The first Movement Day Australia was held in Sydney on 1st-2nd May 2018. Roger and Stephen Sutton were there sharing our UK stories and learning some new ones.
One of the biggest learning points for me was the focus of pain in the city. Taking time to ask do you feel the pain of your city? There were such heart wrenching stories told of the pain felt by children, women and the poor across the cities.
Another brilliant example of God's kingdom was the number of great stories where businesses and churches are working together. In West Sydney a group of businesses have funded a Hub where 40 local churches are able to run and share administration, training and meetings. This is a wonderful resource and expression of unity.
Movement Day Australia gathered city leaders from across the nation in Sydney for 2 days. The people gathered came from every Church tradition under the sun, but all of them had the conviction that Jesus' Church was there to serve a Kingdom vision of the transformation of their cities.
We heard story after story of how the Church has been coming together in relational unity and starting to strategically impact their places. We had our hearts powerfully tuned into the brokenness and pain of our cities through some powerful testimonies and we were led to a place where we wept with Jesus over the city.
After hearing this, we knew that we cannot afford to have a Church that is internally focused. The world can't afford it. The world needs a church that is sent, released, equipped and empowered out to the people and power structures of our cities. Then and only then will we see the true power of the scattered Church.


text:
\section{Introduction}
Quantum computation (QC) has been proposed already in the early 80's when Paul Benioff introduced a quantum Turing machine \cite{benioff1980}, Feynman the universal quantum simulator \cite{feynman1982} and David Deutsch a universal circuit quantum computer \cite{deutsch1985}. In the past years its technical implementation made immense progress partly driven by huge tech companies like Google and IBM. Most recently, strong claims have been put forward that quantum machines have solved sample problems not accessible to the best classical computers to date \cite{dowling2002}.
\par
As full scale programmable quantum computers are technically extremely challenging to implement, many current efforts are devoted to adiabatic quantum simulation. Here one aims to prepare the ground state of a many-body Hamiltonian, which encodes the solution to a classical optimization problem in tailored interactions\cite{das2005}. In a typical approach one starts from the ground state of a simple initial many body Hamiltonian and evolves this state to the desired ground state via a slow ramp up of the particle interactions towards the target Hamiltonian.

Notably, one of the earliest work in laying the foundation of quantum annealing, was done in 1989 \cite{ray1989}, showing that quantum fluctuations can increase the ergodicity in a spin-glass model, by tunneling between "trapping" minima, separated by narrow potential barriers. The idea of using tailored interactions of a many-body Hamiltonian, originally suggested as quantum stochastic optimization~\cite{apolloni1989}, was later renamed quantum annealing (QA) \cite{apolloni1990}. Nearly a decade later, in 1998, the present form of QA was introduced by considering adjustable quantum fluctuation instead of thermal ones \cite{kadowaki1998}. This basic idea, of integrating an artificial kinetic term, introducing quantum fluctuations in a controlled way, still remains a powerful tool and also provides the principal technique for our work.
The theoretical foundation for this kind of adiabatic evolution is given by the adiabatic theorem \cite{born1928} which states, that the systems stays in its ground state, if the Hamiltonian is changed slowly on the time scale set by the energy gap from the ground to excited states.
\par
The QA protocol promises practically useful results even for small scale quantum simulators with less than a hundred q-bits. Experimental examples are trapped-ion simulators \cite{britton2012}, superconducting qubits \cite{bunyk2014} or ultra cold atoms in optical lattices \cite{jotzu2014}. A commercially available superconducting quantum annealer was launched already in 2011 by D-Wave \cite{johnson2011} and is continuously enlarged and improved. However, it is still highly debated, if quantum annealing devices offer an actual speedup over classical devices\cite{hauke2020}. In several cases, optimizing algorithms on classical computers lead to a comparable or even better performance than the quantum machine at current size and speed\cite{heim2015}. Interestingly, in several cases quantum inspired algorithms\cite{arrazola2019}, i.e. the efficient numerical solution of the Schrödinger equation, proved to be the fastest available classical computer based method to solve the problem.
\par
Let introduce here some central early papers and reviews on this subject. With a main focus on quantum annealing and analog quantum computation the review by Das et al. in 2008 \cite{das2008} gives an introduction to the initial progress of the subject matter and a clear picture of the fundamental physical properties and mechanisms of QA. Further, a more recent review by Hauke et al. in 2020 \cite{hauke2020} focuses more on the present state of QA and new pathways and possibilities in theory and experiment. Finally, the review from Albash et al. in 2018 \cite{albash2018a} gives a more comprehensive perspective on quantum adiabatic computation in general, its theoretical development, algorithms and computational complexity.
\par
A generic example to study a possible advantage of quantum annealing versus classical computation was put forward in a recent proposal for a quantum annealer using ultra-cold atoms in an optical lattice within a cavity\cite{torggler2017}. Here the cavity modes mediate controllable all to all interactions between the atoms in the lattice. As key example an implementation of the quantum annealing process is predicted to generate solutions of the N-queens completion problem\cite{letavec2002,torggler2019}, which is known to be NP-complete \cite{gent2017}. Interestingly one finds that for the optimal quantum implementation of the problem one only needs a linear increase in resources (Q-bits and lasers) with problem size. Thus the record size classical solution of N=23 found so far\cite{das2005} seems well in reach of current optical lattice experiments. Numerically, corresponding solutions of the time dependent Schrödinger equation are hardly possible for more than 8 q-bits. Unfortunately the precise system size scaling of the minimal gap of the corresponding Hamiltonian could neither be analytically calculated nor numerically reliably estimated. Hence the confirmation of a corresponding quantum advantage is left to experiment.

Nevertheless the numerical studies of the above model reveal some interesting properties, which indirectly could shed some extra light on the beneficial role of quantum mechanics in the annealing process. Implementing different approximate numerical models to simulate the time-dependent numerical annealing dynamics, one finds, that the most reliable algorithm to find the ground with high probability required a full quantum description of the cavity field dynamics and the atomic motion. A so-called semi-classical mean-field approach, where the cavity fields are approximated by coherent fields failed to find the correct solution with a useful probability. As solutions for nontrivial problem sizes (i.e. chess board sizes N$>$8)  are numerically very complex, the detailed physical origin behind this form of a quantum improvement could not be studied in detail.

Note that here the notion of quantum improvement or advantage appears in a bit unusual and more literal sense. We simply tie it to the observation that a full quantum description of the cavity fields in the numerical annealing simulation yields a significantly higher probability to end up in the desired final ground state than using a classical description of the light modes. Note that the classical field dynamics is numerically much simpler to implement and thus, in principle, the solution can be computed faster. This could compensate the lower success probability for a single run but for our line of argumentation towards a quantum improvement we compare success probabilities for equal simulation times.
\par
The idea of this work here is to take one step back and devise a related, but sufficiently simplified toy model to unravel the origin of this special sort of quantum advantage or improvement. The challenge here is to allow for enough model complexity to clearly see the improved performance of a full quantum treatment but still keep the model numerically tractable and conceptually clear enough to analyze the underlying dynamics in sufficient detail.

As we will exhibit below, the study of self-ordering in a finite one-dimensional optical lattice with long range interactions mediated by two independent cavity modes satisfies both requirements. When we add a small defect in the lattice, the semi-classical approach largely fails to find the correct ground state for a wide and well defined range of parameters, whereas the full quantum dynamics still reliably arrives at the correct solution. Note that finding the ground state in a system with very small disorder also is a complex problem for larger instances\cite{dagotto2005complexity}. Hence we now have found a suitable test ground to study the physical origin and conditions for the superior performance of a quantum simulator, which in much more complex configurations could be the central ingredient to obtain a quantum advantage.
\par
This work is organized as follows.  In section \ref{sec:model} we present our quantum gas cavity QED Bose-Hubbard (BH) Hamiltonian\cite{mekhov2012} and shortly review the basic concepts of quantum annealing based on the the adiabatic approximation. In the next chapter \ref{sec:analysis quantum} we study the conditions and parameters needed for successful quantum annealing and the role of entanglement in this process. This is followed by a comparison of the quantum dynamics to the semi-classical mean-field description \ref{sec:semi-class}. In a final chapter we present the somewhat surprising and counter-intuitive dependence of the optimization efficiency on the numerical photon cut-off, where sometimes a numerically less precise implementation of the quantum time evolution improves the annealing efficiency as shown in section \ref{sec:cut-off}.

\begin{figure}[h!]
	\centering
	\includegraphics[scale=0.3]{model.png}
	\caption{Scheme of the model system of two bosonic particles moving in a four site lattice with long range interactions mediated by light scattering into two independent cavity modes.}
	\label{fig:model}
\end{figure}

