text:
\section{\label{sec:intro}Introduction}

Quantum errors stem from undesired interactions with an outside environment.
There are many different interactions which may occur and their nature as well as their strength depend on the particular hardware architecture.
A natural assumption on the errors is that they are not adversarial, but are randomly distributed and localized.

It was shown by Shor~\cite{shor1995qec} that we can preserve quantum information by using \emph{quantum error correcting codes}.
The main idea is similar to what is done in classical error correction: redundancy is introduced by encoding some number of qubits $k$ into a larger number of \emph{physical qubits} $n$.
While for classical information (bits) we can introduce redundancy by keeping several copies, for quantum information it can be shown that copying of states is not possible by the laws of quantum mechanics, i.e. there is no device which takes any quantum state as an input and produces several copies of this state.
Despite this limitation it is possible to effectively encode a quantum state.
This is done by mapping the states of the $k$ logical qubits into non-local degrees of freedom of a highly entangled state of the physical qubits.
Although classical codes can not be used directly, there exists a construction due to Calderbank, Shor and Steane (CSS)~\cite{Calderbank1996,Steane1996} which takes two linear classical codes as an input and returns a quantum code.

In a quantum computer we manipulate quantum states using
a small set of unitary operators called quantum gates.
Gates applied to the encoded qubits are called \emph{logical gates}.
As the application of gates is prone to errors itself we would like to implement the logical gates using shallow depth circuits, meaning that only a small number of gates are being applied to the physical qubits to induce the logical gate.
Finding such circuits is a major challenge in quantum error correction and has thus far been done on a case-by-case basis.
For example, codes which are generated by the CSS construction (CSS codes) and encode a single logical qubit are known to have a fault-tolerant CNOT gate: it can be implemented on two copies of the same code by applying a CNOT between all pairs of physical qubits.

Here we apply the technique of variational circuit optimization to find fault tolerant logical gates for a given quantum error correcting code. Variational circuits have been used to parametrize wavefunctions, i.e. parametrize a unitary circuit transforming the $\ket{0}$ initial state. This approach has been used successfully to perform quantum chemistry calculations on Noisy Intermediate-Scale Quantum (NISQ) computers \citep{Peruzzo2014, Kandala2017, YingLiErrorMit, 1805.04492, 1808.10402}. The popular basic building blocks, called \textit{unit cells}, of these variational circuits are rotational gates $R_x,\,R_y,\,R_z$ and $\mathrm{CNOT}$ gates (see the Nomenclature and notation section of \cite{nelson_bible} for a definition). The specific mathematical properties of these gates makes optimizing the variational circuit relatively easy \cite{rotosolver, arXiv1903.12166}. In our case, we propose using variational circuits to find fault-tolerant logical gates for given quantum error correcting code.
Our procedure finds logical gates and their quantum circuit implementations by numerically optimizing
the variational circuit ansatz for both logical gates and their physical implementations (Fig.~\ref{fig:central_fig}).
Our procedure offers several benefits and much flexibility.
The ansatz used for the physical operation can be tailored to take advantage of the property of a specific quantum computing architecture.
The ansatz for the logical gate is variational and thus our procedure automates the discovery of logical gates given a quantum error correcting code.
The procedure can also target a specific logical gate when we fix the ansatz to this gate.
Therefore, for stabilizer codes and in particular for non-CSS codes, our procedure provides a straightforward first choice to find logical gates.
Furthermore, the procedure can be implemented on a quantum computer using quantum process tomography and is resource friendly for quantum codes requiring a small number of physical qubits.
It is hence feasible for an implementation on near-term quantum computers.

We note that in the literature, previous research has applied numerical optimization techniques to the field of quantum error correction for different purposes. Work in \citep{RobustQECViaCO, ChannelOptQEC, QECviaConvex, mario2018} used optimization algorithms (mostly convex optimization algorithms) to find error correcting quantum channels. Work in \citep{QVECTOR} demonstrated learning a circuit for preserving quantum information using a variational ansatz circuit. In \cite{CodesFromNN, RLforQEC} authors constructed quantum error correcting codes using neural networks. There is also a body of research using neural networks for decoding \cite{NeuralDecoderForTC, ScalableNNDecoder, RLDecoder, NNDecoderCircuitNoise, MLAssistedCor}. In this work, we applied similar optimization techniques to the novel problem of finding logical operators for quantum error correcting codes.

\textbf{Paper structure}. In this paper, we describe the procedure in detail in the Sec.~\ref{sec:results}
where we also present the results of simulation on a classical computer where we apply the procedure to several CSS codes and non-CSS codes.
The technical details of the simulation and the optimization are mentioned in Sec~\ref{sec:methods} and the data are attached with this paper in the Supplementary Information.
Among these results there are several new logical gates for the [[5,1,2]] code, the [[6,3,2]] code, and the [[8,3,2]] code,
which to our knowledge have not appeared previously in the literature, and which we discuss in detail in the Sec.~\ref{sec:new_gates}.
Finally, we make several comments on the benefits and disadvantages of our procedure in Sec~\ref{sec:discuss}.

\section{\label{sec:results}Results}

Here we present the procedure to find circuits which implement logical gates for error correcting codes. The procedure is inspired by the idea of circuit learning and uses ansatz circuits for both the logical gate and the physical operations that implement this logical gate in the encoded Hilbert space. Before we define this procedure, we first introduce the notation.

Commonly, an error correcting code encodes logical qubits (whose corresponding Hilbert space will be denoted as $H_A$),
into the subspace, denoted by~$L$, of another Hilbert space $H'=H_A\otimes H_B$.
This mapping is unitary and is denoted as $E: H_A\to L \subset H'$.
We call~$G$ a physical operation implementing the logical gate $g$ if it is
a unitary automorphism on~$L$ such that $E^{-1} G E \ket{\psi} = g \ket{\psi}$
for states $\ket{\psi}\in H_A$.

Now we present the procedure. We first describe how the procedure can be performed via simulation on a classical computer, and we describe its extension to quantum computer afterwards.
On a classical computer, we simulate the encoding, the physical operation, and the inverse encoding~$E^{-1}$.
While the encoding/inverse encoding circuit is fixed by the choice of a particular error correcting code, we use ansatze for both the physical operation~$G$ and the logical gate~$g$.
The ansatz for the physical operation is variational and may map logical states outside the logical space.
Because of this possibility, we instead apply a projector onto the codespace after the physical operation. This is achieved by measuring the stabilizer generators and applying a correction, where the correction is the minimum weight error compatible with the observed syndrome.
The stabilizer measurements and corrections are simulated classically as a unitary circuit acting on the extended Hilbert space $H'\otimes H_C$. Here the qubits in the~$H_C$ are all initialized to the $\ket{0}$ state.
We use a variational circuit as the ansatz for the logical gate, to enable automatic discovery of logical gates for the quantum error correcting code. Alternatively, we can set a fixed unitary gate as the logical gate, and try to vary the ansatz for physical operation to find an implementation for this unitary gate.

Our goal is to optimize the parameters for the ansatz circuits such that the for all possible input quantum states, a physical operation~$G$ together with the encoding, syndrome removal, and decoding circuit, act in the same way as a logical operation~$g$ (See Fig.\ref{fig:central_fig}).
Specifically, we minimize the loss function

\begin{equation}\label{eq:loss_classical}
    \mathcal{L}(\theta_1, \theta_2) = \sum_{i} \left(
        1 - \mathrm{F}\left(
        \mathrm{tr}_{B\otimes C} \left( \ketbra{\phi_{1,i}} \right), \ketbra{\phi_{2,i}}
        \right)
    \right) .
\end{equation}

Here $\phi^1_i$ ($\phi^2_i$) is the output of the trial logical circuit (comparison circuit) (see Fig.\ref{fig:central_fig}).
The input states $\{\psi_i\}_i^{N}$ form a tomographically complete set (the particular set of states we used in simulation is described in the Sec.~\ref{sec:tomography_complete}).
The trace $\mathrm{tr}$ is taken over the ancilla Hilbert space used for syndrome removal and the Hilbert space~$H_A$.
For two quantum states~$\rho$ and~$\sigma$, we define~$\mathrm{F}(\rho,\sigma)$ to be the fidelity between them. When the minimization is successful and the average fidelity is zero excluding float point errors, the procedure succeeds in finding a logical gate for this code.

