text:
\section{Introduction}

Quantum process tomography
\cite{Nielsen2007,Chuang1997,Poyatos1997,Dariano2001,Dur2001,
  Altepeter2003} is {\it the} standard for the verification and
characterization of quantum operations on well-controlled quantum
systems. Among others, recent experimental demonstrations of quantum
simulators of multi-partite quantum systems
\cite{Jurcevic2014,Richerme2014} have demonstrated that, by now, the
number of well controllable qubits is in a regime for which
conventional tomography techniques fail as the required experimental
and numerical post-processing resources scale exponentially with the
number of qubits. While there has been a considerable effort to
introduce scalable techniques that allow for an efficient
reconstruction \cite{Cramer2010, Baumgratz2013, Baumgratz2013a,
  Landon-Cardinal2012, Toth2010, Schwemmer2014, Steffens2014,
  Steffens2014a, Banaszek2013} and verification \cite{Silva2011,
  Flammia2011, Kim2014} of quantum states, quantum process tomography
still leaves much to be desired.

\begin{figure}[t]
  \begin{center}
    \includegraphics[width=0.95\columnwidth]{fig_1.pdf}\vspace{-0.3cm}
  \end{center}
  \caption{(Color online) Two equivalent ways to obtain the necessary
    measurements for the scalable process tomography
    scheme. \textit{Top row:} System and ancilla are prepared in a
    maximally entangled state
    $|\Phi\rangle\propto\bigotimes_{i=1}^{N}[|0\rangle_{2i-1}|0\rangle_{2i}+|1\rangle_{2i-1}|1\rangle_{2i}]$
    (with pairwise entanglement indicated by vertical lines), the
    channel $\mathcal{E}$ is applied on the system, and products of
    Pauli observables are measured on all blocks of $r$ consecutive
    sites (exemplified for $r=3$ and
    $\hat{\sigma}_2^y\otimes\hat{\sigma}_3^x\otimes\hat{\sigma}_4^z$),
    which serves as input to reconstruct the resulting state
    $\hat{\varrho}_{\mathcal{E}}$ and thus the channel~$\mathcal{E}$.
    \textit{Bottom row:} Equivalently, these expectation values may be
    obtained without the ancillary system. The initial states have
    eigenstates of Pauli matrices (here, $\hat{P}_{\uparrow_x}$,
    $\hat{P}_{\downarrow_x}$, so those of $\hat{\sigma}_2^x$) on those
    sites where a Pauli matrix would have been measured on the
    ancilla. After application of the channel, the system part of the
    ancilla + system measurement is carried out (here, that of
    $\hat{\sigma}_1^y\otimes\hat{\sigma}_2^z$).}
    \label{fig:measurement-scheme}
\end{figure}

The most straightforward approach to process tomography is based on
the idea of probing the quantum channel with an informationally
complete set of states. After sending each of these input states
through the channel, the process underlying the dynamics is
characterized by performing full state tomography on all of the output
states. The so-obtained map fully characterizes the channel
\cite{Nielsen2007,Chuang1997,Poyatos1997}. This strategy is referred
to as \textit{standard quantum process tomography} (SQPT) and works
well as long as the underlying system is of low dimension. Considering
multi-partite quantum systems, however, reveals the disadvantages of
this technique: Not only the number of states to be sent through the
channel and to be indentified grows exponentially with the number of
subsystems $n$, but also the number of parameters that need to be
determined for each of the output states. There is, however, a
strategy to overcome the exponential scaling of the number of input
and output states: \textit{ancilla-assisted process tomography} (AAPT)
\cite{Dariano2001,Dur2001, Altepeter2003, ft:aapt-other-schemes}. AAPT
requires an ancillary system of the same size $n$ as the system
itself, the preparation of a maximally entangled input state
$\ket{\Phi} \propto \sum_{i}\ket{i}\ket{i}$ on the combined system,
and full tomography of the resulting state after application of the
channel,
$\hat{\varrho}_{\mathcal E} = (\mathbbm{1} \otimes \mathcal
E)(\ket{\Phi}\!\bra{\Phi})$,
see Fig.\ \ref{fig:measurement-scheme}.  This method is based on the
correspondence between quantum states and quantum processes known as
the Choi-Jamio{\l}kowski isomorphism
\cite{Choi1975,Jamiolkowski1972}. The incorporation of an ancillary
system considerably reduces the complexity of the preparation stage
(as opposed to exponentially many input states in SQPT, only one state
has to be prepared and only one output state has to be characterized)
but comes at the cost of needing access to an independent ancilla
system of the same size as the system that is to be analyzed. Still,
for a complete characterization of the output state
$\hat{\varrho}_{\mathcal{E}}$, a number of measurements exponentially
large in $n$ is required \cite{Mohseni2008}.

In this work, we combine recent results from efficient and scalable
state tomography \cite{Cramer2010,Baumgratz2013a} with the idea of
AAPT and discuss how to avoid the need for an ancilla system (see,
e.g., \cite{Flammia2012,Bendersky2008}) as summarized in
Fig.~\ref{fig:measurement-scheme}.  This allows us to formulate a
scalable process tomography scheme where the number of input and
output states, together with the experimental measurement settings to
characterize the latter, grows only linearly with the number of
qubits.

We restrict our attention to unitary processes and demonstrate our
scalable process tomography technique with numerical simulations of
quantum circuits and of time evolution under local one-dimensional
Hamiltonians. In Sec.~\ref{sec:numerics-circuits}, we consider a
circuit which prepares a Greenberg-Horne-Zeilinger (GHZ) state and the
quantum Fourier transform. Note that the GHZ circuit is a
limited-depth circuit (as defined below, cf.~\cite{Jozsa2006}), which
implies that it has an efficient matrix product operator (MPO)
representation in the sense that the bond dimension scales at most
polynomially with the number of qubits. This is exactly the class of
processes for which one would expect methods based on
Refs.~\cite{Cramer2010,Baumgratz2013a} to work. In turn, the quantum
Fourier transform is a circuit of polynomial depth, but one that
admits an approximate efficient simulation with a classical
computer~\cite{Yoran2007}. For the $n=32$ qubits considered here, an
MPO representation that approximates the circuit exists and our
reconstruction scheme works well.

In Sec.~\ref{sec:numerics-hamiltonians} we simulate process tomography
for time evolutions of one-dimensional local Hamiltonians $\hat H$ and
show how to extract the Hamiltonians from the reconstructed
processes. The reconstruction of a Hamiltonian on $n$ qubits will
require one process reconstruction at time
$\sim 1/\|\hat H\| \sim 1/n$
(Sec.~\ref{sec:numerics-hamiltonians-essentials}) or two process
reconstructions at times $t_{1}$, $t_{2}$ separated by no more than
$\sim 1/\|\hat H\|$
(Sec.~\ref{sec:numerics-hamiltonians-twotimes}). In the latter case,
the only restriction on $t_{1}$ and $t_{2}$ is that the process admits
reconstruction at those times. In both cases, the reconstruction of a
Hamiltonian will require roughly $\sim\!n^{2}$ measurements of each of
the $\sim\!n$ observables.

The quality of the reconstructed processes may be quantified using the
same experimental resources that are also required to obtain the
reconstruction: For unitary processes, $\hat{\varrho}_{\mathcal{E}}$
is guaranteed to be pure such that certifiability of the
reconstruction of $\mathcal{E}$ is inherited by the certifiablity of
$\hat{\varrho}_{\mathcal{E}}$ \cite{Cramer2010}; see
Ref.~\cite{Kim2014} for an analogous mixed-state certificate.

\section{Scalable Process Tomography}

Let us first consider the AAPT scheme and restrict, without loss of
generality, to qubits. Furthermore, we arrange the ancilla + system as
depicted in Fig.~\ref{fig:measurement-scheme} with odd sites
representing the ancilla and even sites denoting the system itself. In
this enumeration, the maximally entangled input state $|\Phi\rangle$
takes the form of a product of Bell states
$|\phi^{+}\rangle_{1,2}\otimes\cdots |\phi^{+}\rangle_{2n-1,2n}$,
$|\phi^{+}\rangle \propto |00\rangle + |11\rangle$, and hence only
requires local two-qubit manipulations for its experimental
generation.  The system (i.e., the even sites) is sent through the
channel and state tomography has to be performed on the resulting
state $\hat{\varrho}_{\mathcal E}$. Without any prior knowledge about
the underlying quantum channel, full state tomography is inevitable
and one seemingly faces the notorious curse of dimensionality. A large
class of quantum states, however, may be reconstructed from a number
of measurements and with post-processing resources that both scale
only polynomially in $n$
\cite{Cramer2010,Baumgratz2013,Baumgratz2013a}.

Post-processing with polynomial resources requires an efficient
representation of the state, which, in one dimension, is provided by
matrix product state (MPS) or operator (MPO) representations
\cite{Fannes1992,Perez2006,Schollwoeck2011}, compare also tree tensor
networks \cite{Shi2006} and the multiscale entanglement
renormalization ansatz \cite{Vidal2007}. There are many examples of
physical states that admit an efficient matrix product representation,
e.g. ground states of gapped local Hamiltonians
\cite{Hastings2007,Plenio2005,Eisert2010}, thermal states of local
Hamiltonians \cite{Eisert2010,Hastings2006} and entangled states like
the GHZ state, the W state and cluster states.

If the output state $\hat{\varrho}_{\mathcal E}$ happens to be close
to this class of states with an efficient matrix product
representation, scalable reconstruction of the channel may be
achieved.  The input to the scalable state tomography schemes
\cite{Cramer2010,Baumgratz2013,Baumgratz2013a} are given by the
measurement data of the following observables (or, alternatively, any
other local operator basis):
\begin{equation}
  \label{Eq:observables}
  \hat{P}_{k;\alpha_1,\dots,\alpha_r}=
  \mathbbm{1}_{1,\dots,k}\otimes \hat{\sigma}^{\alpha_1}_{k+1}\otimes\cdots\otimes \hat{\sigma}^{\alpha_r}_{k+r}\otimes\mathbbm{1}_{k+r+1,\dots,2n},
\end{equation}
for all $\alpha_i\in\{x,y,z\}$, $k=0,\dots,2n-r$, and a fixed $r$
independent of the size of the system. Here, $\hat{\sigma}_i^x$,
$\hat{\sigma}_i^y$, $\hat{\sigma}_i^z$ are the Pauli matrices for
qubit $i$. There are $(2n-r+1)\times 3^r$ such operators, i.e., the
number of observables that are required for these reconstruction
schemes scales linearly in $n$. Note that the restriction to local
information is not mandatory, any output state that is uniquely
characterized by a number of measurements that scales moderately with
$n$ can be reconstructed by these techniques \cite{Baumgratz2013a}
and, hence, belongs to the class of states for which our process
tomography procedure is applicable.