\section{Model Hamiltonian and Approximations}\label{sec:model}
Let us consider a one dimensional lattice described by a tight binding BH model with four sites with periodic boundary conditions filled by two interacting bosons. The particles interact on site via collisions and we introduce tunable non-local interactions via collective light scattering to two independent cavity field modes \cite{maschler2008,mekhov2012} as depicted in \frefa{fig:model}. The open system dynamics of the cavity fields mediating the interaction can be described via quantum oscillators or it can be approximated by classical fields, as c-number amplitudes. As the pump lasers illuminating the atoms are described by coherent fields and working in the weak excitation regime, the latter can be expected to give an approximation for the full quantum dynamics \cite{maschler2008}. As we assume the cavity damping rates much faster than the atomic dynamics, an adiabatic elimination of the field dynamics should well approximate the induced all to all coupling.\\

\noindent
{\bf Full quantum dynamics:} Let us start by introducing the full quantum model for the coupled dynamics of atoms and field modes. For all levels of description of the atomic dynamics we will use the same BH-type particle Hamiltonian

\begin{equation}
 H_{kin}=J\sum_{k_{PBC}}(b_k^\dagger b_{k+1} + h.c.) \;\mbox{and}\; U_{int} =\frac{U}{2} \sum_k n_k(n_k - 1),
\end{equation}
where $k\in \left\{1,2,3,4\right\}$ and $k_{PBC}$ denotes the periodic boundary conditions. Of course, it would be interesting to also consider the case where we replace this by a classical Brownian motion model \cite{torggler2014} but this is beyond the aim of this work.

The interactions between different lattice sites are mediated by cavity modes. As discussed in recent publications \cite{keller2018,kramer2014,torggler2017}, introducing two independent field modes with different wave-vectors already creates surprising complexity into this model. Hence we can expect generic quantum effects play a vital role. Assuming that there is no scattering between the modes, i.e. a big enough frequency spacing, we can simply add the interaction terms induced independently by each mode. Experimentally this simply requires adding an extra pump laser with a mode specific detuning $\Delta_c^m = \omega_p^m - \omega_c^m$. To keep it simple enough we will use two modes, where one has twice the wavelength of the other. In this case the local interaction strengths are periodic with equal strength and simply amount to site dependent sign changes.

Incorporating these symmetries, we can write the long range interaction Hamiltonian as

\begin{equation}\label{Hint}
	H_{int} = \tilde{J}\big(\hat{M}_1 (a_1+a_1^\dagger) + \hat{M}_2 (a_2+a_2^\dagger)\big),
\end{equation}
where we introduced the overall scattering amplitude $\tilde{J}$ and the effective scattering operators determining the light scattering amplitudes into the modes, which explicitly read:

\begin{eqnarray}
\hat{M}_1 &= (-\hat{n}_1 + \hat{n}_2 - \hat{n}_3 + \hat{n}_4) ,\; \\  \hat{M}_2 &= (+\hat{n}_1 + \hat{n}_2 - \hat{n}_3 - \hat{n}_4).
\end{eqnarray}

In our present case the pump strength $\tilde{J}$ is equal for all modes and lattice sites. The cavity-pump detunings $\Delta$ are tuned to equal by adjusting the pump frequencies $\omega_p^1$ and $\omega_p^2$, therefore we can write the cavity radiation Hamiltonian as

\begin{equation}
H_{rad}= -\Delta (a_1^\dagger a_1 + a_2^\dagger a_2). \label{Hrad}
\end{equation}

The complete effective Hamiltonian finally reads

\begin{eqnarray}
	H &= J\sum_{k_{PBC}}(b_k^\dagger b_{k+1} + h.c.)  +\frac{U}{2} \sum_k n_k(n_k - 1)  \nonumber  \\
         -&\Delta (a_1^\dagger a_1 + a_2^\dagger a_2) +\tilde{J}\big(\hat{M}_1 (a_1+a_1^\dagger)
     + \hat{M}_2 (a_2+a_2^\dagger)\big). \label{eq:H}
\end{eqnarray}

As we deal with an open system, in principle we have to include dissipation via the cavity mirrors and spontaneous emission of photons. Assuming operation far from atomic resonance, we neglect the latter and incorporate only cavity loss $\kappa$ via a standard quantum optics master equation:

\begin{eqnarray}
	\dot{\rho} &= -\frac{i}{\hbar}\left[H,\rho\right] + \mathcal{L}[\rho], \\
\mathcal{L}[\rho] &= \sum_{m\in \left\{1,2\right\}}\kappa_m (2a_m\rho a_m^\dagger - a_m^\dagger a_m \rho - \rho a_m^\dagger a_m),
\end{eqnarray}
where $\mathcal{L}$ is a standard damping Liouvillean \cite{breuer2002}. \\

{\bf Adiabatic elimination and semi-classical description of modes:} Our central aim in this work is to study the role of {\sl quantumness} in simulated annealing. In addition to the full quantum dynamics we thus will introduce two additional approximate descriptions, which differ in the description of the cavity mode as quantum fields or as classical fields. In both cases, for direct comparability we assume adiabatic following of the field modes to the atomic state, which allows for adiabatic elimination in the mode dynamics. In the first case we treat the field mode amplitudes as quantum operators governed by their Heisenberg equations, while in the second case they are described by classical coherent fields with c-number amplitudes governed by Maxwell's equations. Note that in the latter case no atom-field entanglement can build up.

Using (\ref{Hint}) and (\ref{Hrad}) the Heisenberg equations for the field amplitude operators $\dot{a}_m = \frac{i}{\hbar}[H_{rad} + H_{int},a_m]$ read:

\begin{equation}\label{adot}
	\dot{a}_m = i \Delta a_m -i\tilde{J} \hat{M}_m  - \kappa_m a_m.
\end{equation}

We can construct an effective particle Hamiltonian by adiabatic elimination of the fields (\ref{adot}), which is valid if $\kappa_m$ and $\Delta$ are larger than the timescale of atomic motion $J/\hbar \ll |\Delta + i\kappa|$. Hence the fields will closely follow atomic dynamics which formally yields:

\begin{equation}\label{eq:a_m}
	a_m = \frac{-i \tilde{J}}{\kappa_m - i \Delta}\hat{M}_m.
\end{equation}

We will now proceed in two ways to derive an effective particle interaction Hamiltonian:

First we can insert the full operator expression $a_m$ in the Hamiltonian (\ref{Hint}) and (\ref{Hrad}), such that the atom-light interaction reduces to an effective interaction of the particles, so that we get:

\begin{equation}\label{eq:Had}
	H_{ad} = \frac{\Delta \tilde{J}^2}{\kappa^2 + \Delta^2}\big(\hat{M}_1^2 + \hat{M}_2^2\big).
\end{equation}

In the second alternative approach we further approximate the field dynamics using a common mean field assumption, where the mode operators are represented by classical c-number amplitudes $\alpha_m(t)$ determined by the expectation values $ \langle a_m\rangle = \alpha_m(t) \in C $ of the corresponding operators:

\begin{equation}\label{eq:alpha}
	\alpha_m(t) = \frac{-i\tilde{J}}{\kappa_m - i\Delta} \langle\hat{M}_m\rangle.
\end{equation}

Inserting these approximate expressions for the fields into the original atom-field Hamiltonian defines our semi classical interaction Hamiltonian

\begin{equation}\label{eq:H-semi-class}
	H_{ad}^{sc}= \frac{\Delta \tilde{J}^2}{\kappa^2 + \Delta^2}\big( 2\hat{M}_1\langle\hat{M}_1\rangle - \hat{{I}}\langle\hat{M}_1\rangle^2 +   2\hat{M}_2\langle\hat{M}_2\rangle - \hat{{I}}\langle\hat{M}_2\rangle^2 \big).
\end{equation}

Here $\hat{{I}}$ denotes the identity operator. Note that semi-classical approximations in this form are a well proven tool in quantum optics, laser physics and quantum gas cavity QED to reduce the complexity of coupled atom field solutions. To solve for the corresponding Schrödinger dynamics one has to evaluate the expectation values of the mode operators self-consistently at each timestep.

 As mentioned we restrict ourselves to two particles within our four lattice sites, i.e. half filling. Accordingly the particle Hilbert space dimension of the space is $3^4=81$. Note that our two approximate Hamiltonians (\ref{eq:H-semi-class}) and (\ref{eq:Had}) formally look very similar, but finally will lead to even quantitatively different annealing results in the important parameter regime.

At this point our 4-site Hamiltonian with periodic boundary conditions still is translation invariant and thus has close to degenerate ground states. In order to create a well defined target ground state for the annealing process, we will introduce a certain amount of impurity, adding a small perturbation $H_d = -(1+ V) \hat{n_3}$ at the third lattice site changing the depth of the third potential well. This part can be incorporated in the mode operators $M_i$ which simply change to:

\begin{equation} \label{M(V)}
\hat{M_1}= (-\hat{n}_1 + \hat{n}_2 - V \hat{n}_3 + \hat{n}_4),\\
\hat{M}_2 = (+\hat{n}_1 + \hat{n}_2 - V \hat{n}_3 - \hat{n}_4).
\end{equation}

With $V > 1$ we lift the degeneracy in the ground state of the energy spectrum and enforce a unique lowest energy solution in form of a two particle occupation state of the third lattice site for large pump $\tilde{J}$.

