We rapidly wrote a theory paper and presented it at several conferences, including the Gordon Research Conference in March 2010. Thiago and I began work on the experimental realization of EIT, if only as a way to make detection of **mechanical** modes in our snowflake devices easier.

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For the RPMD trajectories used to sample the FE profile, to diminish the sep- aration of timescales for the motion of the ring polymer and the rest of the system the mass of the ring polymer centroid is m =12 amu, and the masses of the har- monic internal modes of the ring polymer are scaled so each mode has a period of 8 fs. Changing these parameters does not a↵ect the ensemble of configurations that are sampled in the calculation of the FE profile; it merely allows for the sampling trajectories to be performed with a larger **simulation** time-step (0.001 ps) than would be possible using physical masses. Furthermore, the long-range electro- static contributions are updated every time-step, and we use twin-ranged cut-o↵s [25] in the FE sampling trajectories such that non-bonding interactions beyond 10 ˚ A are updated every 5 fs. Sampling trajectories are performed at constant temperature by resampling the particle velocities from the Maxwell-Boltzmann distribution every 1.3 ps.

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is automatically normalised and the average energy hφ( ~ θ)|H|φ( ~ θ)i can be obtained by measuring each term hφ( ~ θ)|h i |φ( θ)i ~ and linearly combining the measurement outcomes. In Sec. 6, we also introduce other possible ways of realising the trial states. To approximate the ground state, we can minimise hφ( ~ θ)|H|φ( ~ θ)i over the parameter space with a classical optimisation algorithm. For instance, by calculating the gradient of hφ( θ)|H|φ( ~ ~ θ)i, a local minimum of hφ( ~ θ)|H|φ( ~ θ)i can be found via the gradient descent algorithm. Such a hybrid algorithm for solving the eigenvalue of the Hamiltonian is called variational **quantum** eigensolver (VQE) [29–40]. Note that parameters can be complex for classical **simulation** but it suffices for them to be real for **quantum** **simulation**. This is because without loss of generality the trial state can be prepared by a **quantum** circuit by applying unitary gates R k (θ k )

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While randomization has allowed us to make some progress on the challenge of proving better bounds on the performance of product formulas, our strengthened bounds remain far from the apparent empirical performance. We expect that other ideas will be required to improve the product-formula approach [15, 28]. Although our bounds have better asymp- totic n-dependence than the previous commutator bound, they only offer an improvement if the system is sufficiently large. It could be fruitful to establish bounds for randomized product formulas that take advantage of the structure of the Hamiltonian, perhaps offer- ing better performance both asymptotically and for small system sizes. More generally, it may be of interest to investigate other scenarios in which random choices can be used to improve the analysis of **quantum** **simulation** [10, 14] and other **quantum** algorithms.

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the system PennyLane as a Python 3 software framework for optimization and machine learning of **quantum** and hybrid **quantum** / classical computations is introduced. A plugin system makes the framework compatible with any gate-based **quantum** simulator or hardware and provided plugins for Strawberry Fields, Rigetti Forest, Qiskit, and ProjectQ, allowing PennyLane optimizations to be run on publicly accessible **quantum** devices provided by Rigetti and IBM Q. On the classical front, PennyLane interfaces with accelerated machine learning libraries such as Ten- sorFlow, PyTorch, and auto grad. PennyLane can be used for the optimization of variational **quantum** eigensolvers, **quantum** approximate optimization, **quantum** machine learning models, and many other applications. The first industry-based and societal relevant applications will be as a **quantum** accelerator. It is based on the idea that any end-application contains multiple parts and the properties of these parts are better executed by a particular acceler- ator which can be either an FPGA, a GPU or a TPU. The **quantum** accelerator added as an additional coprocessor. The formal definition of an accelerator is indeed a co-pro- cessor linked to the central processor and that executes much faster certain parts of the overall application [7] .