\begin{figure}
\centering
\subfloat[Subfigure 1 list of figures text][Trial logical circuit]{
    \makebox[0.3\textwidth][c]{
    \Qcircuit @C=0.5em @R=1.0em @!R {
    \lstick{H_C: \ket{0}}     &\qw             &\qw                       &\qw                       &\multigate{2}{C}&\qw                     &\qw\\
    \lstick{H_B: \ket{0}}     &\multigate{1}{E}&\multigate{1}{\mathcal{N}}&\multigate{1}{G(\theta_1)}&\ghost{C}       &\multigate{1}{E^\dagger}&\qw & \rstick{\ket{\phi^1_i}}\\
    \lstick{H_A: \ket{\psi_i}}&\ghost{E}       &\ghost{\mathcal{N}}       &\ghost{G(\theta_1)}       &\ghost{C}       &\ghost{E^\dagger}       &\qw \\
    {\gategroup{1}{6}{3}{6}{2.2em}{\}}}
    }
    }
\label{fig:subfig1}}
\qquad
\subfloat[Subfigure 2 list of figures text][Comparison circuit]{
    \raisebox{-53pt}{
        \makebox[0.3\textwidth][c]{
        \Qcircuit @C=0.5em @R=1.0em @!R {
        \push{\rule{1em}{0em}} & & \lstick{H_A: \ket{\psi_i}} & \gate{g(\theta_2)} & \qw & \rstick{\ket{\phi^2_i}}
        }}
    }
\label{fig:subfig2}}
\\
\subfloat[Subfigure 3 list of figures text][Procedure]{
    \includegraphics[width=0.8\textwidth]{learning_logical_gate_loop.pdf}
\label{fig:subfig3}}
\caption{Learning logical gates \label{fig:central_fig}}
\begin{flushleft}
\footnotesize
To learn logical gates, we optimize angles~$\theta_1$ and~$\theta_2$ such that the trial logical circuit and the comparison circuit perform effectively the same unitary as measured by our loss function~$\mathcal{L}$.
Inside the trial logical circuit, the encoding/inverse encoding circuit~$E$/$E^\dagger$ maps input states $\{\psi_i\}_i^{N}$ into/out of the logical space. The ansatz $G(\theta_1)$ performs a series of physical operations and the circuit $C$ performs the stabilizer measurements and minimum weight error correction. In the comparison circuit, only the ansatz circuit $g(\theta_2)$ for the logical gate is performed.
The whole procedure starts with randomly initialize the two angles in both circuits, and then a tomographically complete set of quantum states are fed to the two circuits as inputs.
Their outputs are gathered and fed to the loss function $\mathcal{L}$.
The calculated loss function values are fed to a minimization algorithm which outputs new angles for~$\theta_1$ and~$\theta_2$.
Then we rerun the trial logical circuit and the comparison circuit again and the whole loop continues until $\mathcal{L}$ is zero excluding float point errors, in which case the circuit $G(\theta_1)$ will perform the logical gate~$g(\theta_2)$ on the encoded space.
\end{flushleft}

\end{figure}
Our method can be adapted to run on a quantum computer in order to find logical gates for larger error correcting codes and to tailor the ansatz to the specific quantum computing architecture. We briefly outline such an extension here. The main change with regards to the classical implementation concerns the encoding and inverse encoding circuits. Instead of implementing a (non fault-tolerant) encoding circuit, we need a certain method of reliably preparing encoded Pauli eigenstates on the quantum computer. Given these states, we apply the logical operation ansatz in the same way as the classical implementation. We can also implement an error correcting procedure after applying the logical operation ansatz. Finally, instead of implementing the inverse encoding circuit, we envisage performing logical measurements of the encoded states in the $X$, $Y$ and $Z$ bases. Using these measurement outcomes, we perform logical state tomography~\cite{Vogel1989,nelson_bible} on the output states, and compare the tomography results with the unencoded states obtained via classical simulation, using an analogous loss function to the one shown in Eq.~\ref{eq:loss_classical}.

The requirements of implementing our method on a quantum computer are relatively minor, as long as the number of logical qubits in the code is modest.
The only subroutines we would need to implement on the quantum computer are: preparing encoded Pauli eigenstates, applying a physical operation ansatz, and measuring Pauli observables.
Although the number of required logical Pauli measurements grow exponentially in the number of logical qubits, which might be a bottleneck of our proposed method.
Potentially one can utilize a swap test\cite{PhysRevLett.87.167902, quant-ph0105032}  for calculation of the loss functions.
Specifically, we may prepare in another error-corrected quantum computer the unencoded states, and analogously calculate the loss function in Eq.~\ref{eq:loss_classical} by a cross-device swap test.
We emphasize that our procedure can be applied to any code that can prepare encoded Pauli eigenstates and measure Pauli observables, i.e. it is not limited to qubit stabilizer codes.

\subsection{\label{sec:new_gates}Results for small codes}

We applied our procedure to a variety of small codes, as summarized in Table~\ref{tab:founded_gates_summary}. Of particular interest are the cases where non-Pauli logical gates were found by the experiment. In this section, we highlight the results of the experiment for the following codes: [[8,3,2]], [[8,2,2]], [[6,3,2]], and [[7,1,3]] surface code with a twist.

\newcommand{Pauli group}{Pauli group}
\newcommand{\newg}[1]{{\color{red}{\mathbf{#1}}}}
\begin{table}[]
\begin{threeparttable}
\caption{
Summary of quantum gates found by our procedure using classical simulation for a variety of small quantum error correcting codes.
}

\begin{tabularx}{1.0\textwidth}
{ | >{\raggedright\arraybackslash}X
  | >{\raggedright\arraybackslash}X | }
\hline
{\bf Code}                                                                                & {\bf Logical gate found by the procedure}                             \\ \hline
[[4,1,2]]~\cite{Kesselring2018}, [[8,2,3]]~\cite{Grassl:codetables}, [[8,3,3]]~\cite{Gottesman1996,Steane1996a,Calderbank1997}, [[11,5,3]]~\cite{Steane1996a}, [[12,6,3]]~\cite{Grassl:codetables}, [[13,7,3]]~\cite{Grassl:codetables}, [[14,8,3]]~\cite{Grassl:codetables}, [[15,7,3]]~\cite{Calderbank1996,Steane1996a} & Pauli group                                                    \\ \hline
[[4,2,2]]~\cite{Grassl1997,Vaidman1996}                                                                                & Pauli group, CNOT                    \\ \hline
[[5,1,2]]~\cite{Kubica2019}                                                                                & Pauli group, $\newg{S}$, $\newg{H}$                    \\ \hline
[[5,1,3]] (Five-qubit code)~\cite{Laflamme1996,Bennett1996}                                                                                & Pauli group,
$e^{i\pi/4}SH$,
$e^{i3\pi/4}XHXS^{\dagger}$,
$e^{-i3\pi/4}XHXS$,
$e^{-i\pi/4}HS^{\dagger}$,
$e^{-i\pi/4}S^{\dagger}H$,
$e^{-i3\pi/4}SXHX$,
$e^{i3\pi/4}S^{\dagger}XHX$
\\ \hline
[[6,3,2]]~\cite{Grassl:codetables} & Pauli group, $\newg{H}_{12}\newg{CZ}_{12}\newg{H}_{12}$ \\ \hline
[[7,1,3]] (Steane code)~\cite{Steane1996,Calderbank1996}                                                                                & Pauli group, Generators for the group generated by $H$ and $S$ \\ \hline
[[7,1,3]] (Surface code with a twist)~\cite{Yoder2017}                                                                                & Pauli group, $e^{-i3\pi/4}SXHX$, $e^{i3\pi/4}S^{\dagger}XHX$   \\ \hline
[[8,2,2]] (Projective plane 2D color code)~\cite{Vuillot2019} & Pauli group, $CZ$, $H^{\otimes 2} CZ H^{\otimes 2}$, $H^{\otimes 2}SWAP$
\\ \hline

[[8,3,2]]~\cite{Kubica2015,Campbell2016}                                                                                & Pauli group, $\newg{CZ}_{12}$, $\newg{CZ}_{13}$, $\newg{CZ}_{23}$, $CCZ$            \\ \hline
\end{tabularx}

\begin{tablenotes}
\item [1] The new logical gates we found, which have not been reported in the literature, are in highlighted in red and in boldface. For these logical gates, the parity check matrix of the corresponding quantum code and the physical operations which implement them are provided in OpenQASM\citep{openqasm} format in the Supplementary Information.
\item [2] The exact experimental configuration and optimization algorithm we used is discussed in the Sec.\ref{sec:methods}.
\item [3] We found a generating set of logical Pauli gates for the codes which we have labeled Pauli group in the column \textit{Logical gate found by the procedure}.
\end{tablenotes}
\label{tab:founded_gates_summary}
\end{threeparttable}

\end{table}

The [[8,3,2]] code is the smallest non-trivial 3D color code~\cite{Kubica2015,Campbell2016}. We found three transversal Clifford gates for this code which (to the best of our knowledge) have not previously appeared in the literature: $CZ_{12}$, $CZ_{13}$, and $CZ_{13}$, where $CZ_{ij}$ denotes a logical~$CZ$ acting on logical qubits $i$ and $j$. Our optimization procedure also provided a simple implementation of these gates, which we now explain.

Logical gates in the [[8,3,2]] code can be understood geometrically. Suppose we place qubits on the vertices of a cube, as shown in Figure~\ref{fig:CZ_832}. The stabilizer group of the [[8,3,2]] code can be generated by an operator consisting of Pauli-$X$ operators acting on every qubit, alongside operators that are associated with the faces of the cube, i.e.\ for each face, $f$, we have an operator $\Pi_{v\in f}Z_{v}$, where $Z_{v}$ denotes a Pauli-$Z$ operator acting on the qubit on vertex~$v$. With this definition, the logical $X$ operators of the code are associated with the faces of the cube ($\overline{X}_{1}=\Pi_{v\in f}X_{v}$ etc.) and the logical $Z$ operators are associated with the edges of the cube. We note that opposite faces support logical $X$ operators that act on the same encoded qubit, and the corresponding logical $Z$ operators are supported on the edges linking these faces.