Note, that we work in the regime of weak excitation in the modes, hence low photon numbers and large detuning, and we consider a damping rate $\kappa$ faster than the timescale of the atomic dynamics, resulting in close to adiabatic field dynamics. Thus, the photon number fluctuations are fast and essentially average out, resulting in a coherent interaction. This allows us to consider only trajectories with unitary evolution. In principal, decay should be further investigated but, for simplicity, is not pursued in this work. Therefore, whenever we refer to the dynamics of the \emph{full quantum description} we consider evolution in terms of \ref{eq:H}.

\section{Quantum annealing }\label{sec:analysis quantum}
In this section we analyze the detailed properties of the annealing procedure based on a full quantum atom and field description. We dynamically evolve the ground state of the initial Bose Hubbard Hamiltonian without the laser induced interactions $\tilde{J} = 0$ adiabatically towards the ground state of the full interacting Hamiltonian at large pumping $\tilde{J} \gg J$, including weak impurity.

Here it is helpful to first look at the energy spectrum of the time dependent Hamiltonian as a function of the pump strength allowing to identify the minimum excitation gap as decisive parameter determining the quality of the annealing process. This gap limits the minimum time for an adiabatic ramp up procedure of the laser induced interactions. All energies and parameters here are given in units of the recoil energy $\hbar \omega_r = \hbar\; \frac{\hbar k^2}{2m}$, corresponding to the kinetic energy of an atom with mass $m$ with a momentum equal to the single photon momentum $\hbar k$, with $\omega_r$ the recoil frequency.

In \frefa{fig:energy-spectrum} we plot the numerically determined lowest 10 eigenvalues $H(s)\ket{\psi_n(s)}=E_n(s)\ket{\psi_n(s)}$ relative to the ground state, i.e $E_n(s) - E_0(s)$, for different effective pump strength $\tilde{J(s)}$. Note that the parameter $s=t/t_f$ describes the time dependence of the pump strength, with the simulation time $t_f$ and $t\in[0,t_f]$. At this point it is important to note that we need to introduce a photon number cut-off (denoted by \textit{nc}), as the Hilbert space of a field mode (= harmonic oscillator) would have infinite dimension. For the following simulations we use a cut-off of $nc=3$ and further investigations will be presented in the final section. We see that for any chosen finite final impurity $V$ a gap remains open and takes on its minimum of about a recoil energy close to unit pump strength $\tilde{J} = 1$.

\begin{figure}[h]
	\centering
	\includegraphics[width = 0.6\textwidth]{spectrum.png}
	\caption{Energy spectrum of the full quantum atom-field  Hamiltonian (\ref{eq:H}) up to the 10th eigenstate. Energies are plotted relative to the ground state as a function of effective pump strength $\tilde{J}(s)$ with $s\in [0,1]$. The minimal energy gap $\Delta_{min}\approx0.1275$ between ground and first excited state is annotated by a dashed vertical line depicted. The chosen operating parameters are: $J=0.1$, $U=0.7$, $V=1.1$, $\tilde{J}^2=5=\Delta$.}
	\label{fig:energy-spectrum}
\end{figure}
The gap size depends on the impurity potential $V$ as depicted in \frefa{fig:energy-V} and \frefa{fig:delta-V}. As expected from symmetry arguments, without added impurity $V=1$ we get two almost degenerate ground states and thus a vanishing gap for large pump strength $\tilde{J}$.
\begin{figure}[h!]
	\centering
	\includegraphics[width = 0.66\textwidth]{spectrum-V.png}
	\caption{First excited state energy for different impurity well-depth $V$ relative to the ground state as a function of $\tilde{J}(s)$ with $s\in [0,1]$. An energy gap and a lifting of the ground state degeneracy at large pump only occurs when we introduce impurity with $V > 1$ increases. System parameters are chosen as: $J=0.1$, $U=0.7$, $V\in [1.0,1.2]$, $\tilde{J}^2=5=\Delta$.}
	\label{fig:energy-V}
\end{figure}
Note that the minimum gap depends nonlinearly on $V$ as shown in \frefa{fig:delta-V}.
\begin{figure}[h!]
	\centering
	\includegraphics[width = 0.5\textwidth]{delta-V.png}
	\caption{Minimum energy gap between ground and first excited state as a function of the impurity magnitude $V$ for: $J=0.1$, $U=0.7$, $V\in[1.0,1.2]$, $\tilde{J}^2=5=\Delta$}
	\label{fig:delta-V}
\end{figure}

Let us now start to study the corresponding annealing process. In its simplest form we start the dynamics with the system ground state at zero pump $\tilde{J} = 0$ and linearly increase pump strength towards $\tilde{J} = \sqrt{5}$. For a sufficiently slow ramp time much longer than the recoil time we evolve this state via the corresponding Schrödinger equation with a time dependent Hamiltonian $H$. In \frefa{fig:Hf_evo} (a) we show the site occupation probabilities as a function of time for the example of a sufficiently slow sweep, such that the state evolves adiabatically. As expected, around $\tilde{J} \approx 1$ both atoms are transferred to the deeper third well with very high probability.

\begin{figure}[h!]
	\centering
	\includegraphics[width = 0.75\textwidth]{Hf_evolution.png}
	\caption{State evolution for the full quantum Hamiltonian during one adiabatic sweep. In the left graph (a) the expectation values of the lattice site occupations are plotted, while the right figure (b) exhibits the corresponding evolution of the overlaps (fidelity) between the evolving state and the target solution as well as the initial state. The dashed line gives the probability for two atoms in the third well as an alternative measure of the annealing success. Parameters are: $J=0.1$, $U=0.7$, $V=1.1$, $\tilde{J}^2=5=\Delta$.}
	\label{fig:Hf_evo}
\end{figure}

The efficiency of this process can be quantified by the probability to reach the ground state of the final Hamiltonian as a function of various simulation parameters. This is shown in \frefa{fig:Hf_evo} (b) together with probability for the two atom occupation probability of the third well. We clearly see that both probabilities almost reach unity at the end for slow enough annealing. Note that the overlap of the field component of the full quantum state with the adiabatic eigenstate is significantly lower during evolution. This shows that the field dynamics lags somewhat behind its adiabatic value without preventing very good annealing success at the end.

\begin{figure}[h!]
	\centering
\includegraphics[width = 0.3\textwidth]{nph1.png}
\includegraphics[width = 0.3\textwidth5]{nph3.png}
\includegraphics[width = 0.3\textwidth5]{nph5.png}
	\caption{Evolution of the average cavity photon numbers in both modes and their sum as a function of the time-dependent pump-strength for three different choices of cavity detunings $\Delta = -1 $ (a), $\Delta = -3 $ (b) and $\Delta = -5 $ (c).The final pump amplitudes are increased as $\tilde{J}=\sqrt{-\Delta}$. The kink is directly connected to atomic ordering.}
	\label{fig:photons}
\end{figure}

The reordering of the atoms is accompanied and thus can be directly monitored by the buildup of the cavity field amplitudes as depicted in \frefa{fig:photons}. Here the time evolution of the photon numbers is depicted as a function of momentary pump strength $\tilde{J}(s)$. Increasing detuning and pump strength leads to lower photon numbers during the annealing process without much influence on the success. This operating regime allows to reduce the effective dissipation via cavity loss and also allows to use a lower photon cutoff in the numerical simulations saving computational time.\par

As mentioned above, adiabatic following requires a slow time evolution of the Hamiltonian. It is, of course, of vital interest here to find out, how fast one can progress without significantly lowering the success rate. In general one operates in the regime where the particle-particle interaction mediated by the field modes closely follows the particles state, i.e. the relaxation time scale of the modes is fast. However, as we shall see, instant following of the fields relative to the atomic dynamics, as mathematically assumed in the adiabatically eliminated quantum Hamiltonian, is not always optimal. To exhibit this, the success probability as a function of simulation time is depicted in the next two graphs, where we plot the final state overlap with the target state as a function of ramp time. Here we compare the full dynamic and the adiabatically eliminated case.

\begin{figure}[h!]\centering
	\includegraphics[scale=0.4]{nc3fid.png} \includegraphics[scale=0.4]{nc3infid.png}
	\caption{(a) The fidelity between the final state after adiabatic evolution and the desired target state as a function of simulation time. The green curve corresponds to the Hamiltonian with full dynamic quantum fields (\ref{eq:H}) while the red line represents the adiabatic elimination model (\ref{eq:Had}).
(b) The negative logarithm of the infidelity as a function of simulation time. Parameters are: $J=0.1$, $U=0.7$, $V=1.1$, $\tilde{J}^2=5=\Delta$ and $\kappa=1$.
 }
	\label{fig:nc3fid}
\end{figure}