Interestingly, the necessary information may also be obtained without
the need of an ancilla (see, e.g., \cite{Flammia2012,Bendersky2008}),
yet then increasing the demand at the preparation stage: By virtue of
the identity
\begin{equation}
  \text{tr}[(\hat{A}\otimes \hat{S})\hat{\varrho}_{\mathcal E}]=\frac{\text{tr}[\mathcal E(\hat{A}^t)\hat{S}]}{2^{n}} ,\;\;\;\hat{A}^t=\sum_{i,j}\langle j|\hat{A}|i\rangle |i\rangle\langle j|,
\end{equation}
which holds for any operator $\hat{S}$ ($\hat{A}$) acting on the
system (ancilla), and the fact that each
$\hat{P}_{k;\alpha_1,\dots,\alpha_r}$ is of the form
$\hat{P}_A\otimes \hat{P}_S$ ($A$: ancilla, $S$: system), one may
obtain the necessary expectation values by preparing the eigenstates
of the Pauli matrices in $\hat{P}_A$ on the system, sending them
through the channel and measuring $\hat{P}_S$ on the resulting state
(see Fig.~\ref{fig:measurement-scheme} and Appendix\
\ref{appendix:equivalence_details} for details) -- a scheme that
requires no ancilla, the preparation of linearly many states and the
measurement of linearly many observables.

While the preparation and measurement strategy we just outlined may be
favourable from an experimental perspective, we will present our
scheme in the framework of AAPT as certain intuitions are particularly
transparent in this setting. In the remainder of this section, we
discuss how unitary operators and the Hamiltonians governing time
evolution can be constructed from $\hat\varrho_{\mathcal{E}}$. In
principle, the scheme is applicable to non-unitary channels as well,
as long as the corresponding state $\hat \varrho_{\mathcal E}$ permits
reconstruction.

\subsection{Reconstruction of Unitary Channels\label{sec:reconstruct-unitaries}}

We aim at reconstructing unitary channels, so channels of the form
$\mathcal{E}(\hat{\varrho})=\hat{U}\hat{\varrho }\hat{U}^\dagger$. For
those, it is guaranteed that the resulting state is pure, i.e.,
$\hat{\varrho}_{\mathcal{E}}=|\psi_{\mathcal{E}}\rangle\langle\psi_{\mathcal{E}}|$.
The unitary may then be obtained from the identity
$\langle j|\hat{U}|i\rangle=2^{n/2}\langle i|\langle
j|\psi_{\mathcal{E}}\rangle$.
The output of the state reconstruction algorithms of
Refs.~\cite{Cramer2010, Baumgratz2013a} provide us with a pure
estimate $|\psi^\text{rec}_{\mathcal{E}}\rangle$ of
$\hat{\varrho}_{\mathcal{E}}$ given in the form of a matrix product
state (MPS) \cite{Fannes1992,Perez2006},
\begin{equation}
  \ket{\psi^{\text{rec}}_{\mathcal{E}}} =
  \sum_{i_{1},\ldots,i_{2n}}
  A^{(1)}_{i_{1}} \cdots A^{(2n)}_{i_{2n}}
  \ket{i_{1}, \ldots ,i_{2n}},
\end{equation}
where $A^{(k)}_{i_{k}} \in \mathbb C^{D_{k-1} \times D_{k}}$ with
$D_{0} = 1 = D_{2n}$ and summation is over all $i_k=1,2$;
$k=1,\ldots,2n$.  The $D_{k}$ are called bond dimensions. Given this
form, the matrix product operator (MPO) representation of the estimate
$\hat{U}_\text{rec}$ to $\hat{U}$,
$\langle j|\hat{U}_\text{rec}|i\rangle=2^{n/2}\langle i|\langle
j|\psi^\text{rec}_{\mathcal{E}}\rangle$,
may straightforwardly be obtained by grouping the $n$ pairs of ancilla
and system sites:
\begin{widetext}
  \begin{equation}
    \label{eqn:MPO}
    \hat{U}_{\text{rec}} =
    2^{\frac n2}
    \sum_{i_{1},\ldots,i_{2n}}
    \Bigl[A_{i_{1}}^{(1)} A_{i_{2}}^{(2)}\Bigr] \cdots
    \Bigl[A_{i_{2n-1}}^{(2n-1)} A_{i_{2n}}^{(2n)}\Bigr]\,\,
    \ket{i_{2}}\!\bra{i_{1}}
    \otimes \cdots \otimes
    \ket{i_{2n}}\!\bra{i_{2n-1}}.
  \end{equation}
\end{widetext}
As the input state $|\Phi\rangle$ can efficiently be represented as an
MPS (given the sites are labeled as depicted in
Fig.~\ref{fig:measurement-scheme}), the process $\hat U$ having an
efficient MPO representation will imply that the exact state
$\ket{\psi_{\mathcal E}}$ has an efficient MPS representation, and
successful reconstruction may be possible.
We now show that circuits with an at most logarithmic depth have an
efficient MPO representation. Our condition is equivalent to the
condition given in Ref.~\cite{Jozsa2006}, but we give a tighter bound
on the bond dimension.  Let a circuit $\hat U$ be composed of $N$
two-qubit gates,
\begin{align*}
  \hat U = \prod_{j=1}^{N} \hat U_{j}, \quad
  \hat U_{j} \text{ acts on } l_{j} \text{ and } r_{j} > l_{j}.
\end{align*}
We define the depth of the circuit at the bipartition $i|i+1$ by
\begin{align*}
  d_{i} = |\{ j \colon l_{j} \le i \text{ and } r_{j} \ge i+1 \}|
\end{align*}
and denote the maximal depth by $d_{\text{max}} = \max_{i} d_{i}$.
This definition is motivated by the fact that an MPO representation of
$\hat U$ with bond dimension at most $4^{d_{\text{max}}}$ is easily
obtained from the MPO representations of the $\hat U_{j}$: The
$\hat U_{j}$ have bond dimension $D_{i} \le 4$ for
$l_{j} \le i \le r_{j}-1$ and $D_{i} = 1$ everywhere else, and the
bond dimension of the product $\hat U$ is given, in the worst case, by
$D_{i}(\hat U) = \prod_{j=1}^{N} D_{i}(\hat U_{j})$
\cite{Schollwoeck2011}.
If the depth $d_{\text{max}}$ grows at most logarithmically with~$n$,
we obtain an MPO representation of the circuit that is efficient in
the sense that it has a number of parameters at most polynomial in
$n$.

\subsection{Hamiltonian Reconstruction\label{sec:reconstruct-hamiltonians}}

Assume that the quantum process is in fact the time evolution under a
local one-dimensional Hamiltonian, i.e.,
$\hat{U}=\mathrm{e}^{-\mathrm{i} \hat{H} t}$, with $\hat{H} = \sum_{i} \hat{h}_{i}$,
where $\hat{h}_{i}$ only acts on a fixed number of neighbouring sites
(we will consider nearest-neighbour Hamiltonians throughout) and where
$\|\hat h_{i}\| \le J$ for a constant $J$. With the tools to
reconstruct unitary processes at hand, it remains to address the
question of how to find a valid estimate of the Hamiltonian $\hat{H}$
governing the time evolution. To obtain $\hat{H}$ from this unitary,
we will use the identity
\begin{align}
  x &= \sin(x) \frac{\arccos(\cos(x))}{\sqrt{1-(\cos(x))^{2}}}, &
  x &\in (-\pi, \pi),
  \label{eq:trigon-sin-cos-arccos}
\end{align}
together with the power series
\begin{align}
  \frac{\arccos(z)}{\sqrt{1-z^{2}}} &= \sum_{k=0}^{\infty} c_{k}
  (z-1)^{k}, & c_{k} = \frac{(-1)^{k}}{2^{k}} \prod_{j=1}^{k}
  \frac{j}{j+\frac12}
  \label{eq:arccos-series}
\end{align}
which converges for $|z-1| < 2$ %
\cite{[][{{. Print compantion to: NIST Digital Library of Mathematical
      Functions. \unexpanded{\url{http://dlmf.nist.gov/}}, Release
      1.0.9 of 2014-08-29. Derived from Eq.~4.24.2, available at
      \unexpanded{\url{http://dlmf.nist.gov/4.24\#E2}}.}}]Olver2010nocompanion}.  %
The %
basic idea is that from $\hat{U} = \mathrm{e}^{-\mathrm{i} \hat{H} t}$, we know that
$2\mathrm{i}\sin(\hat{H} t) = \hat{U}^{\dagger} - \hat{U}$,
$2\cos(\hat{H} t) = \hat{U}^{\dagger} + \hat{U}$, and Eq.\
(\ref{eq:trigon-sin-cos-arccos}) holds up to times limited by
$\| \hat{H} t \| < \pi$.  While this appears to limit the accessible
time interval for Hamiltonian reconstruction,
Sec.~\ref{sec:numerics-hamiltonians-twotimes} will explain how to
extend this result to longer times.

For practical purposes, we only want to evaluate a finite number of
terms of the series in Eq.~\eqref{eq:arccos-series} and enforce
Hermiticity. To this end, we approximate
\begin{equation}
  \label{eqn:RecHamiltonian}
  \hat{H}_\text{rec}t =\frac{1}{2}
  \sin(\hat{H}_{\text{rec}}t) \sum_{k=0}^{N-1} c_{k} (\cos(\hat{H}_{\text{rec}}t)-\mathbbm{1})^{k}+\text{h.c.}
\end{equation}
for a given $N$ and $\sin(\hat{H}_{\text{rec}} t)$ and
$\cos(\hat{H}_{\text{rec}}t)$ as above. This approach has two
advantages over using a power series expansion of the logarithm: It is
valid for larger values of $\|Ht\|$ and the series converges much
faster. Note that even if the reconstruction of
$|\psi_{\mathcal{E}}\rangle$ is perfect, $\hat{U}_\text{rec}$ may
differ from $\hat{U}$ by a global phase $\phi$, such that
$\hat{U}_\text{rec}^{\dagger} \mathrm{e}^{\mathrm{i}\phi} \hat{U}=\mathbbm{1}$ and Eq.\
\eqref{eq:trigon-sin-cos-arccos} imposes $\| Ht - \phi \mathbbm{1} \| < \pi$.
To remedy this problem, we use
$\hat{U}_\text{rec}
\tr(\hat{U}_\text{rec})^{*}/|\tr(\hat{U}_\text{rec})|$
as our actual estimate.

The initial state $|\Phi\rangle$ is an MPS of low bond dimension and,
as under local Hamiltonians quantum correlations build up in a
light-cone-like picture, $\ket{\psi_{\mathcal{E}}}$ will still have a
small bond dimension for small times \cite{Eisert2006,
  Bravyi2006}. More precisely, at a fixed time, there is an
approximate MPO representation of $U$ with a bond dimension that grows
at most polynomially with the number of qubits \cite{Osborne2006}.  In
our numerical simulations on $n \le 32$ qubits, we observe that a MPS
representation is feasible at times on the order of $1/J$.

\section{Numerical Simulations}

We carry out numerical simulations as follows: For several exemplary
channels $\mathcal{E}$, we numerically obtain
$\ket{\psi_{\mathcal E}}$ as detailed below and simulate measurements
of the local observables $\hat{P}_{k;\alpha_1,\dots,\alpha_r}$ by
drawing $M$ times per observable according to
$\ket{\psi_{\mathcal E}}$. In this way, we take statistical errors
into account, with statistical errors for measurements without ancilla
being very similar \cite{ft:noancilla-statistical-errors}.
The resulting empirical mean values (i.e., the simulated estimates of
the weights
$\langle \hat{\Pi}_{k;\alpha_1,\ldots,\alpha_{r}}^{s_{1},\ldots,s_{r}}
\rangle_{\hat{\varrho}_{\mathcal{E}}}$
of all eigenprojectors
$\hat{\Pi}_{k;\alpha_1,\ldots,\alpha_{r}}^{s_{1},\ldots,s_{r}}$,
$s_i=\pm 1$, of $\hat{P}_{k;\alpha_{1},\ldots,\alpha_{r}}$) are then
used to obtain a reconstruction
$|\psi_{\mathcal{E}}^\text{rec}\rangle$ of $\ket{\psi_{\mathcal E}}$.
This is done by exploiting the singular-value-thresholding-like
algorithm described in \cite{Cramer2010} to obtain an initial state
for the scalable maximum-likelihood algorithm of Ref.\
\cite{Baumgratz2013a}. The result is an MPS representation of
$|\psi_{\mathcal{E}}^\text{rec}\rangle$ which can be converted into an
MPO representation of $\hat{U}_\text{rec}$ as described above in Eq.\
(\ref{eqn:MPO}).