To implement a logical $\overline{CZ}_{ij}$ gate, we apply $S=\text{diag}(1,i)$ and $S^{\dagger}$ gates in an alternating pattern to the vertices of a face that supports $\overline{X}_{k}$. We show this operator in Figure~\ref{fig:CZ_832}b and we denote it by $U$. We now show that $U$ implements a $\overline{CZ}_{ij}$ gate: namely it maps $\overline{X}_{i}$ to $\overline{X}_{i}\overline{Z}_{j}$, and has no effect on all other logical operators. First, we note that all operators that consist exclusively of Pauli-$Z$ operators are unaffected by $U$ because $S$ and $Z$ commute. Therefore, $Z$-type stabilizers and logical $Z$ operators are mapped to themselves by $U$. Next we consider operators that contain Pauli-$X$, which are transformed by $S$ as follows: $SXS^{\dagger}=Y=iXZ$. Consider the $X$ stabilizer of the code ($X$ on all the qubits). It is straightforward to see that~$U$ maps this operator to a product of itself and a $Z$ stabilizer associated with the face where we applied $U$ (the alternating pattern causes the factors of $i$ and $-i$ to cancel). Finally, consider $X_{i}$ (the blue face in Figure~\ref{fig:CZ_832}b). This operator is mapped to a product of itself and a $\overline{Z}_{j}$ operator with support on an edge that links the $\overline{X}_{j}$ faces (the green edge in Figure~\ref{fig:CZ_832}b). Similarly, $\overline{X}_{j}$ is mapped to $\overline{X}_{j}\overline{Z}_{i}$

\begin{figure}[h]
    \centering
    \subfloat[]{
        \begin{tikzpicture}[scale=0.5]
            \coordinate[label=below:8] (A) at (0,0,0);
            \coordinate[label=below:4] (B) at (0,0,4);
            \coordinate[label=above:7] (C) at (0,4,0);
            \coordinate[label=above:3] (D) at (0,4,4);
            \coordinate[label=below:6] (E) at (4,0,0);
            \coordinate[label=below:2] (F) at (4,0,4);
            \coordinate[label=above:5] (G) at (4,4,0);
            \coordinate[label=above:1] (H) at (4,4,4);
            \coordinate[label={[label distance=-0.5cm]0:$\overline{X}_{1}$}] (X1) at (4.25,2,2);

            \coordinate[label={[label distance=-0.5cm]0:$\overline{X}_{2}$}] (X2) at (2.5,2.1,4);
            \coordinate[label={[label distance=-0.5cm]0:$\overline{X}_{3}$}] (X3) at (2,4,2);
            \draw [dashed] (A) -- (B);
            \draw [dashed] (A) -- (C);
            \draw [dashed] (A) -- (E);
            \draw (B) -- (D);
            \draw (B) -- (F);
            \draw (C) -- (D);
            \draw (C) -- (G);
            \draw (D) -- (H);
            \draw (E) -- (F);
            \draw (E) -- (G);
            \draw (F) -- (H);
            \draw (G) -- (H);
            \draw[fill=red, fill opacity=0.2] (E) -- (F) -- (H) -- (G) -- cycle;
            \draw[fill=blue, fill opacity=0.2] (B) -- (F) -- (H) -- (D) -- cycle;
            \draw[fill=green, fill opacity=0.2] (C) -- (D) -- (H) -- (G) -- cycle;
        \end{tikzpicture}
    }%
    \qquad
    \subfloat[]{
        \begin{tikzpicture}[scale=0.5]
            \coordinate (A) at (0,0,0);
            \coordinate (B) at (0,0,4);
            \coordinate (C) at (0,4,0);
            \coordinate (D) at (0,4,4);
            \coordinate[label=below:$S$] (E) at (4,0,0);
            \coordinate[label=below:$S^{\dagger}$] (F) at (4,0,4);
            \coordinate[label=above:$S$] (G) at (4,4,0);
            \coordinate[label=above:$S^{\dagger}$] (H) at (4,4,4);
            \draw [dashed] (A) -- (B);
            \draw [dashed] (A) -- (C);
            \draw [dashed] (A) -- (E);
            \draw (B) -- (D);
            \draw (B) -- (F);
            \draw (C) -- (D);
            \draw (C) -- (G);
            \draw (D) -- (H);
            \draw (E) -- (F);
            \draw (E) -- (G);
            \draw[green, line width=0.4cm] (F) -- (H);
            \draw (G) -- (H);
            \draw[fill=blue, fill opacity=0.2] (B) -- (F) -- (H) -- (D) -- cycle;
        \end{tikzpicture}
    }
    \caption{$CZ$ gates in the [[8,3,2]] code. Qubits are placed on the vertices of the cube. In (a), we highlight three logical $X$ operators of the code, namely $\overline{X}_{1}=X_{1}X_{2}X_{5}X_{6}$ (red face), $\overline{X}_{2}=X_{1}X_{2}X_{3}X_{4}$ (blue face), and $\overline{X}_{3}=X_{1}X_{3}X_{5}X_{7}$ (green face). Three corresponding logical $Z$ operators are: $\overline{Z}_{1}=Z_{1}Z_{3}$, $\overline{Z}_{2}=Z_{1}Z_{5}$, and $\overline{Z}_{3}=Z_{1}Z_{2}$. (b) Suppose that we apply $S$ and $S^{\dagger}$ gates to the vertices on the face that supports $\overline{X}_{1}$. This unitary maps $\overline{X}_{2}$ (blue face) to $\overline{X}_{2}\overline{Z}_{3}$ (blue face and green edge). Likewise, $\overline{X}_{3}$ is mapped to $\overline{X}_{3}\overline{Z}_{2}$. Therefore, this unitary implements a logical $\overline{CZ}_{23}$ gate.}
    \label{fig:CZ_832}
\end{figure}

In addition, our procedure found a transversal implementation of $CCZ$ for the [[8,3,2]] code. This gate was known previously~\cite{Kubica2015,Campbell2016}, however the fact that our procedure found a non-Clifford gate ($CCZ$) with no prior knowledge about the structure of the code is notable. It is often relatively straightforward to implement Clifford gates and Pauli measurements in error correcting codes. Such operations are classically simulable, but they can be promoted to universality by adding a single non-Clifford gate. However, codes with transversal non-Clifford gates are rare, and understanding the structure of such codes is an active area of research~\cite{Kubica2015a,Kubica2015,Vasmer2019,Vuillot2019,Rengaswamy2019}. Most examples of constructions of code families with non-Clifford gates exploit some specific structure of the code family, such as tri-orthogonality~\cite{Bravyi2012,Campbell2017,Campbell2017a}. Our procedure may be capable of finding fault-tolerant non-Clifford gates for codes whose structure is opaque to us. In particular, the structure of non-CSS codes with non-Clifford gates is poorly understood, so our procedure may be able to shed some light on this area given enhanced computational resources.

We successfully found non-Pauli gates for codes related to 2D color codes: the [[8,2,2]] code (2D color code defined on a projective plane~\cite{Vuillot2019}) and the [[6,3,2]] code (subcode of a 2D color code defined on a hexagon~\cite{Criger2016}). For the [[8,2,2]] code, we found the gates that we would expect to find in a 2D color code with two logical qubits: logical $CZ$ implemented by transversal $S$ and $S^{\dagger}$, logical $H^{\otimes 2} CZ H^{\otimes 2}$ implemented by transversal $\sqrt{X}$ and logical $H^{\otimes 2}SWAP$ implemented by transversal $H$. And we found that the [[6,3,2]] code inherits one of the transversal gates of its parent 2D color code (the [[6,4,2]] code~\cite{Criger2016}): $CZ_{12}$ implemented by transversal $S$ and $S^{\dagger}$.

\begin{figure}[ht]
    \centering
    \includegraphics{cube-octahedron.pdf}
    \caption{An illustration of the Clifford gate $K_{1,1,1}=e^{i\pi/4}SH$. This gate maps $\ket{0}\rightarrow\ket{+i}$, $\ket{+i}\rightarrow\ket{+}$, and $\ket{+}\rightarrow\ket{0}$ (up to global phases). It can be understood geometrically by considering an octahedron embedded in the Bloch sphere. The operation performed by the gate is a clockwise rotation of $2\pi/3$ around the axis which is normal to the face marked with a red circle. The $\ket{+}$ state is at the front unlabeled vertex of the octahedron.}
    \label{fig:my_label}
\end{figure}

Our procedure also found transversal Clifford gates for the [[7,1,3]] surface code with a twist. As was noted in~\cite{Yoder2017}, this code has transversal implementations of the octahedral Clifford gates, which are defined as follows:
\begin{equation}
    K_{x,y,z}=\exp{i\frac{\pi}{3\sqrt{3}}(xX+yY+zZ)},
\end{equation}
where $x,y,z\in{-1,1}$. These gates cyclically permute the Pauli operators. We can decompose these octahedral gates into products of more familiar Clifford gates as follows:
\begin{equation}
\begin{split}
    &K_{1,1,1}=e^{i\pi/4}SH, \\
    &K_{1,-1,1}=e^{i\pi/4}HS, \\
    &K_{1,1,-1}=e^{i3\pi/4}XHXS^{\dagger}, \\
    &K_{-1,1,1}=e^{-i3\pi/4}XHXS,
\end{split}
\qquad
\begin{split}
    &K_{-1,-1,-1}=e^{-i\pi/4}HS^{\dagger}, \\
    &K_{-1,1,-1}=e^{-i\pi/4}S^{\dagger}H, \\
    &K_{-1,-1,1}=e^{-i3\pi/4}SXHX, \\
    &K_{1,-1,-1}=e^{i3\pi/4}S^{\dagger}XHX.
\end{split}
\end{equation}
The specific gates we found in our experiments were transversal realizations of $K_{-1,-1,1}$ and $K_{1,-1,-1}$.

\section{\label{sec:discuss}Discussion}

\newcommand{\texttt{Rotosolve}}{\texttt{Rotosolve}}

We comment on several aspects of our procedure here.
Firstly, we mention here a rough resource estimate of our proposed procedure. For the calculation of the loss function in Eq.~\ref{eq:loss_classical}, we require the the full process tomography of the encoded logical space, which requires a number of quantum circuit runs growing exponentially with respect to the number $k$ of logical qubits. However, this cost is benign when $k$ is small and can further mitigated by running these circuits in parallel on multiple computers. Also, due to the fact that transversal ansatz is mostly likely to be used as the ansatz for logical gates, we expect a friendly linear growth of the number of parameters with respect to the number of physical qubits ($n$) in Eq.\ref{eq:loss_classical} which we need to optimize. In the classical simulations we have done, typically one optimization converge in less than 5 hours running on a commercially available GPU (Nvidia~RTX~2080~Ti).