As we see, for simulation times $\omega_r*t_f > 250 $ the success probability (fidelity) shown in \frefa{fig:nc3fid} (a) in both cases well surpasses $0.9$ for the full and the adiabatic Hamiltonian (\ref{eq:Had}). On this scale the two curves agree pretty well, although the adiabatic Hamiltonian effectively incorporates photon loss via the cavity mirrors by including a damping rate $\kappa$ in the Heisenberg equations of the field operators. Obviously, at the chosen low cavity decay rate of $\kappa = 1 \omega_r$ the effect of photon loss does not change the dynamics significantly. Note that already the initial state of the system $\ket{\Psi_0}$ has a nonzero overlap with the solution, so that we do not start at zero overlap.
To highlight the limits of the success rate for very long ramp times in more detail, we also plot the negative logarithm of the infidelity, i.e. the deviation of the fidelity from one, i.e., ($1-\mathcal{F}$) in \frefa{fig:nc3fid} (b). Somewhat surprisingly, already at about $\omega_r t_f=300$ the fidelity for the adiabatic Hamiltonian flattens and then even decreases, which could be attributed to the openness of the system. In contrast, the accuracy obtained from propagation of the full quantum Hamiltonian improves further and reaches a much higher maximum around a simulation time of $\omega_r t_f \approx 1300$. Again also in this case much longer simulation times do further reduce the fidelity, hinting for an ideal simulation time to maximize the fidelity. The reason behind this is not obvious and finding out in detail would probably need extensive simulations with higher numerical accuracy.

As shown e.g. in Ref. \cite{hauke2015}, there is a close connection between the atom-field entanglement at the end of the adiabatic sweep and the success probability, as any remaining entanglement would lead to a mixed state in atomic space after tracing out the field degrees of freedom. Hence, while, as we will see below, large entanglement during the annealing process is vital for success, it is detrimental if it remains at the end. To quantify the amount of entanglement in our system we use the entanglement entropy, i.e. the Von Neumann entropy of the reduced mode density matrix. We will thus concentrate at two specific properties here, namely the maximum entanglement present during a sweep and the remaining amount of entanglement at the end of the evolution, further on called the "final entanglement".\par

\begin{figure}[h!]
	\centering
	\includegraphics[scale=0.4]{nc3ent.png}

	\caption{Maximum entanglement entropy attained during the sweep (dashed line) and the final entropy remaining after the sweep (solid line) as a function of total simulation time for parameters as in \frefa{fig:nc3fid}.}
	\label{fig:nc3ent}
\end{figure}
\frefa{fig:nc3ent} depicts these two key quantities as a function of the total simulation time $\omega_r t_f$. We see that with increasing simulation time the final entropy at the end of the evolution shrinks towards zero and the particles end up in the correct factorized state representing the sought solution. Note also the build up of a peak of maximum entanglement with simulation time until a certain optimal time. For longer time less entanglement builds up but it reaches a finite plateau at very long sweep times while the final entropy drops down to zero again. The splitting of the two values coincides with a peak in the process fidelity shown in \frefa{fig:nc3fid}. This suggests a close relation of success fidelity and the ability to get rid of the entanglement for a given simulation time.

\section{Annealing with semi-classical approximation}\label{sec:semi-class}

Let us now turn to the central question that we want to address in this work and compare the success of the annealing procedure in the quantum case as above with a semi-classical Hamiltonian (\ref{eq:H-semi-class}) based on mean fields to mediate the atom-atom interactions. Of course, for such a classical field description, no atom field entanglement can build up. In particular, we are looking for parameter regions, where the semi-classical model fails to reliably produce the desired solution, while the full quantum model still succeeds.\par

By evaluating the solution fidelity of the semi-classical model for a wide parameter range, we find a very strong dependence of the success fidelity on the particle-particle interaction parameter $U$ and the introduced impurity magnitude $V$. Only for small onsite interaction strength, the semi-classical approximation of the dynamics reliably finds the correct solution. Increasing interactions we see a surprisingly sudden jump of the success rate to low probability below $0.5$. Further increasing repulsive interaction, so that the final ground state energy only exhibits a very small gap to the first excitation, the classical model virtually never succeeds.

\begin{figure}[h!]
	\centering
	\includegraphics[width=0.45\textwidth]{Fid_U_V_ed.png}
       \includegraphics[width=0.45\textwidth]{phase_full.png}
	\caption{ (a) Color density plot (phase diagram) showing the solution fidelity after an adiabatic sweep using the Hamiltonian with classical mean-field approximation (\ref{eq:H-semi-class}) and as well as (b) for  the full quantum Hamiltonian as a function of the impurity strength $V$ along y and the particle interaction strength $U$ along x. Chosen parameters are: $t_f=1000$. For (a): $\Delta = -1$, $\tilde{J}=1$ and for (b): $\Delta = -5$, $\tilde{J}=\sqrt{5}$.}
	\label{fig:phase_diag}
\end{figure}

Hence, here we can identify a clear quantum improvement as shown in \frefa{fig:phase_diag} (a) the color density plot of the fidelity for a range of $V$ and $U$ parameters. The plot resembles a phase diagram a lot when we show the success fidelity of the final state using (\ref{eq:H-semi-class}). These results hint at a simple qualitative explanation. Since local particle-particle interaction favors systems where particles are separated, increasing $U$ reduces the wave-function amplitudes for the particles to occupy the same lattice site. However, in the energy spectrum of the system for corresponding values of $U$, we still find a gap from a de-localized state to the ground state with two particles occupying $\hat{n}_3$. Accordingly, the adiabatic sweep using the full quantum Hamiltonian (\ref{eq:H}) finds the correct solution with almost $99\%$ probability also for higher $U$ values as shown in \frefa{fig:phase_diag} (b). Note the different color scale range for the two plots differing by two orders of magnitude.

{\bf Entanglement and Fidelity:} It is, of course, important to compare this behavior to the appearance of atom-field entanglement during the time evolution of the full quantum dynamics. While the final entanglement almost vanishes at the end, we still find a strong maximum during evolution as shown in \frefa{fig:Entanglement_t} for the same parameters as above.
Studying the plots side by side reveals a correlation between regions of high entanglement during quantum annealing and a very low fidelity of the semi-classical solution. Especially in the right lower corner, where the classical fidelity is close to zero, we observe a peak in the entanglement, which continues along the x-axis but reduces in intensity. One can faintly also recognize a similar triangular area of the high entanglement region.

 \begin{figure}[h]
  \centering
    \includegraphics[width= 0.45\columnwidth]{Entropy_max_U_V_2.png}
    \caption{Maximum of the entanglement entropy attained for the full quantum model during a slow sweep as a function of the impurity strength $V$ on the y-axis and the particle interaction strength $U$ along x. Chosen parameters are: $t_f=1000$, $\Delta = -5$, $\tilde{J}=\sqrt{5}$.}
    \label{fig:Entanglement_t}
\end{figure}

Obviously, regions of high fidelity are correlated to regions of low entanglement entropy and vaguely exhibit the same transition line. In particular in low fidelity - high entropy regions the indication of a direct connection between entanglement and the success probability for the semi-classical model look convincing although the transition lines are not as clear cut. As we have discussed above a classical field approximation removes the possibility of entangled particle-mode states. Hence, it is not surprising that the discrepancy between the success probabilities for the full quantum model and the semi-classical model is connected to the entanglement. Interestingly, we can also see a clear correspondence between the entanglement peak and the reduced fidelity in the lower right corner of \frefa{fig:phase_diag} (b). Although the entanglement can be quantitatively small, the maximum entanglement shows a clear correlation with the solution fidelity of the full quantum system.

\section{Speedup of numerical simulations by a lower photon number cut-off}\label{sec:cut-off}
\label{chap:cut-off}
The above considerations strongly support the idea that a real quantum advantage could be found in annealing processes. Of course, numerically we cannot find the exact solution for the quantum evolution, as we always need to truncate the simulation Hilbert space and in particular the maximum photon number allowed in the modes.
However, in our simple model we can still use a sufficiently high cutoff to make the difference to the full solution negligibly small. Surprisingly, it seems that the errors introduced by a lower and even nonphysically low cutoff often are not detrimental, but even help to find a higher fidelity solution. This comes in addition to the numerical speedup gained from a smaller computational basis. Does this mean that there is no quantum advantage in real life after all? Can there be a better model than quantum mechanics to do annealing ?