With the estimate $|\psi_{\mathcal{E}}^\text{rec}\rangle$ and thus the
corresponding operator $\hat{U}_\text{rec}$ at hand, we then quantify
the quality of the reconstruction scheme by
\begin{equation}
  \label{eq:u-fidelity}
  F=F(\hat{U},\hat{U}_\text{rec})=|\langle \psi_{\mathcal{E}}|\psi^\text{rec}_{\mathcal{E}}\rangle|^2,
\end{equation}
and note that this is in one-to-one correspondence to other distance
measures for unitary channels used in the literature
\cite{Raginsky2001, Gilchrist2005, Pedersen2007,
  ft:process-fidelity-relations}.

In the case of Hamiltonian reconstruction, we assess our reconstructed
estimates as follows: First, note that two Hamiltonians $\hat{H}$ and
$\hat{H} + \lambda \mathbbm{1}$, $\lambda \in \mathbb R$, are physically
indistinguishable. Therefore, we measure relative distances between
Hamiltonians according to \cite{ft:dmrg-ground-state-search}
\begin{align}
  D(\hat{H}, \hat{H}^{\prime}) &= \frac{\min_{\lambda \in \mathbb R} \| \hat{H} - \hat{H}^{\prime} - \lambda
    \mathbbm{1} \|} {\min_{\lambda \in \mathbb R} \| \hat{H} - \lambda \mathbbm{1}
    \|},
  \label{eq:hamiltonian-distance}
\end{align}
which is independent of energy offsets in both $\hat{H}^{\prime}$ and
$\hat{H}$.  We choose the operator norm $\|\cdot\|$ motivated by its
property
\begin{align*}
  | \langle \hat{A}(t) \rangle_{\hat{\varrho}} - \langle \hat{A}^{\prime}(t) \rangle_{\hat{\varrho}} | \le 2 |t| \| \hat{H} - \hat{H}^{\prime} \| \| \hat{A} \|,
\end{align*}
where $\hat{A}(t)$ and $\hat{A}^{\prime}(t)$ are the Heisenberg
picture time evolutions of $\hat{A}$ according to $\hat{H}$ and
$\hat{H}^{\prime}$, respectively. In other words, the operator norm
distance defines a timescale on which two Hamiltonians may be
considered equivalent.

For all results below, we repeat the whole procedure of sampling from
the simulated state, reconstructing it, and assessing the quality of
the reconstruction several times. All results shown are mean values of
$F(\hat{U},\hat{U}_\text{rec})$ and $D(\hat{H},\hat{H}_\text{rec})$
over a small number of runs, with deviations that are, for the number
of measurements per observable considered, smaller than the size of
the markers. Next, we present numerical results for the reconstruction
of quantum circuits and Hamiltonians and study the performance as a
function of the number of qubits $n$, the number $M$ of measurements
per observable, and the block size $r$ of the subsystems on which
measurements are performed. We simulate circuits and Hamiltonians on
up to $32$ qubits. Hence, reconstructing the unitary uses pure state
reconstruction on up to $64$ qubits.

\subsection{Quantum Circuits \label{sec:numerics-circuits}}

We demonstrate the feasibility of our scalable tomography scheme by
considering the $\widehat{\text{GHZ}}$ circuit, which prepares an
$n$-qubit GHZ state from $\ket{0 \ldots 0}$ and the quantum Fourier
transform \cite{Nielsen2007},
\begin{equation}
  \label{eq:circuits}
  \begin{split}
    \widehat{\text{GHZ}} &= \widehat{\text{CN}}_{n-1,n}
    \widehat{\text{CN}}_{n-2,n-1} \cdots
    \widehat{\text{CN}}_{1,2} \hat{H}_{1},\\
    \widehat{\text{QFT}} &= \prod_{k=1}^{n} \Biggl[ \Biggl(
    \prod_{j=1}^{n-k} \widehat{\text{CR}}_{k,k+j}(\pi/2^{j}) \Biggr)
    \hat{H}_{k} \Biggr],
  \end{split}
\end{equation}
where we use the convention
$\prod_{j=1}^{k}\hat{U}_i = \hat{U}_{k}\cdots \hat{U}_{1}$ for
products of non-commuting operators. Here, $\hat{H}_k$ denotes the
Hadamard gate acting on qubit $k$, and $\widehat{\text{CN}}_{i,i+1}$
($\widehat{\text{CR}}_{i,j}(\phi)$) denotes the two-qubit
conditional-NOT (conditional rotation) gate \cite{Nielsen2007}.
The $\widehat{\operatorname{GHZ}}$ circuit has depth
$d_{\text{max}} = 1$ and thus admits an exact efficient MPO
representation. The depth of the exact quantum Fourier transform
circuit is $d_{\text{max}} = \lfloor \frac{n^{2}}{4} \rfloor$ and
grows quadratically with the number of qubits (see
Appendix~\ref{appendix:qft-properties}).  However, one can obtain an
approximation $\widehat{\operatorname{QFT}}_{c}$ of the quantum
Fourier transform by dropping all conditional rotations with $j > c$
from the definition in Eq.~\eqref{eq:circuits}
\cite{Coppersmith1994}. This approximation can be simulated
classically with polynomial resources \cite{Yoran2007}. Using
numerical MPO compression techniques~\cite{Schollwoeck2011}, we obtain
an approximate MPO representation with bond dimension 16 and error
bounded by $[2(1-\sqrt F)]^{1/2} < 2 \times 10^{-5}$ for the
$n \le 32$ qubits we consider.

The reconstruction results are summarized in
Fig.~\ref{fig:gate-reconstruction}.  The reconstruction of the
$\widehat{\operatorname{GHZ}}$ performs very well. To discuss the
performance of the quantum Fourier transform reconstruction, we note
that the distance $\epsilon_{c}$ between the exact quantum Fourier
transform and its approximation $\widehat{\operatorname{QFT}}_{c}$ is
upper bounded by $\epsilon_{c} \le n \pi / 2^{c}$ (see
\cite{Yoran2007} and Appendix~\ref{appendix:qft-properties}).
We reconstruct $\widehat{\operatorname{QFT}}$ with high fidelity
$F \approx 0.99$ from measurements on $r=5$ consecutive qubits on the
combined system + ancilla (Fig.~\ref{fig:measurement-scheme}). Naively,
one would expect to be able to reconstruct
$\widehat{\operatorname{QFT}}_{c}$ only for $c \le 2$, because $r=5$
corresponds to information about three neighbouring system qubits
only. However, the upper bound on the approximation error is trivial
for $c = 2$ and $8 \le n \le 32$, and numerical tests show that the
actual approximation error $\epsilon_{c}$ is indeed several times
larger than the reconstruction error $[2(1-\sqrt F)]^{1/2}$ we
achieve. This shows that there are non-local gates which can be
reconstructed without using the corresponding non-local information.

\begin{figure}[t]
  \begin{center}
    \includegraphics[width=0.99\columnwidth]{fig_2.pdf}\vspace{-0.3cm}
  \end{center}
  \caption{(Color online) Reconstruction of the quantum circuits in
    Eq.\ \eqref{eq:circuits}. Figures show the fidelity in
    Eq.~\eqref{eq:u-fidelity} of the exact unitary and its tomographic
    reconstruction as a function of the system size $n$ for $M=\infty$
    (left) and as a function of the number $M$ of measurements per
    local observable for different $n$ (right).  Reconstruction uses
    measurements on all blocks of $r$ consecutive qubits only.  Lines
    are guides to the eye. The numerical data suggest a linear scaling
    of $(1-\sqrt{F})^{1/2}$ with system size $n$ and $1/\sqrt{M}$.  }
     \label{fig:gate-reconstruction}
\end{figure}

\subsection{Hamiltonian reconstruction\label{sec:numerics-hamiltonians}}

\subsubsection{Short times\label{sec:numerics-hamiltonians-essentials}}

We simulate the time evolution $\hat U$ of time-independent local
one-dimensional Hamiltonians $\hat H$ with well-established numerical
DMRG/MPO algorithms~\cite{ft:dmrg-time-evolution}. After obtaining the
estimate $\hat U_\text{rec}$ of the time evolution, we determine an
estimate $\hat H_\text{rec}$ of the Hamiltonian that governs the time
evolution by the series given in Eq.~\eqref{eqn:RecHamiltonian} with
$N = 3$. With this, and the assumption that
$\min_{\lambda \in \mathbb R} \| \hat{H} - \lambda \mathbbm{1} \| = \| \hat{H}
\|$ \cite{ft:h-rec-scaling-prefactor}, one has
\begin{align}
  D(\hat{H}, \hat{H}_\text{rec}) & \le
  \tfrac{\| \hat{H} - \hat{H}_{\text{rec}} \|}{\| \hat{H} \|}
  \le
  \tfrac{1}{140}
  \| \hat{H}t \|^{6} + O(\| \hat{H}t \|^{8}).
  \label{eq:hrec-series-error-estimate}
\end{align}
Fig.~\ref{fig:hamiltonian-reconstruction} shows results for an
isotropic Heisenberg Hamiltonian on $n \le 32$ qubits. We have also
studied the critical Ising model and a Hamiltonian with random
nearest-neighbour interaction, which show very similar behaviour and
the corresponding results may be found in Appendix~\ref{appendix:other
  hamiltonians}. We use $t_{n} = 1/\| \hat H\|$ as a time unit and
recall that the local terms of the Hamiltonian are bounded by a
constant, $\|\hat h_{i}\| \le J$. This gives us $t_{n} \ge 1/n J$ and
$t_{n} \sim 1/n$ if we additionally assume that the local terms all
have similar norm.

\begin{figure*}[t]
  \centering
  \includegraphics[width=\linewidth]{fig_3.pdf}
  \caption{(Color online) \textit{Left:} Fidelity between exact state
    $\ket{\psi_{\mathcal E}}$ and tomographic estimate
    $\ket{\psi_{\mathcal E}^\text{rec}}$ of a unitary time evolution
    $\hat{U} = \mathrm{e}^{-\mathrm{i} \hat{H} t}$, with $\hat{H}$ the isotropic
    Heisenberg Hamiltonian on $n$ qubits. The tomographic estimate is
    based on complete measurements on blocks of $r = 3$ consecutive
    qubits with $M$ measurements per observable.  \textit{Right:}
    Inverse relative distance~$D$ between $\hat{H}$ and
    $\hat{H}_\text{rec}$ reconstructed from
    $\ket{\psi_{\mathcal E}^\text{rec}}$.  The unit of time is
    $t_{n} = 1/\|\hat{H}\| \sim 1/n$, i.e., inversely proportional to
    the number of qubits, and the grey area indicates where
    reconstruction is expected to fail due to
    Eq.~\eqref{eq:trigon-sin-cos-arccos}. The grey lines without any
    markers show the expected behaviour for small times and times near
    $\pi$ (see Eq.~\eqref{eq:hrec-series-error-estimate} and the main
    text).  The data indicates that for $M < \infty$, $M/n^{2}$ fixed
    and $t/t_{n}$ fixed and sufficiently small,
    $D(\hat{H},\hat{H}_{\text{rec}})$ is largely independent of $n$.
    }
  \label{fig:hamiltonian-reconstruction}
\end{figure*}