Secondly, our optimization benefits from the use of \texttt{Rotosolve} \citep{rotosolver} optimization algorithm, which depends largely on the fact that the functional dependency of the lost function in Eq.\ref{eq:loss_classical} is sinusoidal due to the parametrized rotation gates we have used for the ansatze (see Appendix~\ref{sec:expsetup}).
Adapting our procedure for specific quantum computation hardware might require a different set of parametrized gates and might invalidate the use of \texttt{Rotosolve}. In this case, the optimization will be harder due to the non-convex nature of the loss function and the high number of parameters.

A promising future research avenue would be to use our procedure to explore quantum codes that have not been as extensively studied as qubit stabilizer codes. Qudit quantum codes are a natural example, where a qudit is the $d$-dimensional analogue of a qubit. The stabilizer formalism can be extended to prime (or prime power) qudits~\cite{Gottesman1999}, which means that it would be straightforward to generalize our procedure to these cases. Considerably less research has been done into implementing logical gates in qudit stabilizer codes compared with qubit stabilizer codes, so we may be able to find more unknown fault-tolerant gates in the qudit context. In addition, we emphasize that our procedure is not limited to stabilizer codes, and can be applied to non-stabilizer codes e.g.\ the codes described in~\cite{Cross2009}.

In summary, we have proposed a procedure to automate the discovery of logical gates using shallow quantum circuits for a given quantum error correcting code.
The ansatz for the logical gate can be tailored to a specific quantum computing architecture to take advantage of this architecture.
We have shown that it can find logical gates available in the current literature for a number of error correcting codes and it additional produces new logical gates for the [[5,1,2]] code, the [[6,3,2]] code, and the [[8,3,2]] code.
Although the procedure is simulated classically, we have proposed an extension of this procedure on quantum computers and we believe an implementation on near-term quantum computers for error correcting codes requiring a small number of qubits is feasible.

\section{Methods\label{sec:methods}}

\subsection{Experimental setup for Table~\ref{tab:founded_gates_summary}\label{sec:expsetup}}

In the simulation experiments shown on Table~\ref{tab:founded_gates_summary} (except for the [[5,1,2]] code), the ansatz for logical operation is transversal, which is naturally fault-tolerant. A transversal ansatz is formed by using three single qubit rotation gates ($\mathrm{R_{j}} = e^{-i\theta \sigma_{j}/2}$, where $\{\sigma_{j}\}_{j=x, y, z}$ are the three Pauli matrices) on each physical qubit, where each rotation gate has its own angle that can be adjusted independently of other rotation gates.
For the parameterization of the logical gate $g(\theta_2)$, we use the ansatz which parametrizes arbitrary unitary transformation on the Hilbert space $H_A$.
Denote the number of qubits in $H_A$ as $n_a$.
When $n_a=1$, the ansatz is simply the three single qubit rotation gates mentioned before.
When $n_a=2$, the ansatz is the circuit shown in Fig.2 in \cite{quant-ph-0308033}.
When $n_a=3$, we obtain a circuit parametrization for arbitrary three qubit unitary gates using the \texttt{QSD} decomposition provided by \citep{universalQCompiler}.
When $n_a > 3$, only the first three qubits are selected on which we apply the three qubit ansatz mentioned previously. This is because the exponential increase of the possible ansatze makes experimentation infeasible.

We note that for the experiments on the code $[[4,2,2]]$ in the table, the encoder used only encodes one of the two logical qubits and we only experimented on this logical qubits.
In addition, as an early stage proof of principle that our procedure can find entangling gates, we targeted the logical gate CNOT for this code $[[4,2,2]]$ in one experiment
In this experiment, we encoded a pair of qubits in two copies of the [[4,2,2]] code (one encoded qubit per code). We then used a transversal two-qubit gate ansatz, where each gate coupled corresponding qubits in the different codes. Using this ansatz, we were able to find a transversal logical CNOT gate between the codes. The physical operation that implemented this logical gate is simply CNOT gates between corresponding qubits in the different codes. This shows that our method is capable of finding gates acting between separate codes.

In the case of the [[5,1,2]] code, we used a non-trasversal but still fault-tolerant ansatz for the logical gate. Specifically, we used a transversal ansatz (as described above) for three of the qubits, and an parametrization of an arbitrary two-qubit unitary for the final two qubits. This choice of ansatz was motivated by the structure of the code~\cite{Kubica2019}. The fact that we found logical gates (including non-Pauli gates, see Table~\ref{tab:founded_gates_summary}) using this ansatz shows that our procedure can work well with ans\"{a}tze that are tailored to a particular code.

For minimization, we used the minimization algorithm \texttt{Rotosolve}\cite{rotosolver} to minimize the $\mathcal{L}$.
\texttt{Rotosolve} specializes in minimizing function of the form $\bra{0} U(\theta)^\dagger H U(\theta) \ket{0}$, where $U$ is the unitary transformation of a quantum circuit made from constant unitary gates and variational rotation gates $\mathrm{Rx}$, $\mathrm{Ry}$, and $\mathrm{Rz}$.
It is easy to see our loss function defined in Eq.~$\ref{eq:loss_classical}$ follows the same form if we consider $\Tr_\mathrm{ancilla}(\ketbra{\phi_{2,i}})$ to be the $H$, and $g(\theta_2)$ to be the $U$.

We note that for performance issues, the simulation was carried out using proprietary software written by the author HX for Rahko Ltd.

\subsection{Tomographically Complete Set\label{sec:tomography_complete}}

For a quantum channel $\varepsilon$, its action on the any quantum state $\rho$ can be uniquely determined by
its action on some $\{\psi_i\}$ which forms a tomographically complete set\citep{nelson_bible}.
An straight-forward example of a tomographically complete set is $\{\psi_i\}$ such that
$\{\ketbra{\psi_i}\}$ forms a basis for all density matrices. In our case, we only need a set of $1$ qubit states such that $\{\ketbra{\psi_i}\}$ forms a basis for all $2\times 2$ density matrices, since for $2^n\times 2^n$ density matrices, the tensor products of this set of $1$ qubit states form a complete tomography set.

Now we describe the six states, which we call the \textit{six Bloch states}, which we use as the initial states for our experiments. These states are,

\begin{align}
    \{\ketbra{\psi_i}\} = \{
    \ket{0}, \ket{1}, \ket{+}, \ket{-}, \ket{+i}, \ket{-i}
    \}
\end{align}

Here we show that any $2\times 2$ matrix can be expressed (non-uniquely) by the density matrices corresponding to the six Bloch states.
And therefore, any $n$-qubit density matrix can also be expressed by tensor products of the six Bloch states.
Therefore, tensor products of the
six Bloch states forms a complete tomography set for $n$-qubit quantum channel.

Let $\vec{a}=(a,b,c,d,e,f\}$, and let $\vec{b'}$ be the density matrices of states in $\{\ketbra{\psi_i}\}$. We can check that,

$$\vec{a} \vdot \vec{b'} =
\left(
\begin{array}{cc}
 a+\frac{c}{2}+\frac{d}{2}+\frac{e}{2}+\frac{f}{2} & \frac{c}{2}+\frac{f i}{2}-\frac{d}{2}-\frac{i e}{2} \\
 \frac{c}{2}+\frac{e i}{2}-\frac{d}{2}-\frac{i f}{2} & b+\frac{c}{2}+\frac{d}{2}+\frac{e}{2}+\frac{f}{2} \\
\end{array}
\right).
$$

To express any $2 \times 2$ matrix $\rho$ as linear combinations of $\vec{b'}$, we consider the
linear equation $\vec{a}\vdot \vec{b'} = \rho$. It can be written as $A\vdot \vec{a} = \vec{c}$,
where $\vec{c}$ is the vector of elements of $\rho$, $A$ is the coefficient matrix:
$$
A = \left(
\begin{array}{cccccc}
 1 & 0 & \frac{1}{2} & \frac{1}{2} & \frac{1}{2} & \frac{1}{2} \\
 0 & 0 & \frac{1}{2} & -\frac{1}{2} & -\frac{i}{2} & \frac{i}{2} \\
 0 & 0 & \frac{1}{2} & -\frac{1}{2} & \frac{i}{2} & -\frac{i}{2} \\
 0 & 1 & \frac{1}{2} & \frac{1}{2} & \frac{1}{2} & \frac{1}{2} \\
\end{array}
\right).
$$

Since the rank of $A$ is $4$, the rank of the augmented matrix $[A|c]$ is also $4$, hence the above linear equation $A\vdot \vec{a} = \vec{c}$ has infinitely many solutions.