 In this final section we will study this intriguing phenomenon in more detail and work to quantify the influence of photon number cutoff and simulation time on the success probability.

\begin{figure}[h!]
	\centering
	\includegraphics[width = 0.2\textwidth]{pn_nc1.png}
	\includegraphics[width = 0.2\textwidth]{pn_nc2.png}
	\includegraphics[width = 0.2\textwidth]{pn_nc3.png}
	\includegraphics[width = 0.2\textwidth]{pn_nc4.png}
	\caption{Photon number occupation probabilities for one mode at the end of the adiabatic evolution for different cut-offs of the mode Hilbert space  $nc= 1$ (a), $nc=2$ (b), $nc=3$ (c) and $nc=4$ (d) from left to right.}
	\label{fig:occ_nc}
\end{figure}

As we argued above, the photon number distributions obtained in the simulations suggest that a cutoff at $nc=3$ photons leads to a very good accuracy of the numerical solution at a tractable numerical complexity. It allows to reliably describe the field quantum state during the whole evolution time, missing only higher occupations well below a percent and no visible changes in the dynamics for higher cutoffs ($nc=4$).

Nevertheless one can hope that a lower cutoff, which speeds up the calculations, is still good enough to obtain useful results in shorter time. To our surprise it turns out, that not everything behaves as anticipated here. Let us take a closer look at simulations based on lower photon number cut-offs, which clearly reduce the quality of the numerical solution of the Schrödinger equation.

Following the annealing procedure as above, in \frefa{fig:occ_nc}. we plot the final state photon number occupation probabilities for different cut-offs $nc\in\set{1,2,3}$, from left to right. It is sufficient to look at one mode here as the second one does not differ significantly. Of course with growing cut-off the vacuum contribution is decreasing, which clearly proves that the solutions obtained for lower cut-off are not faithful approximation to the full quantum dynamics. Nevertheless, as shown in \frefa{fig:cut-off} (a) the success probability for finding the desired atomic final is virtually the same in all case. Actually for fast ramps the lowest cutoff $nc=1$ simulations, where the modes are essentially approximated by q-bits, lead to an even higher success probability than higher cut-offs. Note that a semi-classical approximation completely fails here and some quantumness is still needed.

Let us zoom in a bit and plot the infidelity for the three different cut-offs on a logarithmic scale. This confirms that the numerically not justifiable nc=1 cutoff leads to the best results for fast sweeps. Hence we can win in several respects by not reliably solving for the full Schrödinger dynamics. We can use a smaller Hilbert space, which saves memory and computation time as well as a faster ramp time, which again speeds up the computation. Of course, it is hard to envisage how this quantum inspired algorithm \cite{heim2015} could be implemented in an experiment.

Fortunately a second look at \frefa{fig:cut-off} (b) reveals a second interesting feature. When we implement a careful and numerically reliable solution using a slow sweep we find the highest single run fidelity. Quantitatively a larger Hilbert space can reduce minimal possible infidelity by even a couple orders of magnitude at the expense of a much slower computation. While this might seem not so useful at the end, the picture could strongly change in much more complex setups, where much lower single run success is expected and only the full dynamics will yield useful performance.

\begin{figure}[h!]
	\centering
	\includegraphics[width = 0.35\textwidth]{cut-off.png}
	\includegraphics[width = 0.35\textwidth]{cut-off_log.png}
	\caption{(a) Solution fidelity between final state of the adiabatic evolution and target state as a function of sweep duration $t_f$ for different photon number cut-offs (blue, yellow, green) and the adiabatic Hamiltonian (red).  (b) The same result shown via the negative logarithm of the infidelity demonstrate a clear improvement for higher cutoffs only for a sufficiently long sweep duration. Parameters are: $J=0.1$, $U=0.7$, $V=1.1$, $\tilde{J}^2=5=\Delta$ and $\kappa=1$.}
	\label{fig:cut-off}
\end{figure}
What else can we learn from this example? As discussed above the atom-field entanglement remaining at the end of the adiabatic evolution interferes with the ability to find a good solution. In \frefa{fig:cut-off_ent} one finds a clear signature of this effect comparing the final states for different photon number cut-offs. As the Hilbert space is larger, higher cut-offs allow for the buildup of more maximal entanglement in the process, which would suggest a better optimization performance. However, for relatively short simulation times, the final entanglement reduces towards zero at the end much faster for lower cutoff than for the higher cut-offs. Hence for short times the penalty of more remaining final entanglement for the full cutoff dominates over the gain from a higher in process entanglement. This fits well to the behavior of the fidelity in \frefa{fig:cut-off}. The logarithmic plot on the right side reproduces the identical behavior for long simulation times. There, the lowest cut-off $nc=1$ reaches a steady state and for the highest cut-off $nc=3$ long ramp times allow to minimize the final entanglement the most.

\begin{figure}[h!]
	\centering
	\includegraphics[width = 0.35\textwidth]{cut-off_ent.png}
	\includegraphics[width = 0.35\textwidth]{cut-off_ent_log.png}
	\caption{ (a) Maximal (dashed lines) and final (solid lines) generated atom-field entanglement as a function of simulation time $t_f$  for the different photon number cut-offs as above. (b) The same results shown on a negative logarithmic scale exhibit the diminishing final entanglement responsible for the higher process success rate at larger cutoff and slower sweeps. Same parameters as in \frefa{fig:cut-off}.}
	\label{fig:cut-off_ent}
\end{figure}

\section{Conclusions}
In this work we identified and studied a generic toy system, where a clear quantitative improvement of the annealing process for a full quantum simulation versus the semi-classical counterpart can be demonstrated. As the two approaches only differ in the representation of the field modes mediating interactions by classical or quantum harmonic oscillators, the beneficial role of quantum dynamics is very clearly revealed. In this sense, we directly compare solutions of the Schrödinger equation and corresponding Maxwell equations. While superposition and interference of field mode amplitudes is possible in both cases, only the quantum description opens the possibility of entanglement, which manifests itself as the key ingredient towards generating a quantum advantage. Although, an in depth discussion in reference to the debate around the \emph{quantumness} of the D-Wave quantum annealer \cite{smolin2014a,wang2013a} is beyond this work, let us emphasis once more the fact that in our comparison of quantum annealing and a semi-classical counterpart, the classicality of the system solely arises from considering classical field modes and hence eliminating the possibility for light-matter entanglement, therefore enabling a clearer investigation into the quantumness of the system.

However, there is not a quantitative one to one correspondence between entanglement and improvement. On the one hand we show a direct connection between the maximal atom-field entanglement in the dynamics and a high probability to find the optimal solution at the end. On the other hand, for a too fast sweep time, the final atomic state keeps some entanglement with the light, which diminishes the final solution fidelity. As the desired final ground state is separable, a strong quantitative anti-correlation between the success probability and final state entanglement is quite obvious. In summary, highly reliable annealing needs strong entanglement during the annealing process but vanishing entanglement at the end.

This feature can help to explain the surprising improvement one gets from using photon number cut-offs too low to accurately represent the full quantum dynamics in the simulations. This unphysical cutoff prevents the buildup of large entanglement at short simulated times, so that only very little entanglement remains at the end of the sweep. For certain operating parameters, the benefit of the final disentanglement turns out to be more important than the extra fidelity gain one obtains from a larger maximum entanglement during the process. Nevertheless we see that the limitation of the Hilbert space and thus maximal entanglement also limits the maximal obtainable fidelity even for very long simulations times. We did not find, however, any regime where a classical description gives the best results.

Of course, to argue for a possible advantage of quantum annealing in general, there is still quite some distance to go. At first, a deeper investigation into the ideal amount of entanglement for finding an optimal solution is vital for identifying the optimal operation parameters. The central question here is the scaling of optimal entanglement with system size and whether this stays essential for large systems. Finally, also the requirement of disentanglement at the end needs to be shown not to scale unfavorably with system size. While all of these assumptions look reasonable, the corresponding substantial proofs are challenging and an experimental evaluation might be a more reasonable approach here. While for implementing quantum inspired numerical algorithms \cite{heim2015} a unfaithful representation of the field Hilbert space can speed up calculations and increase the solution fidelity at the same time, it is unclear how this could be mimicked in experimental devices.

As said above, the central question to be answered is the scaling of the fidelity improvement through entanglement in larger systems. Some preliminary results obtained in simulations of the N-Queens problem hint for the growing importance of entanglement with system size \cite{torggler2019}. Here numerical studies based on the Heisenberg equations of the system operators using a so-called cumulant expansion \cite{heim2015} should be a promising method to better uncover the role of entanglement in the annealing dynamics in larger systems. To study the ultimate performance of an open quantum system approach, the effect of photon decay through the cavity mirrors needs to be systematically included in form of a corresponding master equation approach. Fortunately, using proper operating parameters in open systems, intrinsic cooling could be used to compensate for non-adiabatic errors and allow for a simulation speedup. Hence there are ample options and possibilities for future studies in various interesting directions.