The distance $D(\hat{H}, \hat{H}_\text{rec})$ between the
reconstructed and the exact Hamiltonian shown in
Fig.~\ref{fig:hamiltonian-reconstruction} displays the following
features: First, the reconstruction is expected to fail for
$\| \hat{H} t \| \ge \pi$ (see Eq.~\eqref{eq:trigon-sin-cos-arccos})
and, indeed, $D(\hat{H}, \hat{H}_\text{rec})$ is large in this area
(indicated by the grey background).  Secondly,
Eq.~\eqref{eq:hrec-series-error-estimate} suggests that close to
$\| \hat{H} t \| = \pi$, $D(\hat{H}, \hat{H}_\text{rec})$ should scale
as $ \| \hat{H}t \|^{6}/140=t^6/(140t_n^6)$ (thick grey line in
Fig.~\ref{fig:hamiltonian-reconstruction}).  Thirdly, we observe that
for infinitely many measurements per observable, $M = \infty$, and
fixed $t/t_n=\|\hat{H}\|t\sim nt$, the distance
$D(\hat{H}, \hat{H}_\text{rec})$ decreases with system size, a
behaviour inherited from the quality of the reconstruction
$|\psi^\text{rec}_{\mathcal E}\rangle$ (see left of
Fig.~\ref{fig:hamiltonian-reconstruction}): The fidelity
$F(\hat{U},\hat{U}_\text{rec})$ is limited by the amount of block
entanglement in $|\psi_{\mathcal{E}}\rangle$. At a fixed time $t$, an
area law \cite{Eisert2010} holds for this entanglement such that it is
bounded even for arbitrarily large systems \cite{Eisert2006,
  Bravyi2006}. For sufficiently large systems, we hence expect
$F(\hat{U},\hat{U}_\text{rec})$ at fixed $t$ to be independent of the
system size $n$. If we keep $t/t_n \sim t \cdot n$ fixed, we therefore
expect $F$ to increase with $n$. Finally, let us discuss the
dependence of the distance between the exact and the reconstructed
Hamiltonian in Fig.~\ref{fig:hamiltonian-reconstruction} on the number
$M$ of measurements per observable. First of all, with a finite number
of measurements no reconstruction will be possible at small times,
because the signal of the Hamiltonian in
$\hat{U} \approx \mathbbm{1} - \mathrm{i} \hat{H} t$ will be smaller than the
noise. Furthermore, the data suggests that, for times before
$t/t_{n} \approx \pi$,
\begin{align}
D(\hat{H}, \hat{H}_\text{rec})
  \propto &
  \frac{1}{t/t_{n}} \frac{n}{\sqrt M}.
\label{eq:number-of-measurements-scaling}
\end{align}
This is the behaviour one would expect if one assumes that the
relative error $D(\hat{H}, \hat{H}_\text{rec})$ is proportional to the
ratio $R/S$ of a noise amplitude $R$ and the strength of the signal
$S = \| \hat{H} t \|=t/t_n$, in which $R = n / \sqrt M$ is motivated
by the fact that we have measured $\propto n$ observables, each of
which has been estimated to within a standard deviation given, for
sufficiently large $M$, by $1/\sqrt M$.

The explanation of the scaling properties together with the fact that
all properties described are the same in the other Hamiltonians
investigated (see Appendix~\ref{appendix:other hamiltonians}) suggest
that that the scaling laws apply for many local Hamiltonians on a
linear chain, for a large range of system sizes and any sufficiently
large (as indicated by the examples) number of measurements.

To summarize, measuring at larger times gives a larger signal and a
smaller error, but we are limited by the condition $ t/t_{n} < \pi$
imposed by Eq.~\eqref{eq:trigon-sin-cos-arccos}.  Solving
Eq.~\eqref{eq:number-of-measurements-scaling} for the number of
measurements per observable, we obtain
$M \propto n^{2} (t/t_{n})^{2} / D^{2}$: A constant relative error $D$
at a fixed $t/t_{n} < \pi$ requires $M \propto n^{2}$ measurements per
observable, resulting in a total number of measurements proportional
to $n^{3}$ .

\begin{figure*}[t]
  \centering
  \includegraphics{fig_4.pdf}
  \caption{(Color online) Quality of the reconstruction
    $\hat{H}_\text{rec}$ for $\hat{H}$ the critical Ising (left),
    isotropic Heisenberg (middle) and a random nearest-neighbour
    Hamiltonian (right).  $\hat{H}_\text{rec}$ was obtained from
    $U(t'-t)$ with $t/t_{n} = 3.51$ fixed and
    $U(t'-t) = U^{\dagger} U'$ was obtained from tomographic estimates
    of $U = \mathrm{e}^{-\mathrm{i} \hat H t}$ and $U' = \mathrm{e}^{-\mathrm{i} \hat H t'}$.  The
    inverse relative error $1/D(\hat{H},\hat{H}_{\text{rec}})$ is
    shown for $H_\text{rec}$ (diamonds) and for the projection of
    $H_\text{rec}$ onto a nearest-neighbour Hamiltonian (circles).
    $\hat H$ acts on $n = 32$ qubits and tomographic estimates are
    based on complete measurements on blocks of $r = 5$ consecutive
    qubits with $M$ measurements per observable. The unit of time is
    $t_{n} = 1/\|\hat{H}\| \sim 1/n$.  Most properties are similar to
    Fig.~\ref{fig:hamiltonian-reconstruction}~right where
    $\hat H_\text{rec}$ was reconstructed from an estimate of $U(t)$,
    with the time difference $t'-t$ taking the role of the time
    $t$. Lines are guides to the eye.  }
  \label{fig:hamiltonian-reconstruction-twotimes}
\end{figure*}

\subsubsection{{Long times}\label{sec:numerics-hamiltonians-twotimes}}

In its present formulation, the reconstruction scheme is limited to
$t/t_n<\pi$, a restriction that may be overcome by measuring at two
different times $t$, $t^\prime$: The times up to which the fidelity
$F(\hat{U},\hat{U}_\text{rec})$ is sufficiently high is only limited
by $r$ -- increasing $r$ will increase the time up to which full
information about $\hat{U}$ may be obtained by measuring on $r$
consecutive qubits. In fact, as can be seen on the left of
Fig.~\ref{fig:hamiltonian-reconstruction}, for $n = 32$ and the
relatively small $r=3$, the fidelity $F(\hat{U},\hat{U}_\text{rec})$
is still quite high at $t/t_{n} = \pi$ while the reconstruction of
$\hat{H}$ fails for these times.  Measuring at $t$, $t^\prime$ and
obtaining $\hat{U}=\mathrm{e}^{-\mathrm{i} \hat{H}t}$,
$\hat{U}^\prime=\mathrm{e}^{-\mathrm{i} \hat{H}t^\prime}$ by reconstruction, we are
only limited by $|t^\prime-t|<\pi t_n$ when reconstructing $\hat{H}$
from $\hat{U}^\dagger \hat{U}^\prime=\mathrm{e}^{\mathrm{i} \hat{H}(t-t^\prime)}$.
Fig.~\ref{fig:hamiltonian-reconstruction-twotimes} shows results of
this reconstruction scheme with $t/t_{n} = 3.51$ and $t' > t$.

Reconstructing the Hamiltonian from
$\hat U(t'-t) = \hat U^{\dagger}\hat U'$, the time difference $t'-t$
clearly assumes the role of the time $t$ when reconstructing the
Hamiltonian from $\hat U$ at time $t$ alone. Therefore, all scaling
properties carry over as long as $\hat U_\text{rec}$ and
$\hat U'_\text{rec}$ can be obtained with sufficiently high
fidelity. We simulated measurements on blocks of $r = 5$ consecutive
sites to satisfy this requirement.

For exact measurements, $M = \infty$, the relative error
$D(\hat H, \hat H_\text{rec})$ does not approach zero for
$t'-t \to 0$.  The reason is that the error in
$\hat U_\text{rec}(t'-t)$ remains non-zero as $t'-t\to 0$ because
$\hat U_\text{rec}(t)$
 has a fixed non-zero error at fixed $t$. This
non-zero error may also become larger than the signal amplitude
$\| \hat H t \|$, explaining the increasing error as $t'-t \to 0$ for
some of the Hamiltonians.

Note that, from $\hat U(t'-t)$, we can also reconstruct Hamiltonians
that are time-dependent for times before $t$ and nearly constant
between $t$ and $t'$. In this way, stroboscopic reconstructions of a
time-dependent Hamiltonian may be obtained after large propagation
times.  Furthermore, $t/t_{n}<\pi$ becomes more restrictive as $n$
increases, thus the usefulness of taking measurements at two times
increases for larger systems.

\subsubsection{Enforcing a local reconstruction}

Of course, making use of additional information can only improve
the scheme. As an example, suppose that we know that the
Hamiltonian is nearest-neighbour only. One may then project
the reconstructed $\hat{H}_{\text{rec}}$ onto a nearest-neighbour
Hamiltonian. As can be seen in Fig.~\ref{fig:hamiltonian-reconstruction-twotimes},
this reduces the error dramatically.

\section{Conclusion and Outlook}

We studied in detail the application of recent scalable state
tomography models to quantum process tomography. At the hand of
unitary channels---quantum circuits such as logarithmic-depth
circuits, the quantum Fourier transform and unitary time-evolution
governed by one-dimensional local Hamiltonians---favourable scaling
with the number of qubits was numerically demonstrated. The scheme, as
presented, relies on an ancilla system, the preparation of a maximally
entangled state on the combined system, and local measurements after
application of the channel.  We also discussed an alternative scalable
scheme without the need for an ancilla, which displays the same
scaling properties as the ancilla-assisted scheme. The quality of the
reconstructed unitary channel may be quantified using the certificate
introduced in Ref.\ \cite{Cramer2010}.

We have also shown how one-dimensional local Hamiltonians may be
reconstructed from their corresponding unitary after an evolution time
inversely proportional in the size $n$ of the system and requiring
$\propto n^{2}$ measurements of each of $\propto n$ observables.  We
have discussed and numerically demonstrated how the restriction of
these small evolution times may be relaxed by taking measurements at
two different times. This enables the reconstruction and verification
of a quantum device at arbitrarily large times for as long as the
conditions for efficient state tomography are met, even if,
intermittently, the device has passed through highly entangled states.
Furthermore, the knowledge of the Hamiltonian being local may be
incorporated and has, for the Hamiltonians that we studied, improved
fidelities considerably.