redpajama_set_name: RedPajamaArXiv


1 carbon is the notebook thinkpad x fast and durable. Therefore it is advisable above all as a compact office companion. His display shows crisp content such as photos and videos hot, if also somewhat pale. But due to the anti-reflective coating of the screen. The hammer: with its weight of only 1,192 grams it is among the lightest notebook ever ideal for daily transport from a to b. And thanks to built-in lte module 14 can be with zöller even mobile surfing the internet. Best price on the internet: 1,729.00 euro * per order this product at amazon very high pace of work sharp, brilliant display of long battery life very light weight soft, memory expandable wireless-ac, lte module cons for elaborate games built unsuitable under full load some high heat at the bottom mark of editor 2.23 good users rating now the laptops from the thinkpad rate-x 1 series are no bargain. You should not convince little weight and spacious facilities with plenty of power, about the price. 1 carbon creates lenovo the x windows-10 model? The detailed test by computer clears that image.
as the name of the product implies, the x is 1 in a chic black carbon casing, which is characterised by a high torsional stiffness. The screen is firmly installed, works out but up to 180 degrees backwards. So, the notebook can be lay flat on the table. Tip: thanks to carbon housing the x 1 weighs only 1,192 grams a very good value for a 14-inch notebook. A pity that the power supply is so hard (364 grams).
but the x has a really good display 1 carbon: it shows photos and videos in 16:9-format with 2560 x 1440 pixels pretty hot and it has a slightly matt surface. This ensures less reflections makes colors appear but slightly paler than when not anti-glare screens. Class: the x 1 works with a strong skylake processor. The intel core i7-6500u is a real top model fast and energy-saving. Together with a snappy ssd, it ensures a very high pace of work. For complex games, the power not enough the built-in graphics card. Even with reduced resolution (1366 x 768) calculated at current directx 11 games only seven frames per second. Only older directx 9 games were reasonably liquid across the screen.
Almost 2,000 euros will be due for the lenovo thinkpad x 1 carbon, but that the manufacturer promises too much. The test checks what is on it. Lenovo thinkpad x 1 carbon in the test: high end dream of carbon?
good: the fan of the x 1 carbon remained mostly pretty quiet, video watching, he turned in a whisper mode. Only under full load, the fan noise (1.8 sone) was disturbed. The battery of the carbon has hung much steam: when working, the screen remained after four hours and 37 minutes black, video playback was after four hours and 18 minutes end. Also good: the comparatively short time of one hour and 56 minutes.
Little software, otherwise much about it?
the x 1 is an elegant notebook, but software equipped lenovo too: as standard, there is only windows 10 in the pro version, everything else will cost extra. The hardware is clearly more generous: the tested trim level has a 256-gigabyte ssd and 8 gigabytes of memory. If you want, you can order a larger ssd. Up to 1 terabyte are possible. And the memory can be expanded also.