\ack
We thank Valentin Torggler and Wolfgang Lechner for valuable discussions. The numerical simulations were performed with the open-source framework QuantumOptics.jl~\cite{kramer2018} and the graphs were produced with the open-source library Matplotlib~\cite{hunter2007}. H.R. acknowledges support from the Austrian Science Fund under project P29318-N27.

\section*{References}

\providecommand{\newblock}{}

redpajama_set_name: RedPajamaArXiv


Sekiro: Shadows Die Twice is a fair bit different from the rest of From Software's Soulsborne repertoire. Veering more strongly into the character action sub-genre, its revive mechanic differs as well.
Sekiro Sakura Droplet is the item that'll fuel One-Armed Wolf's repeated revivals, and you'll definitely need it if the game's ridiculously badass boss encounters are anything to go by. Here's how to find and use Sakura Droplet to revive in Sekiro.
How to Revive using the Sakura Droplet in Sekiro?
In Sekiro, getting the Sakura Droplet's additional revive is quite a task. First, you're going to have to assassinate Lady Butterfly, and though the Droplet itself is one of her drops, you're first going to have to defeat Genichiro Ashina, and then still you're going to have to go speak to lord Kuro.
You need to tell Kuro that you're to help him find what he needs, and then you'll have the option to show the Sakura Droplet to him. After the cutscene plays, you'll get an additional revive. Simple, right?
We've also got a number of other guides for Sekiro, including one on how to collect money and loot, and how to cure Dragonrot. If your problems with the game are of technical nature, we can also show you what to do if your DS4 controller isn't working.


text:
Your Season 30 Dancing with the Stars winner: 2016 NBA Champion Iman Shumpert
Shumpert and partner Daniella Karagach won on Monday, and brought a little bit of Chicago to the world in the process
Stephen Knox
This season's Dancing With the Stars winners: Iman Shumpert and Daniella Karagach.
OMG, Iman and Daniella did it! On Monday, Iman Shumpert and Daniella Karagach won the 30th season of Dancing with the Stars, making Shumpert the first NBA player and the 12th athlete to win the competition.
Commissioner For A Day: Let's Get Rid Of The Clock In Basketball
Is 60 > 71? Debating Luka Dončić and Donovan Mitchell's record-breaking games
A March Madness-style NBA playoff would change history
They were announced as winners at the end of the broadcast and hoisted up like Mike Ditka and Buddy Ryan after Super Bowl XX.
In the finals, Shumpert was up against JoJo Siwa, Amanda Kloots, and Cody Rigsby, who all have professional dancing experience. After the broadcast concluded, he said on stage that the victory was for his mother, who is a huge fan of the show.
The congratulations poured in on social media. Carmelo Anthony had already been campaigning for Shumpert and then shouted him out after the victory. The Cleveland Cavaliers tweeted out a picture of Karagach and Shumpert holding the trophy, congratulating a member of their 2016 NBA Championship team. My personal favorite post came from The Athletic's Shams Charania. With no sense of irony, his tweet about Shumpert becoming the first NBA player to win the competition read like he was breaking news that a team signed him.
No one was more excited for the victory than Shumpert's wife, musician Teyana Taylor. Swipe to the second picture of her Instagram post about the victory to see her live reaction.
Shumpert and Karagach's first performance of the night was a cha-cha to Earth Wind and Fire's September. They gave a brief preview of that performance on ESPN's NBA Today after giving a quick dance lesson to Malika Andrews and Richard Jefferson. Then came the final final. Their freestyle performance was a mashup of Missy Elliott's 2005 smash hit Lose Control, and DJ Clent's Chicago Juke classic, Bounce.
Yes, Shumpert brought footworking to network television and it was amazing. It absolutely took this writer back in his mind to a basement party in 2005 and had him footworking in his chair during the performance, and a little bit in his while writing this article — there is no video evidence of this, so don't ask. Elliott and her dancer's footwork in the Lose Control music video so it was a natural transition for the performance. Shumpert is from the Chicago area and said on Good Morning America that Karagach told him that she wanted to learn how to do the dance, so he brought in a guru from Chicago, King Kemo.
King Kemo and DJ Clent on national broadcast television. If only I could find a decent mild sauce spot in Los Angeles, this day would be perfect.
As well as Shumpert and Karagach performed throughout the season, what resonated most was how much fun they were having. You can see the smile on Shumpert's face clear as day during their finale performances. Whether performing on a stage on being judged by millions of people, or in a basement after one too many vodkas, dancing is supposed to be fun. The two of them nailed that part even better than all of the throws and catches.
What's next for Shumpert? On NBA Today he said that he is still trying to get on a team even though he hasn't played since 2019. If a contender suffers an injury late in the season, why not take a flyer on him. If nothing else, they know he can still move.

redpajama_set_name: RedPajamaCommonCrawl


The main idea of gamified scientific research is that through simulation, games, the collaboration process and acquisition of knowledge becomes more effective.
The Matrix-Q Research Institute has know how and games developed by applying the Matrix 9 Game Generation Principles (tools), which are nature inspired, systemic, holistic, synergetic, take in consideration human natural stages of development (human potential human factor) and create a bridge between nature inspired knowledge and technology of ancient civilizations and cultures and the modern emerging global culture needs.
Through gamification tasks are suggested in the form of challenges, players (scientists) will take. According to level of participation, achievements, points, scientists will have the opportunity to participate in more complex or advanced research or join advanced stages of the collaboration process.
Stage zero: reading of general information, publications and research project proposals.
Stage two: identification of disciplines, fields of expertise involved, perspectives to be taken for research.
Stage four: a research project with specific goals will be designed, for example solutions design, technology innovation, publications, education, others.
Stage five: development of stage 4.
The process of collaboration redefines itself according to each challenge.
The Game Levels are created according to how advanced is the participation and complex the level of collaboration of researchers.
For example at a higher level, specific agreements will be suggested, as rights or property over achievements, mostly related to patents and know how innovation, and in reference to the time line and content of contributions by each researcher.
In order to Join the Mr Pool Hub researchers must be invited or apply to join.


Under 10% of disposable income is used to service household debt. This is lower than the 13% before the financial crisis. By this measure, household debt is far more manageable than before the crisis.
The primary reason is lower costs for servicing mortgages. Consumer debt (non-mortgage loans) servicing costs are lower than before the crisis but not as much as mortgage servicing costs. The main reason for lower debt servicing costs is lower interest rates. Rising interest rates could have an impact on debt servicing costs.
This ratio is down from 1.35 from before the crisis to about 1 now. Household debt outstanding is growing far slower than disposable income which is good as it makes household debt more manageable.
By both measures, household debt in the United States is far more manageable than before the crisis.


When you find yourself on a family trip to Tahoe, after a few days, your "vacation mom" self is not quite the laid-back, relaxed, happy self you'd like to be. Sometimes you just need a break.
Book a sitter and try our Top 10 Tahoe Date Ideas for a much-needed hiatus.
10. Hula-Mud Pie at Sunnyside. Who can resist this precipice of deliciousness: cocoa cookie crust, macadamia nut ice cream, fudge topping, with whipped cream on the very peak. Go for dinner or just pop in for dessert — Sunnyside is beautiful, whatever the season. In summer, sit outside and enjoy an amazing sunset. In winter, the cozy dining room makes for a very romantic dinner for two.
9. For something different, book a daytime date. Get sandwiches at PDQ in Homewood (6890 West Lake Blvd.) and take them up to the summit of Eagle Falls. PDQ sandwiches have a sort of cult-like following, so the line can be long, but it's worth it! And, the Eagle Falls hike is not strenuous, but offers enough incline to get your heart racing before you settle in to enjoy the view and eat lunch. Park at highway 89 across from Emerald Bay.
8. Your date doesn't have to be complicated. Head to Fanny Bridge at the crux of Hwy. 89 in Tahoe City. How did it get its name? I'll let you decide as you hang over the side to check out all the big fish and rushing water. Then, get a table at The Bridgetender (65 West Lake Blvd.) and enjoy one of Tahoe's best burgers while taking in great apres-ski /rafting people watching.
7. Historic Truckee can be the perfect afternoon escape. Go early enough to peruse the quaint shops and old-town sights. Then, stay for dinner and a drink at Pianeta Restaurant, a stellar Italian restaurant that offers delectable food and a great wine list.
6. It might be obvious, but the Gondola at Heavenly is still one of Tahoe's gems. Going without the kids can feel like a true escape. Start at the base, where you can shop in Heavenly Village and grab a coffee or lunch before getting on the gondola. Revel in the pure quiet as you climb up and up and take in the view. You can get out half-way up to take photos, and once you get to the very top, enjoy a moment of serenity when you realize just why that long drive to Tahoe is worth it. It's truly breathtaking.
5. Pretend you're in college again and head to Chambers Landing Bar and Grill for some punch and people watching. This one definitely works better in Summer, but you can't beat the throngs of beach bodies, budding romances, and children's cries of joy when they catch a crab or two with a homemade pole and bait.
4. For some real fun, go someplace where you're guaranteed not to see anybody under 21 — a casino. The Hyatt Regency in Incline Village has a great restaurant, the Lone Eagle Grill, where you can dine and enjoy the lake view before heading in to give your luck a try. The casino is actually pretty classy if you can handle the wafts of cigarette smoke and desperation. Craps or slots, you're guaranteed to leave with at least a good story, if not a windfall.
3. If you're the active type, rent bicycles at one of the many rental shops dotted along the lake (Olympic, Tahoe Bike & Ski, etc.) and head out for an adventure. You can ride around the whole lake — most likely a 4-6 hour ride for most non-pros. Or, keep it local and ride along West Lake Blvd. or South Shore. Be sure to end with a hearty lunch or picnic in order to connect and bond over your awesome physical achievement.
2. Dinner at Christy Hill is some of Tahoe's finest. Located in Tahoe City, Christy Hill is a small restaurant (note: make reservations), which makes for a very customized, romantic experience. Recently written up by The New York Times and Bon Appetit, it's sure to meet (or exceed) your standards. And a traditional date can sometimes be the best kind.
1. How about this for a change-up? Tell your sitter to take the children OUT of the house or hotel room and take advantage of being home alone. A sitter can easily haul everybody down to the beach and grab an early dinner at West Side Pizza or Rosie's. Don't forget to give her a specific time to be home. Meanwhile, you and your hubby can have a cocktail, enjoy each other's company while cooking, or even take a walk or watch a movie. There are real joys in being somewhere familiar without the interruption of the kids' demands.