Using the mixed-state tomography methods introduced in Refs.\
\cite{Baumgratz2013, Baumgratz2013a}, we expect non-unitary channels
to be similarly amenable to the scheme studied here.  Assessing the
quality of such a reconstruction, however, will rely on the ability to
quantify the quality of mixed-state reconstructions -- a goal that is,
in particular for many qubits and sufficient generality, still to be
met.

\begin{acknowledgments}
  This work was supported by an Alexander von Humboldt Professorship,
  the EU Integrating Project SIQS, the EU STREP EQUAM, the US-Army
  Research Office grant no. W91-1NF-14-1-0133, and the EPSRC
  (EP/K04057X/1). Numerical computations were performed on the
  bwUniCluster funded by the Ministerium f\"ur Wissenschaft, Forschung
  und Kunst Baden-W\"urttemberg %
  and the Universities of the State of Baden-W\"{u}rttemberg, Germany,
  within the framework program bwHPC.
\end{acknowledgments}

\input{Process_Tomography_Paper.bbl}

redpajama_set_name: RedPajamaArXiv


text:
Laurel's Choices
by Exie Wilde Henson
Genre: FICTION / Historical / General
Buy the 6 x 9 Black & White Paperback directly from the publisher at a 10% discount for $22.46
Will Laurel Worth be able to survive the alien environment into which she and her young family have moved?
Will Laurel Worth~and her marriage~survive the primitive, dangerous environment into which her husband, Justin, has moved the family? Laurel's early experiences in her new home - a two-room, thrown-together logging shack - include the near-fatal rescue of her young child from a rushing river; quarantining herself with a little girl with diphtheria; Justin's kidnapping by moonshiners and a near-death encounter with outlaws. Laurel, the daughter of an esteemed professor, has been a public figure most of her adult life as a well-known speaker for social issues such as women's right to vote. She is also a successful teacher with nurse training. Justin, college educated and already an accomplished, sought-after professional photographer, is an adventurer at heart.. Because of his background and his love for the forest, he impulsively takes a job supervising a logging camp in the remote mountains of western North Carolina. Will their true love for each other stand the test? Will Laurel's faith sustain and empower her? Will Justin overcome his fear of God and come to trust Him? Will they survive? The challenges demand choices. What choices will Laurel make? Set against the background of intriguing national and international historical events from the 1920s through the 1940s, this resolute, patriotic book showcases the indomitable American spirit . . . and the powerful truth that it is not our circumstances but our choices, empowered by God's adequacy, that determine who we become.
Justin was riding Tattoo home from town one Friday afternoon in autumn, enjoying being in the woods on his horse again. The Model-T and dusty roads saved time but couldn't compare with the enjoyment he felt with Tattoo's companionship. As he rounded a curve between two high banks, two masked men on horses faced him with pistols leveled. They were dirty and tattered. Their stance was tense. Justin knew these were the outlaws he had been warned about. His gut clenched as he drew Tattoo to a stop. "Hand over your payroll," one demanded. "Not even a 'howdy,' just orders," Justin said. "I said we want your payroll," "I don't have a payroll. My men go to Deerbrook to get paid." "You're lyin'." "Search me and see." They moved in on him, one on each side to search the saddlebags and his pockets. They kept the few dollars they found in his billfold. As the man on his right straightened up, his kerchief fell off his face down around his neck. Justin recognized a face he had seen on wanted posters all over town - Bill "Bandit" Butler had robbed and killed his way through three states. "Well," Butler drawled, "that's bad luck for you. You know we'll have to kill you now." His cold eyes looked at Justin as he lifted his pistol a few inches from Justin;s chest. Before Justin could react, a familiar voice on the bank said, "Drop your guns, both of you!" The outlaws looked around but held on to their pistols. "We've got two shot guns and two rifles aimed at you! Show 'em, boys!" Four masked men moved to the edge of the bank, their gun barrels pointed. The outlaws' pistols thudded to the ground. "Now listen to me good! This man and his family are friends of our'n. You touch 'em again and we'll hunt you down. We know exactly which cave you're holin' up in! Now git out!" The outlaws galloped away and one of Abner's men picked up their pistols. Abner jumped off the bank and held his hand up to help Justin dismount. Justin mopped his face with relief. "I would;ve met the undertaker if you hadn't happened by - or did you know . . . ?" ""We heard they was plannin' to jump you. The rest was guesswork. The Good Lord was not ready for you yet." "Thank you. I owe you!" "No," Abner said. "We still owe you one life. Your wife saved my wife and my son."
Exie Wilde Henson
Exie Wilde Henson is an educator, conference speaker and author. She grew up in the mountains of North Carolina, the setting of her book. She, her minister husband, Gene, and their three children have traveled, lived and worked internationally in numerous places. The author now lives in upstate South Carolina. Originally published as a book and a sequel, Laurel's Choices has now been revised and condensed into one enthralling novel! The low sales record and reviews is because the author was unable to market Laurel's Choices. She chose to be beside her husband daily as he traveled through the latter stages of Alzheimer's until the journey's end. She had no time or energy to pursue other goals. She is now starting to market her book.
Press the play () button to watch the author's book video

redpajama_set_name: RedPajamaCommonCrawl


text:
Home / Press Information Department / Government providing facilities to make the effective use of latest technologies for disable persons: Chairman NCSW
Government providing facilities to make the effective use of latest technologies for disable persons: Chairman NCSW
in Press Information Department June 28, 2019 232 Views | Short URL
Islamabad, June 28, 2019 (PPI-OT): National Council of Social Welfare (NCSW), Government of Pakistan organized a one-day special training workshop titled "Emerging Technologies for PWDs with Special Focus on their Economic Empowerment" in collaboration with Directorate General of Special Education (DGSE). Dr. Nadeem Shafiq Malik, Chairman NCSW presided the workshop while in the first session Ms. Wajiha Akrma, Parliamentary Secretary, M/o FE and PT was the chief guest and during the second session Ms. Sania Nashtar, Special Assistant to Prime Minster for Ehsaas Program was the chief guest.
A large number of representatives from civil society, prominent social activists, special persons, parents, teachers, students, government officials and other stakeholders attended the workshop. Dr. Nadeem Shafiq Malik, Chairman NCSW said in his presidential address Present Government is providing facilities in order to make the effective use of latest technologies for the persons with disabilities (PWDs), so that they may take part in the progress and prosperity of the country.
The use of latest technology will make Special persons financially empowered. Special persons are the essential part of our society. Many public institutions are working for their welfare. It is need of time that all these departments should work with coordination in order to resolve their problems timely. Ms. Sania Nashtar, Special Assistant to Prime Minster for Ehsaas Program addressed as chief guest and said that the foremost priority of the present government is to uplift poor segments of society. The initiative of Ehsaas Program with provides social protection, besides the austerity measures.
The budget of social protection program has been increased and doubled for the financial year 2019-20. The Prime Minister wants to ensure the social protection of Vulnerable Segments of the Society. It is our collective social responsibility to work with the present government to make a welfare state of Pakistan. The use of latest technology will increase income of special persons. Ms. Wajid Akram, Parliamentary Secretary, M/o FE and PT said that the government is also paying attention to special persons.
Prime Minister wants to remove their grievances. Government is ready to provide assistance to the private sectors in this regard. At this occasion other speakers Mr. Ammar Jafferi, CEO, CIT, Mr. Waqas Ramzan, Chief Web Officer, Blind Help Project, Mr. Shahmir Qudwai, delivered their lectures and said that latest technology have changed the lives of people. Universities should establish research centers and allocate more funds to get fruitful results. The students of Hamdard University performed practical demonstration of the use of latest technology for the help of special persons.
Principal Information Officer,
Press Information Department (PID)
Tel: +92-51-9252323, +92-51-9252324
Fax: +92-51-9252325, +92-51-9252326
Email: piopid@gmail.com
Website: www.pid.gov.pk
PID 2019-06-28
Tagged with: PID
Previous: Collaborative efforts by Muslim Ummah, imperative for stopping atrocities and human rights abuses by Israel: Qasim Khan Suri, National Assembly Deputy Speaker
Next: National seminar on "Pakistan's Economy: Challenges and Way forward" organized by Institute of Strategic Studies, Research and Analysis at National Defence University
Second Ehsaas Saylani Langar opens in Islamabad
Call on the Foreign Minister by the United States under Secretary of Defense


The accommodation is situated on the historic square of the town of Sušice on the 1st floor of the house with the view of the city center and the Otava River, bringing the piece of Šumava to Sušice.
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Between helping patients, learning and spending time with family (and dogs Otto and Henry!), there isn't a whole lot of free time in my busy schedule. However, when I find it, I squeeze in some (unconventional) reading, watching films, and live entertainment.
My top picks and my musical tastes? My favorite movie is Rio. This 3D computer-animated adventure-comedy was made in 2011 by the creators of Ice Age. (If you have little ones, I'm sure you remember this one!) Set in Rio de Janeiro, it features the voices of several Hollywood stars who tell the story of Blu, a little blue macaw (like "Flossie," the bird in our logo!), that falls in love with a female macaw named Jewel. Together they must get away from Nigel, a cockatoo that wants to smuggle them.
Why do I give it two thumbs up? It's all comes down to the parade scene, when Túlio's dentist sends an important message: "Don't forget to floss!" The dentist in me is always there!
I'm not your typical bookworm… Instead of escaping to a fictional world or getting into a series, I prefer (love) dental journals and textbooks. You heard correctly! Yes, I know I'm a bit obsessed … and it really doesn't leave time for pleasure reading.
Elton John rocks! I can't get enough of this legendary rock/pop icon. In fact, I'm such a big fan that I've seen him perform – not once, not twice, but THREE times! He's an incredible artist and he loves cocker spaniels! Sadly, his own beloved furry companion, Arthur, passed away earlier this year at age 14. Just like Otto, Arthur was always there by his owner's side – even serving as the Best Man at Elton's civil partnership ceremony. May Arthur play forever on the other side of the Rainbow Bridge.
During your next visit … tell me about your favorite books, movies, and adventures! I'd love to get to know you better.


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Detectives investigating the murder of a Russian exile in London believe he was previously the target of a poisoning attempt carried out by two mysterious men from Moscow who visited him in a Bristol hotel room, the Guardian has learned.
Nikolai Glushkov, a friend of the late oligarch Boris Berezovsky and a prominent Kremlin critic, was found dead in March at his home in New Malden, south-west London. He had been strangled.
Russia has been a useful bogeyman since its annexation of Crimea in 2014. UK military chiefs were spooked when Russia, during an intervention in Ukraine, used a combination of drones and artillery to destroy Ukrainian armour, and raised questions about whether the UK would be able to do much better than the Ukrainians in similar circumstances.


Brian Pasch and Orbee continue efforts to identify automotive marketing fraud.
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Toronto, Ontario ~ random streets ~ August 2015.
Very cool black and white series of random streets. Transfers a lot of atmosphere to the viewer.
Excellent street shots. Enjoy the festival.
Another set of superb, evocative images. I love the way you see things.
Great street shots, Hedy. Some have an air of mystery to them and I like that you present them in B&W. Have a great day. Cheers!
Wonderful street shooting and with the final stanza of the post, a face not spoiled by beauty is just perfect.