text:
Home Social Security Disability New Jersey Salem County
Salem County Social Security Disability Lawyers
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Marianne Rebel Brown
Gloucester County, NJ Social Security Disability Attorney with 37 years of experience
(856) 881-5000 103 S. Main St.
Glassboro, NJ 08028
Social Security Disability, Divorce, Domestic Violence and Family
New England Law | Boston
My practice focuses on legal issues within the family. My firm handles divorce, civil union dissolution, custody, child support, adoption, parenting time, domestic violence victim representation, parental representation in DYFS matters, representation for child abuse registry defense. We also handle personal injury, criminal, municipal court, academic discipline, faculty tenure and workman's compensation matters. Our primary counties are Camden, Gloucester, Cumberland, Salem, Burlington, Atlantic, Ocean and Cape May.
Mr. Michael Joseph Dennin
Camden County, NJ Social Security Disability Lawyer with 17 years of experience
(856) 577-9138 5709 Westfield Ave.
Free ConsultationSocial Security Disability, Nursing Home, Personal Injury and Workers' Comp
Widener University Commonwealth Law School and University of Scranton
Mr. Michael Dennin is an experienced personal injury trial attorney, now in his 16th year of practice. Mr. Dennin rose up through the ranks at the Camden County Bar Association, where he is President for the 2019-2020 year. Mr. Dennin is Co-Chair of the New Jersey State Trial Lawyers Association's Worker' Compensation Section, and multi year award winner of SJ and South Jersey Magazine's Top Rated Personal Injury and Workers Compensation Lawyer. Mr. Dennin has been selected as a Rising Star and Superlawyer in the State of New Jersey. Mr. Dennin has a track record of...
Suzanne Holz Meola
Camden County, NJ Social Security Disability Attorney with 34 years of experience
(888) 675-7607 Beowulf Plaza
1814 E. Rt 70, Suite 336
Free ConsultationSocial Security Disability and Workers' Comp
Ms. Holz Meola heads the Social Security Disability Department at Petro Cohen, P.C. and has nearly 30 years of legal experience. In addition to Social Security disability, she handles workers' compensation claims for the firm. Ms. Holz Meola graduated cum laude from Mount St. Mary's College (Emmitsburg, MD) in 1986 with a Bachelor of Arts degree, majoring in political science and minoring in business. In 1989, she received a Juris Doctor degree from Dickinson School of Law of Pennsylvania State University (Carlisle, PA). As part of her legal education, Ms. Holz Meola assisted in providing free legal services to victims of...
Eric A. Shore
(800) 226-8967 8 Ranoldo Terrace
Social Security Disability, Employment, Personal Injury and Workers' Comp
President/Managing Attorney, since January 1, 1999 of Law Offices of Eric A. Shore. Eric A. shore has helped more than 40,000 injured and disabled workers to receive a total of more than $250,000,000 in settlements and expected lifetime benefits. Areas of Practice: Social Security Disability, Personal Injury, Workers' Compensation
Richard Lowell Frankel
(856) 795-8880 725 Kenilworth Ave
Ste. 2
Free ConsultationSocial Security Disability, Employment, Insurance Claims and Workers' Comp
We get to work when you can't. Out practice has helped thousands of people who are disabled or unable to work, and veterans who suffer from injuries or illness that are service-connected. We help individuals apply for an appeal long-term disability insurance claims, Social Security disability and SSI, Veterans benefits, Workers Compensation claims, and employment discrimination and wrongful termination cases.
Philip Wolf
(800) 974-6670 52 Haddonfield-Berlin Road
Social Security Disability and Military
As the founding partner of Wolf & Brown Law Offices, Mr. Wolf has been representing Social Security claimants since 1980.
Mr. Wolf is a 1968 graduate of Temple Law School and completed his undergraduate studies at Temple University as well. A native of South Philadelphia, Mr. Wolf knew adversity from a very young age, as he was stricken with polio in his right arm at a scant 12 months old. While this might have proved a hindrance to some, Mr. Wolf persevered, and did not allow this limitation to stifle him in any way; quite the contrary, he remained competitive in...
Samuel Gaylord
(856) 673-4147 1814 East Route 70
Social Security Disability and Workers' Comp
Samuel M. Gaylord is a founder and partner of Gaylord Popp, LLC. He focuses his practice on workers' compensation, Social Security Disability, Medicare Set Aside claims, and pension appeals.
Edith Pearce
(856) 354-5688 5 Split Rock Dr
Free ConsultationSocial Security Disability, Animal, Construction and Personal Injury
William A. Nash Esquire
(856) 228-2206 1001 Melrose Ave
Gloucester Township, NJ 08012
Free ConsultationSocial Security Disability, Bankruptcy, Business and Personal Injury
Michael Joseph Brown
(800) 974-6670 52 Haddonfield-Berlin Road Suite 3000
As a partner at Wolf & Brown Law Offices, Michael J. Brown is passionate about providing his clients with expert representation and fighting for the benefits they deserve.
Mr. Brown is a graduate of the Widener University School of Law and completed his undergraduate work at the Camden campus of Rutgers University. Like most of his classmates, he worked his way through college, in his case, as a hotel desk clerk, and as a night auditor. This experience led to his first career managing, at various times, hotel rooms, beverage and banquet services. It is here where he, as a young...
Karen Ford Edler
Free ConsultationSocial Security Disability, Education, Employment and Estate Planning
Karen Edler is the founder of the Price, Meese, Shulman & D'Arminio, P.C. Education Law Group. She advocates for parents and students to obtain a free, appropriate public education for students with disabilities under the Individuals with Disabilities Education Act ("IDEA"), Section 504 & related laws. Ms. Edler's services include reviewing Individual Education Plans ("IEP") & Section 504 Plans, attending meetings and filing due process petitions when necessary. Ms. Edler represents students with any educational issues including academic issues, school disciplinary cases, bullying cases and collegiate academic and disciplinary matters. Ms. Edler handles special needs planning, Special Needs Trusts, guardianship...
Manfred F Ricciardelli Jr.
Morris County, NJ Social Security Disability Lawyer with 31 years of experience
(973) 285-1100 180 Speedwell Avenue
Morris Plains, NJ 07950
Free ConsultationSocial Security Disability, Personal Injury and Workers' Comp
Manfred "Manny" Ricciardelli, Jr. is a dedicated advocate for accident victims in New Jersey and has been practicing workers compensation law for over two decades. Before opening his Morristown personal injury law firm in 2001, he worked in-house for a large insurance company and also with a defense firm where he managed the Northern New Jersey Workers Compensation Department. In addition to handling workers comp claims, his firm represents injured victims of New Jersey car accidents, construction accidents, and social security disability claims.
William R. Marth
Somerset County, NJ Social Security Disability Attorney with 27 years of experience
(908) 561-5577 501 Watchung Avenue
Watchung, NJ 07069
Free ConsultationSocial Security Disability, Criminal Defense, Medical Malpractice and Personal Injury
Mr. Marth received his J.D. from Rutgers School of Law at Camden and his B.A. in Political Science from Rutgers College. He is admitted to the New Jersey State Bar, the Pennsylvania State Bar, and the U.S. District Court for the District of New Jersey. He is a member of the New Jersey State Bar Association and the New Jersey Chapter of the Association of Trial Lawyers of America. Mr. Marth's practice areas include civil litigation including personal injury, workers' compensation, and condominium construction as well as commercial cases and criminal litigation including municipal court, juvenile law, and indictable offenses....
Jeffrey Goldblatt
Middlesex County, NJ Social Security Disability Attorney with 48 years of experience
(732) 238-8700 9 Auer Ct. Suite E
Free ConsultationSocial Security Disability, Divorce, Family and Traffic Tickets
Jeffrey Goldblatt represents clients in all areas of family law including divorce, custody, alimony, child support, domestic violence, post judgment modification or enforcement applications, college issues, relocation, and emancipation. He also is a state qualified mediator and can mediate your divorce issues. He is collaboratively trained and can represent you in a collaborative setting. He is a selected panelist in the Middlesex County Early Settlement Program. Mr. Goldblatt handles all Municipal court matters including traffic violations and criminal offenses. He is a former Municipal Court Prosecutor. He also represents clients who are seeking Social Security...
John Rachinsky
Hudson County, NJ Social Security Disability Attorney with 26 years of experience
(201) 437-8787 29 West 8th Street
Chicago-Kent College of Law, Illinois Institute of Technology
John has been voted by his peers as a Rising Star of Worker's Compensation for six consecutive years, as appearing in New Jersey Monthly. Throughout his career, John has represented both injured workers and employers throughout the State. Mr. Rachinsky also appears regularly before the United States Social Security Administration. He is the author of Exceptions to the Rule, which was published in New Jersey Lawyer newspaper and is an accredited Veterans Benefits Attorney
Jorge L. Hernandez
Union County, NJ Social Security Disability Lawyer with 29 years of experience
(800) 856-7438 100 Jefferson Avenue
Jorge L. Hernandez has been licensed to practice law since 1993. He devotes his practiced to workers compensation, civil law and municipal court. In 2007, after many years as a partner in a larger New Jersey based litigation firm, he established his own practice offering services in the area of workers compensation, civil litigation, municipal court and Social Security law. Mr. Hernandez focuses his practice on the importance of balancing excellence, respect and passion. Since the first day he was admitted to practice law, he has followed these doctrines and has taken pride in gaining a reputation...
Joseph Ginarte
(888) 446-2783 352 New Brunswick Ave.
Perth Amboy, NJ 08861
Free ConsultationSocial Security Disability, Medical Malpractice, Personal Injury and Workers' Comp
Rutgers Law School and Rutgers School Of Law
Joseph A. Ginarte launched his legal career in 1982, and in the ensuing years he has seen his practice expand into a full service trial law firm with a steadily growing staff of lawyers and support personnel.To Ginarte, the success of his firm is directly attributable to a philosophy of hard work and commitment that was instilled in him by his parents when he was a boy growing up in Newark. Both parents worked in factories, and when Ginarte was a college student at Kean University in Union , he too worked in a factory—as a full-time forklift operator—while completing...
Oliver Minott
Essex County, NJ Social Security Disability Lawyer with 26 years of experience
(866) 683-4200 30 Clinton Street 5th floor
Western New England University School of Law
The Law Offices of Oliver C. Minott specializes in Workers Compensation and Social Security Disability Law. Our Highly experience attorneys represent clients in New York and New Jersey with over 35 years of combine experience. We guide clients through their Workers Compensation and Social Security Disability cases from the beginning to the end. Our attorneys will represent you at your Workers Compensation and Social Security hearings.Call the firm at 1-866-683-4200 for a free consultation.
Gary E. Adams J.D.
Mercer County, NJ Social Security Disability Attorney with 46 years of experience
(609) 520-0900 100 Nassau Park Boulevard
Social Security Disability, Employment and Workers' Comp
Since 1929, the New Jersey law firm of Pellettieri, Rabstein & Altman has worked hard to build a track record of honest, smart, responsive and responsible legal representation. Our lawyers have earned the respect of the courts, judges, regulatory authorities, and other attorneys. Gary Adams is a partner with Pellettieri, Rabstein and Altman who has been representing injured workers in New Jersey for more than thirty years. He has been certified by the New Jersey Supreme Court as a Workers' Compensation Trial Lawyer. He can be reached at 609-520-0900 or http://www.pralaw.com.
John E Biggiani
(908) 469-3710 40 Parker Road
Southwestern Law School
With more than 30 years of practice, John E. Biggiani, Esq. has extensive experience in the areas of Workers Compensation, Social Security and SSI Disability. A graduate of Villanova University and Southwestern Law School, Mr. Biggiani is admitted to practice in all state courts of New Jersey, the United States District Court for the District of New Jersey and U.S. Third Circuit Court of Appeals. Mr. Biggiani is a member of the New Jersey Bar Association and serves on the Executive Committee of the Workers Compensation Section. He has been certified by the New Jersey...
(609) 683-1500 475 Wall St
Social Security Disability and Landlord Tenant
Maria Blancato
(908) 277-2410 783 Springfield Ave
Summit , NJ 07901
Free ConsultationSocial Security Disability, Personal Injury, Traffic Tickets and Workers' Comp
I clerked for a Union County judge in the civil division in Union County to start my career. I then had the pleasure to learn criminal trial litigation at the Somerset County Prosecutors Office for nearly four years.
Over the last twenty years my practice has focused on helping individuals in workers compensation litigation, personal injury litigation, social security disability and municipal and juvenile court matters.
I work with people who need my help. I would be honored if you gave me the opportunity to help you.
Renata A. Mizak
Morris County, NJ Social Security Disability Attorney with 17 years of experience
(973) 347-3347 500 International Dr
Budd Lake, NJ 07828
Free ConsultationSocial Security Disability, Elder and Probate
Krycztee O Battista
Monmouth County, NJ Social Security Disability Attorney
Social Security Disability, Criminal Defense, Family and Real Estate
Cary Winslow
(609) 419-4414 707 Alexander Road
Free ConsultationSocial Security Disability
Attorney Cary L. Winslow represents clients throughout New Jersey in their claims for Social Security and/or SSI disability benefits and other related legal matters. Attorney representation is provided at all administrative levels, including the hearing and Appeals Council levels, as well as in federal court. Mr. Winslow is also an accredited attorney for the preparation, presentation, and prosecution of claims for benefits before the Department of Veterans Affairs (VA)and is admitted to practice before the U.S. Court of Appeals for Veterans Claims. Mr. Winslow's more than 25 years of legal experience includes heading the Government Benefits units...
Chad Williams
Warren County, NJ Social Security Disability Lawyer with 28 years of experience
Free ConsultationSocial Security Disability, Personal Injury, Real Estate and Workers' Comp
Charles Patterson McKenna
Mercer County, NJ Social Security Disability Lawyer with 18 years of experience
(609) 218-5120 Community Justice Center
310 W. State Street, 3rd Floor
Jeffrey Vincent Stripto
Monmouth County, NJ Social Security Disability Attorney with 23 years of experience
(732) 449-3304 900 Highway 71
Spring Lake Heights, NJ 07762
Elisabeth Haub School of Law - Pace University
Mr. Stripto has always known that he wanted to be a lawyer. He began his legal education in high school while working at the law firm of Drazin & Warshaw in Red Bank, NJ. Mr. Stripto attended High School at Christian Brothers Academy in Lincroft, NJ. He attended college at Seton Hall University, where he received a Bachelor's Degree in Political Science with minor in Business Administration. He began his formal legal education at Pace University School of Law where he focused on becoming a trial attorney as a member of the civil mock trial...
Melissa A. Gertz
Shiohban Royster
Union County, NJ Social Security Disability Lawyer
310 Morris Ave
Social Security Disability, Elder, Real Estate and Workers' Comp
Social Security Disability, Appeals, Business and Elder
Marc Jay Brenner
(973) 326-8902 222 Ridgedale Avenue
Social Security Disability, Personal Injury and Workers' Comp
John Gregory Devlin
(609) 896-2222 3131 Princeton Pike
Social Security Disability, Medical Malpractice, Personal Injury and Workers' Comp
Shana Siegel, Esq. CELA
Ext. 710 209 Cooper Ave., Suite #2
Social Security Disability, Elder and Estate Planning
Shana Siegel, Esq., CELA, Senior Associate, is a certified elder law attorney. Ms. Siegel has been involved in health and long term care issues for over twenty years, almost ten of which she has been in private practice. She is a senior associate with WanderPolo Law in Montclair. Prior to her legal career, she worked as a regulatory specialist at AARP. Ms. Siegel is a member of the New Jersey State Bar Association, NJSBA Elder Law Section, and the National Academy of Elder Law Attorneys. Ms. Siegel earned her JD with honors from Georgetown University and her BA...
Michael Eli Quiat
Bergen County, NJ Social Security Disability Lawyer with 41 years of experience
(201) 342-7100 433 Hackensack Ave
Social Security Disability, Civil Rights and Insurance Defense
Social Security Disability Attorneys in Nearby Cities
Swedesboro
The OneCLE Lawyer Directory contains lawyers who have claimed their profiles and are actively seeking clients. Find more Salem County Social Security Disability Lawyers in the Justia Legal Services and Lawyers Directory which includes profiles of more than one million lawyers licensed to practice in the United States, in addition to profiles of legal aid, pro bono and legal service organizations.