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it could also be an operator that prepares a trial state with Givens rotations [33] or implements a unitary coupled-cluster operator [39]. In any case, we will expect there to be a large number of strings in H, so we would like to apply the gadgets [Fig. 2(c)] in parallel to keep the **simulation** shallow whenever possible. Let us coordinate the **simulation** of all those propagators by switching to layout diagrams like the one in Fig. 2(b), instead of using circuit diagrams like in Fig. 2(c). This gives us an idea of all the qubits involved and how they are coupled, but leaves out certain details about for instance the specific **simulation** algorithm. Our ability to parallelize the **simulation** is determined by the fermion-to-qubit mapping, in particular in the shape of the strings that it outputs. In regard of our connectivity setup [Fig. 2(c)], we consider a fermion- to-qubit mapping as good if it outputs Hamiltonians H with Pauli strings that are short, continuous, and nonoverlapping. We will now explain these criteria:

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The purpose of reduction of trochanteric fractures is to acquire the support of the anterior cortex at the fracture site on lateral view [10]. The classification of fracture alignments on lateral view is shown in Fig. 1 [11, 12]. Re- duction to a “positive” or “neutral” fracture alignment is necessary to acquire anterior cortical support. Reduction to the positive fracture alignment is ideal, as it provides sufficient support of the anterior femoral neck cortex. The most commonly encountered alignment is a reduction to the neutral fracture alignment, and it has been considered clinically acceptable, but postoperative displacement often occurs because of loss of anterior cortical support at the fracture site (i.e., displacement from the neutral fracture alignment to the negative fracture alignment). Several fac- tors have been suggested to cause this postoperative dis- placement, and fracture alignment with an angulation deformity at the fracture site on lateral view is reported to be one of the main causes of displacement [11] (Fig. 2). We have postulated that unusual loading at the fracture site leads to fracture collapse, subsequent postoperative displacement, and cut-out of the lag screw (i.e., protrusion of the lag screw from the femoral head) in some cases. Therefore, this study aimed to investigate local stress dis- tribution in models with an angulation deformity at the fracture site and to evaluate the risk factors for postopera- tive displacement using the finite element (FE) **method**.

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folded sandwich core materials—fold-core—can solve the problem of humidity accumulation by featuring an open cellular design which enables ventilation of the foldcore (Miura 1972; Miura 1975; Zakirov et al. 2005; Zakirov et al. 2006; Kolax 2004; Kehrle & Kolax 2006; Hachenberg et al. 2003). So, the foldcore is an interesting alternative sandwich core material to foam cores and honeycomb. To unlock the potential of **mechanical** properties and help designing the foldcore ’ s unit cell to specific needs, **simulation** methods have to be used. A modelling **method** which allows realistic **simulation** is presented in this paper.

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This paper is concerned with the development of a parallel algorithm on cluster of workstation with Parallel Virtual Machine (PVM) for solving the finite difference Navier-Stokes and energy equations. The numerical procedure is based on SIMPLE (Semi Implicit **Method** for Pressure Link Equations) developed by Spalding. The governing equations are transformed into finite difference forms using the control volume approach. The hybrid scheme which is a combination of the central difference and up wind scheme was used in obtaining a profile assumption for parameter variations between the grids points. The Domain Decomposition **Method** (DDM) was used to decompose the domain into a small domain and each of the domains was solved by different processors. The accuracy of the parallelization **method** was done by comparing with a benchmark solution of a standardized problem related to the two dimensional buoyancy flow in a square enclosure. The results are shown in the forms of contour maps of non-dimensional temperature and velocities.

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which may be due to the logical positivism (or, the tradition of Aristotle’s syllog- ism). However, as seen in Sections 3-6, Hempel’s raven paradox, Hume’s prob- lem of induction, Goodman’s grue paradox, Peirce’s abduction and flagpole problem are related to the concept of measurement (=inference), and thus, these problems cannot be adequately handled by logic alone. Thus, we think that logic is the language of mathematics, and not the language of science. Mathematical logic ( i . e ., the language of mathematics) should not be confused with usual logic. As seen throughout this paper, we believe that the representation using “logic” is rough in most cases. So-called logic plays an essential role in everyday conversa- tion (e.g., trial, business negotiations, politics, romance, etc.). On the other hand, science requires quantitative discussion, and thus, science may choose statistics (or, **quantum** language) rather than logic. It should be noted that

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