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WHITE GRAVY BEATS
White Gravy Blog
THIS DAY IN HIP-HOP...THE REALNESS
On this day in hip-hop history, Cormega released his debut studio album The Realness on Landspeed.
The former member of the group The Firm, Cormega, released his debut studio album The Realness on this day in 2001. The album featured production from a number of producers including Havoc and the Alchemist.
The album included features with Prodigy on the track "Thun & Kick," Mobb Deep on the hidden track "Killaz Theme II," and Tragedy Khadafi on the joint "They Forced My Hand."
The Realness reached #24 on the R&B/Hip-Hop chart.
Also on this day...
1997 - Company Flow released their full-length album Funcrusher Plus on Rawkus.
2014 - Common released his tenth studio album Nobody's Smiling on Def Jam.
2016 - Gucci Mane released ninth studio album Everybody Looking on Atlantic.
White Gravy
Sample Sunday
This Day In Hip Hop
This Day In Hip-Hop


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Apple May Be Tabling Health-Monitoring from its Watch, But It'll Still Pack a Punch
Ryan WallaceFeb 20, 2015 09:49 PM EST
(Photo : Apple)
While other wearable tech may be ahead of the curve, Apple continues to miss the mark when it comes to the development of its upcoming watch. While other models offered by competitors boast the ability to monitor heart-rate, amongst a myriad of other important vitals, Apple has announced that they are scrapping the health-monitoring tech from its upcoming product on account of problems with sensors and their regulators.
While the upcoming device has garnered quite a lot of attention from tech watchdogs eager to report what Apple will bring to the table next, it appears that inconsistencies with sensor readings have failed to meet the company's strict product standards. And seeing as factors such as hairy arms and sweaty skin greatly impacted the readings, Apple has rather decided to scrap the health-monitoring tech from the device and stick with what it does best.
"Apple also experimented with ways to detect blood pressure or the amount of oxygen in the blood, but the results were inconsistent" sources told the Wall Street Journal. "Moreover, if Apple interpreted the numbers to provide health or behavior advice, the company likely would have needed approval from the US Food and Drug Administration and other regulators."
But that doesn't mean they're throwing in the towel just yet.
According to reports, the company has asked its suppliers in Asia to begin the first quarter by making an estimated five to six million Apple Watches, leading many to believe that the product will finally hit shelves in April.
And it appears that the modified, more vanilla form of the Apple Watch will still pack quite a punch.
While headlines have pointed to Apple CEO Tim Cook implying that the new Apple Watch could help prevent cancer, the company has made it clear that its new features will help keep wearers active with a particular focus on new research. As new studies prove that a sedentary lifestyle further adds to growing risks of developing cancer, Apple has decided to get its customers up and moving.
"Some doctors now think that sitting down for long periods is the new cancer" Cook said in his keynote address at the recent Goldman Sachs Technology and Internet Conference. "So, ten minutes before the hour the Watch software taps you to make you have a walk around."
"It's quite funny to be in a meeting at Apple and ten minutes before the hour people get up and start moving around."
"But people like it."
More: Apple, Watch, technology, Apple Watch, Apple Inc., science, news, Ryan Wallace, health, medicine, health-monitoring, cancer


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Football - American
Subjects>Sports>Team Sports
What year was Super Bowl XLII?
Q: What year was Super Bowl XLII?
When did Super Bowl XLII happen?
Super Bowl XLII happened in 2007.
Who was the mvp of Super Bowl xlii?
Eli Manning was named the MVP of Super Bowl XLII.
Which was the better football game 2007 tostitos Fiesta Bowl or super bowl xlii?
Super bowl xlii
Super Bowl C?
only XLII superbowl's have been played super bowl C is superbowl 100!!!!! and superbowl XLII means 42!!!!! which the gaints won last year (2008 super bowl)
Who lost last year's Super Bowl?
As of 2009, last year's Super Bowl was XLII, which was lost by the New England Patriots.
What is the super bowl number for 2018?
Super Bowl XLII.
Who was the Super Bowl MVP this year?
The MVP of the most recent Super Bowl, Super Bowl XLII, was QB Eli Manning of the New York Giants.
Has Randy Moss won a Super Bowl?
no he has not won a super bowl his first super bowl was super bowl XLII
What time will the gates open for Super Bowl XLII?
Super Bowl XLII has already occurred. Super Bowl XLII happened on February 3, 2008 between the New England Patriots and New York Giants.
Who won Super Bowl XLII?
The New York Giants defeated the New England Patriots, 17-14, to win Super Bowl XLII. Click on the 'Super Bowl XLII' link below to read about the game.
What channel will broadcast Super Bowl XLII?
Super Bowl XLII was broadcast on FOX on February 3, 2008. That year, the New York Giants defeated the New England Patriots, 17-14.
How many Super Bowl rings does the Manning Family have?
Through Super Bowl XLII, the Manning family has two Super Bowl rings. Peyton won one in Super Bowl XLI and Eli won one in Super Bowl XLII.
Who's the G.O.A.T of the NFL?
Asked By Jason Legare
What was the BONUS ROUND answer last night?
Asked By Brian Norton
3/4 of the spectators are adults and 1/5 of the audits are woman what percentage of the spectators are woman?
Asked By epic hero
Why are professional headshots important?
Asked By Stuart Bailey
Strong team spirit, including ability to organize work according to needs and requirements of multiple team members and stakeholders?
Asked By Evans Dompreh
What platform can I watch all sports live?
Asked By tizi Ramos
which sports is more interested football and cricket?
Asked By fahees pc
what team do you play for now?
Asked By Vivek Dhavali


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ANDY RUIZ VS. ANTHONY JOSHUA II TO STREAM EXCLUSIVELY ON DAZN IN THE UNITED STATES
Press Release: By DAZN- NEW YORK, Sept. 4, 2019–The rematch between Andy Ruiz, Jr. and Anthony Joshua OBE will stream exclusively on DAZN in the United States on Saturday, Dec. 7.The three-continent press tour kicks off today in the fight's host city of Riyadh, Saudi Arabia, followed by stops in New York on Thursday and London on Friday.
Ruiz (33-1, 22 KOs) shocked the sports world in June when he toppled then-undefeated heavyweight world champion Joshua (22-1, 21 KOs) at Madison Square Garden, spoiling the former titlist's U.S. debut. Following the biggest heavyweight upset in decades, Joshua triggered an immediate rematch and the two now prepare to meet at a neutral site for this historic fight, which has been dubbed the "Clash on the Dunes."
"Their first fight captured the world's attention and once again illustrated that you never know what will happen when two heavyweight boxers enter a ring," said Joseph Markowski, DAZN EVP, North America. "Ruiz vs. Joshua II is by far the most-anticipated rematch in recent memory and adds to DAZN's year-end schedule, which will be the best stretch of boxing that fans have seen in years."
Joshua, 29, was scheduled to face Jarrell Miller on June 1in his U.S. debut, but when Miller failed multiple drug tests ahead of the bout, Ruiz, 29, was brought in as a replacement one month before the fight. Despite handicappers pegging Ruiz as a double-digit underdog, he scored boxing's most consequential upset in years, which catapulted him as an overnight celebrity. As the first heavyweight champion of Mexican descent, he will look to defend his titles against Joshua and prove that his victory was not a fluke, while Joshua looks to regain his status as the heavyweight division's kingpin.
Promoter Eddie Hearn said: "June 1, 2019 was a day that will be forever etched in boxing history. Andy Ruiz caused one of the great boxing upsets of all time when him and Anthony Joshua engaged in an epic battle in front of a sold-out MSG. The noise about the rematch has been deafening: Will it happen? Where will it be? Who will win? Step up the Kingdom of Saudi Arabia who will now host one of the biggest and most iconic boxing events of our generation. Held at a 16,000-person purpose built stadium that will stand within the UNESCO heritage site in Diriyah, 'Clash on the Dunes' will follow in the footsteps of the 'Rumble in the Jungle' and 'Thrilla in Manila.' The whole world will stop to watch this fight and sports fans across America will get the chance to watch it all unfold live on DAZN."
Since its launch in the U.S. one year ago, DAZN has quickly reshaped the boxing landscape by putting together the best schedule in the sport and making premium fights more affordable for fans. The 2019 "Fight Season" on DAZN is quickly coming together, featuring some of the biggest names and matchups in the sweet science, including:
Sept. 13– Devin Haney vs. Zaur Abdullaev & Amanda Serrano vs. Heather Hardy
Sept. 14– Jaime Munguia vs. Patrick Allotey & Ryan Garcia vs. Avery Sparrow
Oct. 5– Gennadiy "GGG" Golovkin vs. Sergiy Derevyanchenko
Oct. 12– Oleksandr Usyk vs. Tyrone Spong
Oct. 26– Regis Prograis vs. Josh Taylor (WBSS Junior Welterweight Final)
Nov. 7– Naoya Inoue vs. Nonito Donaire (WBSS Bantamweight Final)
Nov. 9– KSI vs. Logan Paul II
Dec. 7– Ruiz vs. Joshua II
Download DAZN on your TV or connected device to catch all DAZN live events, including the Ruiz vs. Joshua rematch on Dec. 7.Fans can keep up with the busy "Fight Season" schedule on DAZN's social media channels, including Twitter, Instagram, Facebookand YouTube, and can sign up now at www.DAZN.com.
About DAZN:
DAZN is the largest global sports streaming platform in the world. Since launching in 2016, DAZN has expanded across four continents with the app currently available for download in the United States, Canada, Germany, Austria, Switzerland, Italy, Spain, Japan and Brazil. In the U.S., DAZN has made its mark as an attractive alternative to pay-per-view within the combat sports industry. The platform features big fights from Matchroom Boxing, Golden Boy Promotions, GGG Promotions, Bellator MMA, the World Boxing Super Series and Combate Americas, all for one affordable price, on any device - including smart TVs, smartphones, tablets, games consoles and PCs. DAZN also features live MLB action each day of the season with its new daily show, ChangeUp. In September, the much-anticipated daily program The Pat McAfee Show debuts on the platform.
Material Courtesy of: DAZN Used with permission.
For more information about DAZN including schedules, availability around the world, list of compatible streaming devices/platforms/Smart TVs, and to subscribe please visit: www.DAZN.com
The Boxing Truth®is a registered trademark of Beau Denison All Rights Reserved.
Posted by Beau Denison at 12:27 PM
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In May 2013, Robyn Williams from Radio National's The Science Show interviewed veski innovation fellow Associate Professor Tiffany Walsh about her research in the area of materials science.
Nature has had millions of years for molecules and substances to be optimised for maximum effect. Be it hardness, stickiness, toughness or colour, nature has been working at it for a long time. Now materials scientists are combing the natural world for these chemicals to learn what allows them to perform as they do. The aim is to copy their techniques in the lab and create new materials for our use in manufacturing.