redpajama_set_name: RedPajamaCommonCrawl


text:
Cardi B's sophomore album slated for early 2023 release
Style. 1 post
stanLOONA 1 post
SpookyFish13 1 post
stanLOONA
This is like Normani's album "is ready to release" and here we are
SpookyFish13
I'll believe it when I see it! I really enjoyed 2018's "Invasion of Privacy" as well as the follow up standalone singles... But she should be promoting album 3 by now. "Money" "WAP" and "Up
I'll believe it when I see it!
I really enjoyed 2018's "Invasion of Privacy" as well as the follow up standalone singles... But she should be promoting album 3 by now. "Money" "WAP" and "Up" should have been the first, second and third single off her follow up project with "Press" being an album pre-order bonus promotional track. I don't know why she just let those songs grow stale without attaching them to a project...
Seems like a MAJOR missed opportunity.
Nicki will chew her up! Her little summer run is kinda over.
PinkBarbie
Can't wait for it to debut at #200
Why has she taken so long to release it?
MikeHunt
Britneys new album is also coming out early 2023!
Zara Larsson teases new single 'Can't Tame Her'
FLO announce new single 'Losing You'
Cardi B tells dedicated fan to get a job
By Body ache
Did Cardi B release the best female rap verse of 2022 with 'Tomorrow 2'?
By Style.
Paris Hilton says she'll be announcing a new 'very iconic song' on New Year's Eve
Paris Hilton talks upcoming book, new music & britney's wedding
Paramore release 'The News' music video
SZA reveals 'SOS' track list & release date
Rumour: Lana Del Rey's new single "Did You Know There's A Tunnel Under Ocean Boulevard" released on Friday
Selena Gomez teases her upcoming 'feel good' album


In the autumn 2006 issue of The Kintyre Magazine, Mr. Ron Bruce asked for information about the Bruce family in 'the Campbeltown area'. As I have a card file, compiled over 20 years ago, of Kintyre people related to my own ancestors, the name that sprang to mind immediately when I read this appeal was Rose McCorkindale, a granddaughter (b. 1806) of my great great great grandfather Adam McCorkindale, who was born in the parish of Killean before 1760, and married Rose McNeill from the parish of Southend in 1783.
In the Old Parish Register (OPR) Rose was 'Rossie' McNeill. She reappeared in the 1841 Census aged 80, in the household of her son-in-law Archibald McPhail and daughter Janet. This age suggests she was born around or before 1760, as the 1841 Census rounded ages to the nearest factor of five. She must have died between 1841 and 1851, before Civil Registration, which was introduced in 1855.
When I was 11, and reading romantic stories by L M Montgomery, I noticed that Canadian heroines often had 'Scotch' great aunts living in Prince Edward Island, Presbyterian ladies who were conscious of their Scottish heritage. But I, too, living in Scotland, had many great aunts who were my grandmother's sisters, brought up in Kintyre and on the Isle of ColI, where my grandmother's father, Duncan McCorkindale, became the factotum of John Lorne Stewart, the Kintyre landowner who bought Coll.
My grandmother, Janet McCorkindale, born in Kintyre in 1865, talked of her ancestral home as a land flowing with milk and honey. In fact, around the year of her birth, the peninsula could barely sustain its population of around 17,000, mostly employed in agriculture and fishing. There was a family story that her father, Duncan, son of Donald McCorkindale and Janet McGill in Beachmenach, being a good scholar, wanted to go to university, and did indeed set off for Glasgow with his sack of oatmeal, in the 1850s. But his mother, Janet McGill, died, and the father soon remarried. His new wife, Mysie McMillan, from Gigha, who has the reputation in my family of being nothing less than a wicked stepmother, refused to allow any money from their tight budget to finance Duncan's studies, and although he matriculated in the Free Church College in Edinburgh, he was unable to complete his divinity course. Instead, he married Catherine Mathieson, who lived at Margmonagach, a daughter of the thrice-married Dugald McMath and his last wife, Betsy Taylor.
Duncan and Catherine lived in Campbeltown, where he was in turn a jail warder, a teacher, and a colporteur, before impressing John Lorne Stewart with his numeracy and literacy, as well as his rather high-minded religious principles, and going off to the island of CoIl, c. 1874, to look after nearly everything - the grocer's shop, the post office, the church and the tenants' rents.
But in 1867, Duncan's oldest brothers, Archibald, William and Malcolm, with their wives and children, had taken a much longer sea voyage, along with many other Kintyre people. Archy was 46, William 44 and Malcolm 36 when they went to New Zealand under the auspices of the Free Church of Scotland, and settled near Havelock.
In 1947, my grandmother still spoke of her uncles Archy, William and Malcolm as if they had left only yesterday, but they were long dead. It had been 80 years since they left Scotland, but their letters to her father telling of their early trials and tribulations in New Zealand, poorly spelt and confused as these were, had been preserved in the family, keeping the drama alive. I stayed with my grandmother when she was in her seventies, and the stories she related were all about Kintyre (the Garden of Eden), the New Zealand family, and some other people who had settled in NZ. One of those others was 'Granny Bruce', nee Rose McCorkindale, my grandmother's second cousin, who, widowed at the age of 52, and seeing all her children about to depart from Killegruar, decided to go with the young folk. She arrived in New Zealand aged 60 and died there in 1897, with the typical longevity of the McCorkindales, at the age of 91.
So, you see, the shipload of pious Free Church people from Kintyre were kith and kin. My grandmother had made jokes about the first McCorkindale being Adam, but most of those pioneers were his descendants; with Adams and Roses conspicuous among them. Adam's granddaughter, Rose McCorkindale, was born in 1806, the daughter of Malcolm McCorkindale (or McCorquodale) 1787-1865, and Kate McGeachy, 1780-c.1845. She grew up at Achadaduie. In 1828 she married Hector Bruce in Amod, Barr Glen, son of Neil Bruce and Anne Kennedy, who married in Kintyre in 1803. The Bruces seem to have come from Ayrshire in one of the Plantations of Ayrshire farmers who were brought in to teach Gaelic-speaking inhabitants of Kintyre how farming should be done. Kennedy can also be an Ayrshire name, but I do not know when the Bruces and Kennedys arrived.
In the 1841 Census, Hector Bruce was 35, Rose was 35, and their children were Mary (12), Anne (10), Niell (8), Malcolm (6), George (3), and Catherine (1). Ten years later they have a daughter Rose, aged 9, and daughters Janet (7), Catherine (5) and Annabella (1). The older children worked on the farm of Killegruar.
In 1858, Hector Bruce died of apoplexy at the age of 54. Three years later, the 1861 Census of Killegruar shows Rose Bruce, aged 55, with her son George (23), daughters Rose (18), Janet (17), Catherine (14) and Annabella (9), and a young grandson, Hector, aged 4. Also at Killegruar in 1861, Neil Bruce, the oldest son, has his own wife and family. He had married an Ayrshire girl, Martha Sheddan, born in Kilwinning, so not of the Plantation, but demonstrating that links with Ayrshire were kept alive, although she had lived on the farm called Charlotteton, in the district of Barr. Martha and Neil Bruce have three young children: May (2), Rose (1) and Hector (2 months).
The next settlement to Killegruar farm in the 1861 Census is Margmonagach. This (as I remember it from a visit in 1979) is a stretch of joined-up cottages, where there were 13 separate households in 1861. The ruins are still visible if you climb up from Muasdale. I think it would be constructed for farm workers around the early 1800s. In 1861, three of the families are Stalkers, two are McCorkindales, and the rest are McLartys, McCulkins (later Wilkinsons) then my own Taylor ancestors, getting on in years: 81-year-old John McIntaylour and his wife, 70-year-old Catherine McKinlay. There is a couple called Aird, and finally my ancestors from Largiebaan, the Mathiesons or McMaths.
The ancestral home was not exactly the land of milk and honey my grandmother had described so lyrically. The 1861 Census tells how many rooms with windows each cottage had. Two of the Stalker families had three windows, as had my ancestor Dugald McMath. Donald Stalker had 11 people in his household; our Dugald had a family of 9. Meanwhile, next door to Margmonagach, in Killegruar, the Bruce family, with Rose as its head, have a farmhouse with only two windowed rooms for eight occupants.
Angus Martin, in his Kintyre: The Hidden Past, mentions Ayrshire fishermen who settled in Tarbert in the nineteenth century, and includes the name of Bruce among families there who were noted as Gaelic-speaking in the 1881 Census - meaning that they had learned Gaelic in the two or three generations after their arrival in Argyll. It is now possible, with new computer search methods at Register House in Edinburgh, to see how many Bruces were in Argyll in the 1841, 1851, 1861, 1871, 1881, 1891, and 1901 Censuses. In 1861 there were 98, predominantly in Tarbert and Lochgilphead. The other Kintyre Bruces are to be found in Killean and Kilchenzie, Saddell and Campbeltown parishes, the Campbeltown contingent being one family - wife and children of William Bruce, aged 35, a retired army captain in Kildalloig. William's wife, Charlotte O'Grady, is Irish-born, as are three of her four children. Only the new baby girl, one day old and still unnamed, has been born in Campbeltown. By the next Census, this family has left.
In 1871, there is a 31-year-old tobacconist, James Bruce, born in Neilston, Renfrewshire, at 93 Shore Street, Campbeltown, with his wife Isabella, a Campbeltown girl. There are no children, but an aunt, Janet Sawers, 68, and a widowed cousin, Bella McEachran, are dressmakers, both locally born, suggesting that the tobacconist already has family links with the town, and has not simply 'jumped' across the Firth of Clyde.
In April, 1861, Rose Bruce's daughter, also Rose Bruce, married a fisherman, Neil Thomson, whose address was Barr. In the parish of Saddell, in 1871, a Duncan Bruce, aged 30, was a fisherman, with a wife Ann and a 6-year-old schoolgirl niece, Mary Bruce. This is all I know about the Bruces in Kintyre.
To return to the ColI connection mentioned above, I had aroused my own curiosity by recalling that my great grandfather went to CoIl at the invitation of John Lorne Stewart. So I visited Register House and keyed in McCORKlNDALE and COLL to the census-search in Digros, and found that in 1871 a John McCorkindale, born in Campbeltown, was farming at Bailard, with his wife Flora, also born in Campbeltown. 1 traced them back. They were married in Breachacha Castle, ColI, in 1866. She was Flora Baxter, daughter of John Baxter, factor in ColI, and veterinary surgeon, and Orsla McFarlane. John was the son of John McCorkindale and Margaret Smith. When I traced back again, I found that a Robert Baxter had married a Flora McNeill in Campbeltown in 1810, and their first child, John Baxter, was born there in 1811. In the 1841 Census of Brickfield, Campbeltown, John Baxter, aged 25, was a veterinary surgeon, with his wife Orsla, or Ursula, aged 25, and their children Donald (5), Robert (2) and Flora ( 4 months).
Was this the first 'vet' to practice in Kintyre? Why did he go to CoIl to be Mr. Stewart's factor, and - only incidentally - the island vet? What was the family connection between John McCorkindale and Duncan McCorkindale, linking them both to Mr. Stewart's Coll? Much the same degree of affinity, I should think, that took Bruces and McCorkindales to New Zealand in the same ship.
This branch of Bruces may not be the one Ron Bruce is looking for, but Neil Bruce and his wife Anne Kennedy are the nearest I can get to his date of 1800, and Amod the closest I can get to 'the Campbeltown area'.