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https://blogs.wsj.com/indiarealtime/2014/03/28/ramachandra-guha-on-the-pre-election-landscape/
India Real Time
Ramachandra Guha on the Pre-Election Landscape
Joanna Sugden
Mar 28, 2014 11:19 am IST
Supporters of Hindu nationalist Narendra Modi wore Modi masks before a rally in New Delhi, Mar. 26.
Adnan Abidi/Reuters
India is just over a week away from the start of the largest democratic exercise on earth. As voters prepare to cast their ballots in the polls, India Real Time asked leading Indian historian and prolific author Ramachandra Guha to survey the political landscape.
Professor Guha, author most recently of "Gandhi Before India," spoke about the reality behind political marketing, the strength of India's democratic institutions and why the "anarchic Aam Aadmi Party" is good for the health of India's democracy.
Edited excerpts:
The Wall Street Journal: What do you think is driving the Bharatiya Janata Party's apparent surge in popularity ahead of national polls?
Ramachandra Guha: Several things. One is what is perceived, largely with justification, as the poor performance of the Congress to stem inflation, generate jobs, and stop corruption scandals. Largely it's a sense of being let down by government and its weak and ineffectual leadership.
But there is also superb marketing [from Narendra Modi, the party's prime ministerial candidate]. We don't know what is going on in Gujarat, many of his achievements have been reported to be exaggerated. They are selling dreams to the young, but I know, as an old historian, that one man can't solve all the problems.
WSJ: If Mr. Modi does become the next prime minister of India, what forces will shape his policies?
Mr. Guha: I don't pretend to be an economist, but there's a consensus among some who are, that there's some low hanging fruit to get the economy going. How effectively he's broken away from the RSS; education is critical for them, they want to shape the narrative, they'll want a tough home minister and some flexing of muscles towards India's neighbors.
But there's such an air of disgust with the present government, so people are willing to overlook his angularities because he can't be worse than what's come before.
The culture of democracy has been advanced, admittedly in an ugly way, by social media, [and by] expressing opinions freely through street protests and institutions of democracy such as state legislatures and courts.
Is Modi potentially fascist? No, because the institutions of culture and democracy are too strongly in place.
WSJ: What do you make of the ruling Congress party's decision to make subsidies for the poor the centerpiece of its manifesto?
Mr. Guha: Firstly, no one reads the manifesto, or less than 1% do. But subsidies are a political philosophy of Sonia Gandhi and Rahul Gandhi [president and vice president of Congress], so they won't abandon it so easily.
More In Elections 2014
What You Read in 2014: Modi, Mars and a Man-Eating Tiger
Indians 'Liked' Politics and Cricket on Facebook This Year
Unscrambling Data to Keep Politicians Honest
The Never-Ending Antics of Arvind Kejriwal
Tough Test Awaits the BJP in Rajya Sabha
India's Muslim Minority Apprehensive About Narendra Modi
WSJ: How do you rate the record and the chances of the Aam Aadmi or Common Man's Party?
Mr. Guha: After their extraordinary success in Delhi, they had a difficult decision whether to focus on a few constituencies where they had a greater chance of winning, or whether to go thoroughly national. Both were legitimate strategies. I would have preferred the first, but I'm cautious. Kejriwal [Arvind Kejriwal, the leader of AAP] is a real risk taker, he plays for high stakes. I can't see them getting more than 15 to 20 seats, it's too soon. They lack local leadership and they haven't built a base.
If they have five to 10 MPs, those MPs will be effective and persistent. AAP is a good thing for the health of Indian democracy, if they are anarchic. They ask some difficult questions, particularly about crony capitalism, which no one else asks.
They may only get 10 instead of 20-25 seats because they've spread themselves too thin, but I've been wrong about their chances before.
WSJ: The electorate now has 100 million more potential voters than in 2009 when polls last took place. Many say the demographic of the electorate has changed. Who are these new voters, and what do they want?
Mr. Guha: Of course there's a large number of young voters. What is important to note is that all the Rahul Gandhi marketing is that he is the voice of the youth, but largely the youth are disenchanted with him. But that doesn't mean though that they are enchanted by Modi. Some will go with regional parties, or AAP. In large sections of the country, the BJP has no presence at all.
But Congress' so-called young, charming leader has failed to attract young voters. It remains to be seen what would be the voting percentage among the first-time voters. Will they register themselves and go and vote?
Follow Joanna @jhsugden. Follow India Real Time on Twitter @WSJIndia.
Aam Aadmi Party
Ramachandra Guha
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The EU's common Regulation on Port Services means an opportunity for Finnish ports to create a strategic business policy. The enterprises can think of what the role of their own port involves. Should they create a landlord model, just focus on administration of infrastructure, or facilitate different services? This is an opportunity that is worth taking.
The Regulation on Port Services was not formulated instantly but took three preparation rounds. The EU finally decided on a Regulation instead of a Directive, which means a slightly weightier legal instrument. While Directives are enforced in different ways in different countries, Regulations are enforced uniformly throughout the EU, both in Northern and Southern Europe.
I share the view that in this case harmonisation was a good solution, as it supports equal competition conditions. In ports the international dimension is always present. Thus the competition position is very important.
The Regulation is entering into force on 24 March 2019. Some of the current service agreements may, however, continue up to 2025.
The Regulation on Port Services releases four different port services to the markets, of which the mooring and unmooring service is perhaps the most relevant, and then there are three others: towage, bunkering and waste collection. In Finland, that concerns 16 ports, one of which is Turku.
The Regulation strengthens the free movement of services in the EU's markets of port services. Up to now, ports have been closed or isolated in different ways in different countries, and accessing the services market has not necessarily been very easy. Now the gates are being pushed open.
Here in the north, we apply a very modern way of working. Our points of comparison can be found in the Netherlands, Great Britain, Denmark, Ireland, and to some extent in Sweden. In southern Europe, state-owned ports using the landlord model are typical.
For port enterprises the Regulation gives an opportunity to take control of their operations. It is possible to get a better look at the port: how do we want to arrange the services. The services can also be provided by the port itself, as the EU Regulation respects the autonomy of the port administrator. At the same time, neutral competition is required. If something is required from others regarding the service, it also has to be required from yourself. The port enterprise shall report on its website how the services are arranged and mention the minimum criteria and procedures that are used in choosing the service providers.
It is important to ports that the operations are smooth and continuous. Hence it is to be expected that port enterprises will determine the provision of services in such a way that they need to be available on all days of the year, 24 hours a day to all vessels that need the services in the port (e.g. mooring and unmooring services). It is possible to determine first just some minimum criteria and see how the services markets are working.
The Regulation requires the finances of the port enterprise and the service providers to be transparent. That will also prevent distortion of competition and aim at eliminating any prohibited state subsidies. In Finland that will just strengthen the current practice: the operating of ports in company form means public financial statements in the Trade Register and reporting obligations related to the company law. These requirements are already met.
No major changes are expected in Finnish ports. We are, however, going through a unique and interesting phase. Within a few years we will be able to see whether new service providers have emerged in the industry and whether the port enterprises have adopted models for providing services that differ from the present ones.