I also don't have much experience with lingonberry – actually, I've never used it in anything I cooked before, and I don't also eat it often, if ever. But in this recipe, it makes an incredible little twist in the cake – adding sour taste to the whole thing.
In the original recipe the surface of the cake is really smooth. I don't know how she did it and I don't have any spatula to do such a thing, so I just left it rough. In any case, I like rustic look for the foods anyway..
The cake is kept in the fridge – I kept it a little more than 24 hours in the fridge so that the tastes would develop slowly and nicely. As it is not kept in the freezer, it is soft enough to cut even as soon as you take it out of the fridge. However, in order to get the taste and the combination of all the layers and ingredients well enough, I would suggest to keep in room temperature for about 15 minutes before eating.
And one other good thing: the cake is both gluten free and vegan! Enjoy your raw cake!
1. Make the crust: Put ALL THE INGREDIENTS FOR CRUST in a food processor / blender and process until it's crumbly but feels like a dough, which can stick to the cake pan.
2. In the base of a springform cake pan (or any other mould you want) which is covered with non sticky baking sheet, put the crust dough and pressing with your hand, cover all the base. Put it in the fridge while you are working on the next layer.
3. Make the middle layer: Put ALL THE INGREDIENTS FOR MIDDLE LAYER EXCEPT LINGONBERRIES in a food processor / blender and process until they blend well and get as smooth as possible.
4. Add lingonberries in the mixture and mix well, but try not to crush the berries. Spread this on the crust layer. You can use a spoon or another tool to spread it firmly and in the meantime some of the berries will be crushed for sure. Just try to do it as carefully as possible. Put the cake back into the fridge while making the last layer.
5. Make the top layer: Put ALL THE INGREDIENTS FOR TOP LAYER in a food processor / blender and process it until it is as smooth as possible.
6. Pour the top layer on the rest of the cake and spread evenly. Try to make the surface as smooth as possible, or leave it in a rustic look. Put back in the fridge, overnight. I left for a little more than 24 hours. Decorate with lingonberries while serving.
I absolutely love your photography, the cake looks so moreish! And I completely agree about the expense of vegan baking, the cost of a packet of cashews is outrageous!
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Navicular bone
The navicular bone /nəˈvɪkjʊlər/ is a small bone found in the feet of most mammals.
For the bone in the human wrist/hand formerly called navicular, see scaphoid bone.
Bones of the human foot, with Navicularis labeled at upper left in image.
os naviculare
Anatomical terms of bone
The navicular bone in humans is one of the tarsal bones, found in the foot. Its name derives from the human bone's resemblance to a small boat, caused by the strongly concave proximal articular surface. The term navicular bone or hand navicular bone was formerly used for the scaphoid bone,[1] one of the carpal bones of the wrist.
The navicular bone in humans is located on the medial side of the foot, and articulates proximally with the talus, distally with the three cuneiform bones, and laterally with the cuboid.
It is the last of the foot bones to start ossification and does not tend to do so until the end of the third year in girls and the beginning of the fourth year in boys, although a large range of variation has been reported.[2]
Navicular bone. Superior view.
Navicular bone. Inferior view.
Fracture of the navicular bone
The tibialis posterior is the only muscle that attaches to the navicular bone. The main portion of the muscle inserts into the tuberosity of the navicular bone.[3] An accessory navicular bone may be present in 2–14% of the general population.[4][5][6]
The human navicular is not a commonly broken bone but it breaks due two reasons. The first mechanism is an stress fracture which happens commonly in athletes [7] and the other mechanism is a high energy trauma. Navicular bone is a keystone of the foot, it is part of coxa pedis and articulates with the talus, 1st,2nd and 3rd cuneiform, cuboid and calcaneus. It plays an important role in the biomechanic of the foot helping in the inversion eversion and also motion, it is a structural link between midfoot and forefoot and it is part of the longitudinal and transverse arch of the foot.
Horse anatomy
The horse has a sesamoid bone called the navicular bone, located within the hoof, that lies on the palmar aspect of the coffin joint between the second phalanx and third phalanx (coffin bone). The navicular bone in the horse is supported by the distal sesamoidean impar ligament and two collateral sesamoidean ligaments. The navicular bursa is located between the flexor surface of the navicular bone and the deep digital flexor tendon, which runs between the bursa and the distal phalanx.[8] The central tarsal bone in the hock of the horse is homologous and analogous to the navicular bone of the human foot, and thus the navicular bone in the horse is a different structure from the eponymously labeled bone in humans.[9]
The navicular region is an important structure in relation to lameness, particularly in the front feet, and is involved with a significant disease process called navicular disease or navicular syndrome. Recently much of the original literature concerning navicular disease has been called into question, particularly the significance of radiographic changes as a sole diagnostic criterion.[10] Navicular syndrome may be responsible for as much as 1/3 of all cases of lameness in horses, but radiographic changes in the navicular bone do not always provide a definitive diagnosis. Newer imaging techniques have shown that damage to the soft tissues in the region may be significant contributors to lameness and that multiple causes may result in visible lameness.[8]
Bone terminology
Terms for anatomical location
Equine forelimb anatomy
Wikimedia Commons has media related to Navicular bone.
"Gray's Anatomy, 6b. The Hand. 1. The Carpus. 4". 1918. Retrieved 11 May 2018.
Louise Scheuer & Sue Black (2004). The Juvenile Skeleton.
Bojsen-Møller, Finn; Simonsen, Erik B.; Tranum-Jensen, Jørgen (2001). Bevægeapparatets anatomi [Anatomy of the Locomotive Apparatus] (in Danish) (12th ed.). p. 293. ISBN 978-87-628-0307-7.
"Top Rated Foot Surgeons - Foot & Ankle Institute in Baltimore- Mercy".
"Wheeless' Textbook of Orthopaedics".
www.mynameiskaan.com. "Macrorad Teleradiology Case Report - SYMPTOMATIC ACCESSORY NAVICULAR BONE".
"Medical Update On Pau Gasol". Milwaukee Bucks. Retrieved 8 December 2019.
R. Wayne Waguespack, DVM, MS, DACVS R. Reid Hanson, DVM, DACVS, DACVECC (December 2010). "Navicular Syndrome in Equine Patients: Anatomy, Causes, and Diagnosis" (PDF). Surgical Views. Auburn University. Archived from the original (PDF) on 21 October 2012. Retrieved 11 January 2013. CS1 maint: multiple names: authors list (link)
Chapter 32, FRACTURE AND LUXATION OF THE TARSUS AND METATARSUS "Textbook of Small Animal Orthopaedics" written by Charles D. Newton, D.V.M., M.S. and David M. Nunamaker, V.M.D. J.B. Lippincott Company, 1985.
Citing Clinical Anatomy and Physiology Laboratory Manual for Veterinary Technicians, Colville, Thomas and Bassert, Joanna M. 2008 Publ. Mosby/Elsevier, Canada. "Navicular Bone - The distal sesamoid bone of the horse. The navicular bone is located deep in the hoof behind the joint between the middle and distal phalanges."
3D printable navicular bone model, free download in STL format (Embodi3D.com)
Bones of the human leg
greater trochanter
lesser trochanter
quadrate tubercle
upper medial: merges with intertrochanteric line
upper intermediate: pectineal line
upper lateral: gluteal tuberosity / third trochanter
adductor tubercle
patellar surface
epicondyles
medial
condyles
intercondylar fossa
posterior
intercondylar eminence
lateral tubercle
medial tubercle
tuberosity
soleal line
medial malleolus
Anterior colliculus
Posterior colliculus
fibular notch
lateral malleolus
calcaneal tubercle


text:
Q: Laravel Blade Template : combine string with variable from controller for @yield parameter My statement
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results in
 mastram masti mein aag lage <?php echo e($mast->basti); ?> mein

A: You need to do the concatenation of the variable here.
So you should do this
@section('description', 'mastram masti mein aag lage ' . $mast->basti . ' mein')

instead of
@section('description', 'mastram masti mein aag lage {{ $mast->basti }} mein')