text:
Police investigate 'suspicious' shooting death in El Cajon
by: Domenick Candelieri
EL CAJON, Calif. — Authorities are investigating a shooting Sunday evening that left a 29-year-old man dead in El Cajon.
Power restored for thousands after morning outage hits North County
Strong winds, significant rain expected Tuesday
Construction begins on massive Terminal 1 overhaul at San Diego airport
Officers with the El Cajon Police Department responded to Grossmont Hospital around 8:15 p.m. after the victim was brought to the medical center by family members due to a single gunshot wound, the hospital staff reported to authorities. However, police confirmed the man died upon arrival at the hospital.
Border Patrol agent hit by DUI suspect at Temecula checkpoint
The man's death has been deemed "suspicious," according to Sgt. James Juns, of El Cajon police. Authorities believe the shooting happened on the 500 block of Jeffree Street.
Police say the investigation remains ongoing.
Anyone with information about this incident should contact the El Cajon Police Department at 619-579-3311 or Crime Stoppers at 888-580-8477.
SACRAMENTO, Calif. (AP) — California would allow children age 12 and up to be vaccinated without their parents' consent, the youngest age of any state, under a proposal late Thursday by a state senator.
Alabama allows such decisions at age 14, Oregon at 15, Rhode Island and South Carolina at 16, according to Sen. Scott Wiener, a Democrat from San Francisco who is proposing the change. Only Washington, D.C., has a lower limit, at age 11.
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Entertainment / 49 mins ago
Politics / 1 hour ago


What exactly is a mobile home?
A mobile home is a single-family house constructed entirely in a controlled factory environment, built to the federal Mobile Home Construction and Safety Standards - better known as the HUD Code.
Mobile Homes: These are homes built entirely in the factory under a federal building code administered by the U.S. Department of Housing and Urban Development (HUD). The HUD Code went into effect June 15, 1976. Mobile homes may be single- or multi-section and are transported to the site and installed. The federal standards regulate manufactured housing design and construction, strength and durability, transportability, fire resistance, energy efficiency and quality. The HUD Code also sets performance standards for the heating, plumbing, air conditioning, thermal and electrical systems. It is the only federally-regulated national building code. On-site additions, such as garages, decks and porches, often add to the attractiveness of mobile homes and must be built to local, state or regional building codes.
Panelized Homes: These are factory-built homes in which panels -a whole wall with windows, doors, wiring and outside siding - are transported to the site and assembled. The homes must meet state or local building codes where they are sited.
Mobile Homes: This is the term used for mobile homes produced prior to June 15, 1976, when the HUD Code went into effect. By 1970, these homes were built to voluntary industry standards that were eventually enforced by 45 of the 48 contiguous states.


text:
March 18, 2017 10:20PM PT
Malaysian Censor Wanted to Cut Four Minutes Out of 'Beauty and the Beast'
CREDIT: Courtesy of Disney
Abdul Halim Abdul Hamid, head of Malaysia's Film Censorship Board, says he sought to cut more than four minutes of material from "Beauty And The Beast" – far more than the three-second "gay moment" that has flustered regulators in some other countries.
Disney refused, and pulled the film from release last Thursday in Malaysia.
In a Q&A published Sunday in the New Straits Times and widely quoted in other Malaysian media, Abdul Hamid said that the Censorship Board (known as the LPF) wanted to cut 4 minutes and 38 seconds from three different points in the film.
The first was during the performance of a song in which the character Le Fou hugs his hero, the villain Gaston, from behind. The second was of "suggestive song lyrics with sexual innuendos." And the third was a scene at the end of the movie that Abdul Hamid declined to identify but that is most likely the bit in which Le Fou has what director Bill Condon calls a "gay moment."
"The length of the [proposed cut to the] song was about three seconds, but we could not recommend a three-second cut as it would make the song choppy and people would be angry. The other cuts are on the actions," said Abdul Hamid.
He also said that publicity surrounding the film and Condon's statements had made the problem more acute for the censors. Abdul Hamid said the LPF's curiosity had been raised by the homosexual elements introduced into the live-action film that were not present in the 1991 animated original. And he said that viewers had emailed the censors prior to the movie's certification.
"Maybe if Condon had not mentioned the 'gay element,' people wouldn't be so curious and we could let it go with a potentially minor cut. And this whole thing may not have been an issue. We at LPF want to preserve films as much as how they are intended by the director, but the moment the 'gay element' is thrown into the mix, we had to protect ourselves," Abdul Hamid said in the published interview.
Muslim-majority Malaysia has often been proud of its racial diversity and moderate version of Islam, but in the current political climate, conservative forces are increasingly dominant and intolerant. Under fire, Prime Minister Mohammad Najib Razak has recently embraced the hard-line Islamic factions that he previously shunned in order to bolster his chances of winning the next general election. Gay sex is illegal in Malaysia under both the criminal code and sharia, or Islamic law. Najib Razak's leading political opponent, Anwar Ibrahim, has twice been jailed on sodomy charges.
Quoted by official press agency Bernama this weekend, Deputy Home Minister Nur Jazlan Mohamed said: "Any films on LGBT [themes] the government will not allow, because the elements portrayed in the movie could influence us."
"Malaysia does not recognize the LGBT ideology, so we have to be extra cautious in our work. If we let these scenes pass, people will wonder if Malaysia recognizes LGBT," Abdul Hamid said in the New Straits Times Q&A.
Malaysia's film bodies have made clear their position on LGBT matters in the past. In 2010, the Malaysian Producers Assn. said that gay characters would only be tolerated on film if they either repent or die.
Despite the LPF's proposed cuts to "Beauty and the Beast," Abdul Hamid said he personally found the film "very funny and entertaining." He also explained that he had hoped to take his granddaughter to see the (edited) film on commercial release.
The LPF's decision is likely to be heard on appeal Tuesday. The film will be screened for the Film Appeals Committee, which is a separate body but which also comes under the wing of the Home Ministry. The committee is made up of about 20 people, including education, information and police officials. Its decision is final and cannot be appealed.


Looking for higher interest from your savings accounts? Consider opening an online savings account. Conventional banks pay less than one percent interest on conventional savings accounts. Online savings account banks offer higher interest rates because they do not have the infrastracture of conventional banks. They do not pay teller salaries, construct buildings in every city, or pay parking lot attendants to watch your car, so they can pay higher interest on their online savings account.
Transfer your money between your conventional checking account and your online savings account with no transfer fees, giving you easy access to your money.
Setup and name sub-accounts within your main online savings account. Create a separate christmas account, a new car account, a vacation account, or as many sub-accounts as you wish for whatever you please.
Setup automatic transfers on any day of the month you choose between your checking account and your online savings account. Transfer any amount to any online savings account you choose. How's that for an easy way to save your money?
Choose a password for your online savings account that includes numeric and alphanumeric characters. Do not use your spouse's, kid's, or pet's name, or other easily guessed words for your online savings account password.
Take steps to safeguard your password and your computer. Install spyware protection and a router with a firewall.
Use the online savings account sub-account feature to save for specific items.
Online banks will send email for each online savings account transaction. Check these emails for accuracy.
Review your online savings account weekly and review monthly online savings account statements for unauthorized transactions. Report unauthorized transactions immediately to the appropriate financial institution.
Be aware of the "phishing email scams" that are circulating the internet. ING DIRECT and VirtualBank will not send email asking you to click on a link to update information for your online savings account. This type if email is fraud, even if it looks official. Follow these links and you may become the victim of identity theft.
Have you opened your online savings account? What do you do next?
After opening your ING DIRECT or VirtualBank online savings account, visit the personal budgeting tips and debt repayment tips pages to learn ways to save even more money. Then visit the prevent identity theft page to learn ways to protect your money and your identity. The goal getting tips page will help you allocate the money in your new online savings account.


Rates are per apartment per night, including 10% VAT, Heating, a set of linen and towels with weekly change, services and final cleaning.
A credit card is required to guarantee your reservation, the balance in full is due at the reception.
The City tax of € 1 per person per night (children under 14 years exempt) is not included and will added to the total amount of reservation and paid directly at the Reception in Cash.
For the Air conditioning is required a small extra charge and it's available in all apartments except in the Apartment with 2 independent bedrooms (5 Adults).
Italian Breakfast served in our Main Hall: 5,00 € per person.
For late arrivals, early departures or cancellations made in less than 72 hours will be charged the amount equal to one night.
For bookings of 6 nights or more and for 3 or more apartments, the cancellation must be requested at least 15 days before the date of arrival.
IMPORTANT: If you use the browser it is necessary to introduce "Via di Montauto" then make sure that there is in the middle of the "di" not to be mistakenly taken to a neighboring village. We also advise you to print from Google maps the various indications.