redpajama_set_name: RedPajamaStackExchange


text:
Istituto di Scienza e Tecnologia dell'Inquinamento Luminoso
Light Pollution Science and Technology Institute
The night sky in the World Home Page
How we surveil the situation of the night sky with satellites
The DMSP satellite and its Operational Linescan System
The World Atlas of sea level artificial night sky brightness
Maps of the artificial night sky brightness
Maps of the total night sky brightness
Maps of the naked eye stellar visibility
Maps of the number of visible stars
Maps of the growth of light pollution
Maps of the night sky in selected sites
Our scientific papers
Our group of study
Light Pollution in Italy Web Site
Dep. of Astronomy University of Padova
National Geophysical Data Center - DMSP Nighttime Lights of the World
International Dark-Sky Association - DMSP nighttime images
NASA - DMSP pages
Earth View
The night sky live
Copyright 2000, P. Cinzano, Thiene, Italy
The night sky in the World
Satellite monitoring of the artificial night sky brightness and the stellar visibility
The night sky satellite surveillance
Our surveillance of the night sky is based on the measurements of the upward light flux emitted by the sources on the Earth surface obtained from the Defense Metereological Satellite Program (DMSP) of the United Stated Air Force. Images of the Earth at night have been obtained by DMSP satellites since early seventies and the first night-time image of the world showing the distribution of sources on the earth surface has been presented by Woodruff Sullivan in 1989. Since 1998 unsaturated data are available (obtained starting from 1996) which provide quantitative information on the upward flux emitted by sources.
Bright cities and towns in valleys of North US and Canada.
However satellite data don't give any direct information on the effects of this flux on the night sky due to light pollution propagation. The aim of our work is to study these effects.
Satellite data reduction
The DMSP satellite F12 is in a low earth polar orbit and carries an oscillating scan radiometer, the Operational Linescan System, with a photomultiplier tube (PMT) as detector. The OLS scans a narrow swath of the Earth, about 3,000 km wide, perpendicular to the orbit and as the satellite moves it constructs a bi-dimensional image of the Earth surface.
What we basically do is a composition of data obtained with different gains in order to improve dynamic range and to avoid saturation. Our data have a pixel size of 30"x30" (less than 1 km) in a latitude/longitude projection. The reduction steps include: (i) detection of cloud-free areas on infrared data; (ii) cleaning; (iii) calibration based on pre-fly radiance calibration of the OLS-PMT (we checked it comparing map prediction with observations and obtained a good agreement); (iv) Richardson–Lucy deconvolution to improve prediction for sites near the sources. We pass from the radiance measured from the satellite to the intensity emission in V band from each land area covered by a pixel, accounting for atmospheric extinction, the average spectrum of night time lighting and the surface of the area. However we need not only the intensity toward the satellite but also the intensity in every other direction. We obtain the average upward emission function by studying the emission per inhabitant of many sources at different distances from the satellite nadir, seen by the satellite under different angles. We can obtain this function for each land area corresponding to each pixel, using a large number of individual orbit data. This kind of study can be done only with a non geo-stationary satellite like DMSP satellites.
We obtain a number of different products which can be used for many purposes. Here a short description:
1) Maps of the upward light flux.
They are the simplest kind of map and show the total light flux emitted upward by the sources on the Earth surface and introducted in the atmosphere.
Map of the upward light flux from North-East Italy in 1996-1997.
They are obtained simply from the radiance calibrated data of the DMSP satellites. The data need to be corrected for the extinction on the light in the path from the source to the satellite. When possible they are deconvolved in order to obtain a better spatial resolution. The total emitted flux must be recovered from the flux emitted toward the satellite, assuming a typical average upward emission function for all the areas or obtaining it based on measurements of each area from different elevation angles made from many individual orbits.
2) Maps of the effects of the light pollution on the night sky.
The general public frequently confuse these maps with the night-time satellite images. Satellite night-time images of the Earth show the light flux emitted upward, these maps shows the effects of this light on the night sky due to its propagation in the atmosphere and its scattering by molecules and particles.
Differences are easily recognizable e.g. in lakes, seas or desertic lands near populated areas, where there are no sources.
Upward light flux (left) and its effect: the artificial night sky brightness (right).
They are black in satellite images but there is nonzero sky brightness (colour) in maps of artificial sky brightness due to light pollution propagation. Moreover the propagation of light pollution gives them a smooth appairance even if the resolution is nearly the same.
Upward light flux from Veneto cities measured by DMSP satellite.
Artificial night sky brightness in Veneto produced by the previous light flux.
These are the outlines of the method that we used to obtain the artificial sky brightness: (i) we divide the earth surface in land areas with the same positions and dimensions as the projections on the earth of the pixels of the satellite image; (ii) we compute the sky brightness seen in the chosen sky direction at the centre of each land area adding the contributions produced by all the areas inside a radius of 200km (for darkest sites we use 300km). The contributions are computed using the Garstang Modelling Technique (Garstang 1986, 1889a,b, 1991,1999, etc.; Cinzano 1999a,b,c) in few steps: a) We compute the light emitted by the source area and arriving to an infinitesimal volume of atmosphere along the line of sight of an observer, accounting for the extinction in the path; b) we account for light arriving in the volume after a previous scattering, for the earth curvature which shields part of the line of sight and, in some maps, for the screening due to terrain elevation and mountains; c) we compute the light scattered by molecules and aerosols in the volume towards the observer and the quantity of light arriving to the observer, accounting for extinction in this path too; d) we integrate along the line of sight.
The resolution of the maps, depending on the results of an integration over a large zone, is greater than the resolution of the original images and is generally of the order of the distance between two pixel centres (30''x30'', i.e. < 1 km).
The beautiful city of Venice send upward a very limited amount of light in comparison with other cities of the same population, due at its "romantic" lighting park (left image: Venice at low right and Mestre at upper left). Venice's zenith sky is imbedded in the pollution produced by Mestre and other cities (right image) but, however, it is still not much bright. Let's save the romantic low-intensity lighting of Venice!
a) Maps of the sea level artificial night sky brightness
The maps of the artificial night sky brightness at zenith at sea level allow to compare levels of light pollution in the atmosphere, to recognize more and less polluted areas and to identify the more polluting districts and the bigger sources.
These maps are intended to show the levels of pollution in the atmosphere rather than the stellar visibility which is the aim of the other maps described afterwards. The assumption of sea level and standard clear atmospherical conditions allows to compare pollution of different areas, to recognize more polluting sources or darker areas (areas with less light in the atmosphere and not areas where you see better the stars) without be confused by the altitude effects.
Map of the artificial night sky brightness in North-East Italy.
However you do not see a big difference accounting for altitude (e.g. in correspondence of Mount Ekar, at the borders of the padana plane, rising from sea level to 1350 m of elevation the artificial sky brightness diminishes less than about 20% whereas color levels in our maps shows each one three times larger brightness than the previous one.)
These maps do not give information on the star visibility, however mainly polluted areas usually are at sea level, so very approximately we can say that the orange level in our standard scale indicates areas where the milky way is not visible anymore. The red areas very approximately indicates zones where less than 100 stars are visible over 30 degrees of elevation. Blue border indicates artificial sky brightness over 10% than the natural brightness which is the definition of "light polluted sky". Yellow indicates an artificial sky brightness equal to the natural so that the total sky brightness is doubled.
b) Maps of the total night sky brightness
These maps of the the total night sky brightness show the quality of the night sky in the territory. They usually are computed at zenith, accounting for the elevation and the natural sky brightness. In smaller maps we also account for screening by mountain and terrain elevation.
Map of the total night sky brightness in North-East Italy.
The elevation has effect on the natural sky brightness, on the artificial sky brightness and on the stellar extinction and is obtained from a digital elevation map (DEM). The natural sky brightness depends on the chosen direction of view and on the altitude and it is obtained with Garstang (1989) models which account for the light coming from the entire sky and scattered along the line of sight of the observer and for the given atmospherical conditions. The mountain screening is obtained evaluating the elevation of each pixel along the line which connect each site with each source and then computing the maximum screening angle from which we determine the fraction of the line of sight shielded. This is very time consuming, in particular if the line of sight is not vertical and requires computation for each of its points.
c) Maps of the star visibility (naked eye limiting magnitude)
The maps of the stellar visibility (naked eye limiting magnitude) show the capability of the population to see the stars. They usually are computed at zenith, accounting for the extinction of the star light in the atmosphere from the top of the atmosphere to the observer and the eye capability to detect point sources over a light background. They are unsuitable to evaluate the light pollution of the atmosphere because the elevation and extinction of the light confuse the behaviour.
As an example, the mountains near the top of the image below could appear unpolluted because they have the same limiting magnitude than unpolluted zones of the sea at lover left corner. However the stellar extinction from an elevated site is less than from sea level and the number of particles and molecules which can scatter the artificial light is less too, so that limiting magnitude and stellar visibility increase with elevation. In conclusion the similar limiting magnitude in the mountains and in the unpolluted areas of the sea implies that the mountains are polluted SO MUCH that the stellar visibility there is comparable with the visibility from sea level. In fact the subsequent figure, a map of the "magnitude loss", shows the large differences between the mountains and the sea.
Map of the naked eye limiting magnitude in North-East Italy.
As Blackwell (1946) and many other authors showed, the relation between limiting magnitude and sky brightness is not linear and, moreover, it is a statistical concept. A number of random factors affect eye measurements (Garstang 2000; Schaefer 1991) like the individual eye capability, the individual pupil size, the experience that makes the observer confident of a detection at a probability level different from another, the duration of the observation and so on. So we can predict only the star visibility by an average observer even if we account for many details (e.g. observer pupil diameter depending on the age; Stiles-Crawford effect (a decrease of the efficiency in detecting photons with the distance from the centre of the pupil); colour differences between the laboratory sources and the observed star; colour differences between the laboratory sources and the night sky; differences between the night vision curve and the V band in computing the stellar extinction.
d) Maps of the loss of naked eye limiting magnitude
The maps of the loss of naked eye limiting magnitude show the loss of the capability of the population to see the stars. They are obtained simply by the difference between the map of the star visibility and a map of the same quantity evaluated assuming no light pollution in the area. The difference with the previous map is that in this case the effects of the pollutions are better shown everywhere but these maps are less useful to find the best observative sites.
Map of the loss of limiting magnitude in North-East Italy.
e) Maps of the number of visible stars
The maps of the number of visible stars shows how many stars are visible in the sky. The limiting magnitude can be related to the number of star which are visible in the sky but a detailed computation requires an evaluation of the stellar visibility in each direction of the sky and not only at the zenith, accounting for the increase of the stellar extinction with the zenith distance. This requires an incredible amount of computational time. This kind of maps are still under study.
f) Maps of the loss of visible stars
The maps of the loss of visible stars are simply obtained by difference between the map of the number of visible stars and a map of the same quantity evaluated assuming no light pollution in the area. Like the maps of the loss of naked eye limiting magnitude, these maps shows better the effects of the light pollution but are less useful to evaluate the capability of the population to see the stars.
3) predictions of the future effects of the light pollution on the night sky.
We are studying the effects of the increase of light pollution which is exponential almost everywhere with average yearly growth rates as large as 5%-10% measured both in US and Europe. Some projections have been already made for Europe and North America.
Growth of the night sky brightness in Veneto 1971-2025
4) Maps of tHE ENTIRE SKY OF INDIVIDUAL SITES.
The maps of the entire sky of individual sites can be obtained with an analogous method. We make maps of the artificial night sky brightness, the total night sky brightness and the naked eye limiting magnitude. All of them account for elevation, mountain and terrain screening, Earth curvature, atmospheric conditions, etc.


Every day people are injured at a worksite because accidents do take place. In most cases, business owners have workers compensation insurance coverage to take care of the hospital bills and forfeited compensation their employees have faced.
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text:
Jennifer Whalen is a Canadian actress and comedian, best known as one of the creators and stars of the sketch comedy series Baroness von Sketch Show.

An alumna of the Toronto company of The Second City, she was a writer for This Hour Has 22 Minutes before launching Baroness von Sketch with her castmates Meredith MacNeill, Aurora Browne and Carolyn Taylor.

At the 5th Canadian Screen Awards in 2017, the troupe were nominated for Best Ensemble Performance in a Variety or Sketch Comedy Series, and won the award for Best Writing in a Variety or Sketch Comedy Series; at the 6th Canadian Screen Awards in 2018, the troupe won the awards in both of the same categories.

She has also had acting roles in the television series InSecurity and The Beaverton, and wrote for the television series The Gavin Crawford Show, SketchCom, Instant Star, The Ron James Show, InSecurity and The Dating Guy.

Filmography

Television

References

External links

Canadian film actresses
Canadian television actresses
Canadian television writers
Canadian sketch comedians
Canadian Screen Award winners
Living people
This Hour Has 22 Minutes
Canadian women comedians
Canadian comedy writers
Canadian women television writers
Year of birth missing (living people)
21st-century Canadian comedians
Canadian Comedy Award winners

redpajama_set_name: RedPajamaWikipedia


This pocket-sized A6 colourful notebook from London's Happy Jackson is perfect for any notebook lover. Decorated with the words 'Stuff to do (when I can be arsed)', it makes the lovely letterbox friendly gift.
Based in London, Happy Jackson like to bring 'more awesome into everyday life' with their collection of fun and quirky gifts and accessories for all ages.


text:
Тара́с Володи́мирович Жирко́ ( 31 січня 1961, Львів, Українська РСР) — український актор театру і кіно, театральний режисер, Лауреат Премії ім. І.Котляревського (1995),Заслужений артист України (2002), народний артист України (2018).

Життєпис
Тарас Жирко закінчив Київський національний університет театру, кіно і телебачення імені Івана Карпенка-Карого у 1985 році (курс Народної Артистки України, професора — Валентини Зимньої).

Працював у Львівському ТЮГу — (1985-86)рр., служба в армії — 1986-87рр. З 1988 р. — актор Національного академічного українського драматичного Театру імені Марії Заньковецької (1988—2004)рр.

Від 2004 року — актор Національного академічного драматичногого Театру ім. І. Франка.

Влітку 2016 року разом з родиною приєднався до патріотичного флешмобу #яЛюблюСвоюКраїну, опублікувавши відеозвернення, у якому разом з дружиною Тетяною, донькою Анною-Марією та сином Володимиром-Іваном продекламували вірш Володимира Сосюри «Любіть Україну».

Фільмографія
 2018 — «Таємний щоденник Симона Петлюри» — Жан Пелісьє, кінооператор
 2012 — «Гайдамака» — Панько Хрущ, режисер Роман Синчук;
 2008 — «Владика Андрей» — Климентій Шептицький, режисер Олесь Янчук;
 2008 — «Батько напрокат» — Максим, режисер Артем Литвиненко;
 2004 — «Залізна сотня» — отець Кадило, режисер Олесь Янчук;
 1998 — «Сьомий Перстень Чаклунки» — Галат, режисер Борис Небієрідзе;
 1997 — «Роксолана 2. Улюблена дружина Халіфа» — Еневер, режисер Борис Небієрідзе;
 1997 — «Роксолана 1. Настуня» — Еневер, режисер Борис Небієрідзе;
 1995 — «Ісус, Син Бога живого» — головна роль, режисер Федір Стригун;
 1990—1996 — «…час збирати каміння», 9 серій— Стась Шиманський, режисер Володимир Андрощук;
 1992 — «Для домашнього огнища» — Поручник, режисер Борис Савченко; 1992 -''Одержима'' — Ісус, режисер Володимир Миронюк;
 1991 — «Одкровення Іоанна Першодрукаря» — Герасим Смотрицький, режисери: Ю.Сорокін, Ю.Швирьов;

Примітки

Посилання
 Жирко Тарас Володимирович  «Енциклопедія Сучасної України»

Українські кіноактори
Українські театральні актори
Заслужені артисти України
Уродженці Львова
Члени НСТДУ