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Which Countries Border France?
Andorra, Italy, Germany, Belgium, and Monaco are the five countries that border France.
Footbridge connecting the cities of Kehl, Germany and Strasbourg, France. Editorial credit: MattLphotography / Shutterstock.com
The French Republic is a sovereign nation located in Western Europe. Its territories comprise of the metropolitan France that extends from the Mediterranean Sea to the English Channel and the Atlantic Ocean. Other overseas territories include the French Guiana in South America and several islands in the India, Atlantic, and Pacific Oceans. France is one of the largest countries in Europe with a total combined area of 248,573 square miles and a total population of 67.15 million people. Being among the oldest countries in the world, France is the product of an alliance of duchies and principalities under a single ruler. Today, the central authority lies with the state but the measure of autonomy has been granted to the country's territories in recent decades.
France's location makes it the most important country in regards to agriculture and manufacturing. It also acts as an economic, geographic, and linguistic bridge joining eight countries in northern and southern Europe. France shares land boundaries with eight countries, which encompass Italy, Germany, Belgium, Spain, Monaco, Andorra, Switzerland, and Luxembourg. France has endeavored to maintain strong and mutually beneficial ties with all the neighboring states as a means of enhancing social cohesion and economic integration in the Eurozone.
Countries Boarding France
The Principality of Andorra is bordered by France to the North. The two countries have strong diplomatic ties, which have existed since 1278 when Andorra acquired its sovereign status through pareage by the Count of Foix in southern France. Albeit being an independent state, Andorra shares a head of state with France with the President of France (currently Emmanuel Macron) being also the co-Prince of Andorra. Bilateral ties were established between the two states through the Franco-Andorran trade agreement that allows easy import and export of goods and services between the two states. France contributes immensely to the GDP growth in Andorra through increased tourism in the country. Furthermore, internet, postal, broadcasting, and education services are partially provided by the French government in Andorra.
France borders Italy to the southeast with the borderline being 488 km long. The two countries established the French-Italy relation in 1861 when the interstate boundary was created. Both countries were among the founders of the G7, NATO, and the inner six countries that formed the European Union. The two nations have established strong economic ties with France being Italy's second-largest trading partner and Italy being the second-largest trading partner of France. Since April 9, 1956, Rome and Paris exclusively and reciprocally twin each other through a popular saying: "Only Paris is worthy of Rome; only Rome is worthy of Paris".
Germany is France's most important regional partner. The diplomatic ties between the two states were established through the Franco-German Friendship. The two nations are among the most influential members of the European Union and often referred to as twin engines. The French and German economies are extremely intertwined and complementary with 30% of the industries established in Germany being subsidiaries of French companies. Various cultural institutions have been established in to facilitate cultural integration and cohesion between the two nations. Most notably, France and Germany maintain the Franco-German Brigade, a special military unit of Euro corps formed by soldiers from the two nations.
Interstate relations between France and Belgium were established between the two neighboring states after Belgium gained independence. Due to their geographic proximities, France and Belgium have smooth strong ties rooted to their historical and cultural backgrounds. Economically, Belgium is France's fifth-largest customer of export goods and services. Moreover, besides being founding members of the European Union, the two states are members of NATO and the Francophonie. There are also strong cultural, scientific, and technical ties between the two countries enhanced by the devolution of academic and cultural services.
Since 2000, Monaco and France established diplomatic relations governed by the Treaty of Versailles. The two countries have mutually beneficial economic relations initiated by the European External Action Service that integrated Monaco in the Schengen zone. The EU council authorized France to negotiate inter alia use of the Euro in Monaco as well as create an integrated customs union to enable Monaco to participate in the EU market system. French and Monaco share French as their official language that facilitates further ties in tourism. Approximately two-thirds of Monaco's workforce comprises a vast majority of French nationals. Furthermore, Monaco has established a legal system that is in line with the French Napoleonic Code.
Luxembourg is one of the strategic trading partners with France due to its geographic proximity and the strength of its economy. The liberal trading rules in the Grand Duchy of Luxembourg has attracted about 900 companies from France in the banking and insurance sectors. Strong cultural ties dating back to 1945 exist between the two states with numerous cultural institutions of French origin being established in Luxembourg. An action is underway to support Luxembourgish as a language promoting integration and social cohesion in the region by having the language as a teaching language in primary schools. France is also taught in Luxembourg from the second year thus aiding in social integration and cohesion.
France and Spain border each other along the Pyrenees border. The two states are among the founding nations of the Latin Union and the European Union. Albeit having a troubled past that was characterized by the 24-year Franco-Spanish War, the two nations have integrated through the G6 in matters pertaining to economic development, defense, and European Constitution. After the Second World War, a vast majority of the Spaniards moved to France in search of employment opportunities that were readily available. The strong economic ties between the two countries were strengthened in 1975, following the death of Franco, thus paving way for liberalization of the Spanish society.
The French Republic borders Switzerland to the east with a 600km shared borderline that prompted strong cross-border cooperation. Their active bilateral ties were established in 1516 through the Treaty of Perpetual Peace. Bilateral ties focus on economic, fiscal, and financial issues, research and innovation, infrastructural projects, and the Basel-Mulhouse airport (Euro Airport). In particular, France is Switzerland's third largest trading partner with an economic integration established through the European Union and the Schengen Area that abolishes international trading borders between member states. There are also established cultural ties embedded in the language where French is one of the four official languages in Switzerland.
Five countries border France: Andorra, Italy, Germany, Belgium, and Monaco.
This page was last updated on June 29, 2018.
By Molly John
Which Countries Border Germany?
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The first scene of Anna Christie takes place in a small waterfront bar in the New York City harbor around 1910. For our production at Triad Stage, the design had a large back bar and front bar which could appear for that scene and strike backstage when it ended. The scenic designer drafted the front bar and the back bar for the props shop to build, and away we went. Standing nine and a half feet tall, at almost twelve feet long, the back bar really pushed the limits of the definition of a "prop".
The back bar was built mostly out of lauan with half-inch plywood framing pieces to make it as light as possible, since it would need to be pushed on and off stage a vista by three crew members.
It was constructed in three sections to make transportation to the theatre possible. You can see two of the sections below, showing where the piece broke apart. You can also see the beginnings of the wood grain paint treatment which I wrote about last week.
Most of the vertical surfaces on the top section of this piece were meant to be antique frosted mirrors. I used some silver Mylar as the mirror, laid a section of lace on top, and spray painted through it. This left a lace-like design on the Mylar, and after a few more coats of spray frosting over the whole thing, it looked just like a mirror.
The unit was originally on wheels, but when it got to the theatre, the noise it made while moving was deafening. The stage floor consisted entirely of expanded steel panels. We discovered that plastic furniture gliders actually made moving the unit completely silent and fairly effortless. They also ensured the unit remained stationary when no one was touching it.
With some practical sconces, some lace runners and doilies, and a whole bunch of vintage liquor bottles, the piece was complete. Below is a photo of the whole setup, which includes the front bar that our prop shop also constructed.
You can also see a side-by-side comparison of the final piece with a research image. Obviously the proportions and specifics were changed in the design, but the inspiration is fairly clear.
It is a little over a week since Elon University's Wild Party closed, so I thought I would share some of the props I built while working as the props master on it. First is the sleek Art Deco bar. This production featured a lot of dancing and movement (in fact, the show was more of a dance piece with singing than a traditional musical) and the bar was key in a lot of the dancing. Actors jumped up and down off of it constantly and danced on top of it. Needless to say, it had to be sturdy.
The other hurdle was that I only had a bout a day to build the bar to a point that they could use it in rehearsal; it did not have to be finished, just usable. The bar had a sort of boomerang or banana shape to it. I knew it would take awhile to layout the shape, not to mention all the pieces I would need to cut that followed the shape but were inset or offset by varying amounts. Since the scenic designer, Natalie Taylor Hart, already had the footprint of the bar drafted in CAD, we decided to CNC these pieces and save some time.
The top was two layers of plywood. We were putting lights in the bar that would shine upward, so the top also had squares to hold three pieces of 3/4″ plexiglass; the squares on the top piece were large enough to fit the plexiglass, while the squares on the bottom piece were a touch smaller to create a lip for the plexiglass to sit on.
I also cut the footrest, a piece for a shelf in the middle, and some formers to nail the wiggle wood to. This pile of pieces would have taken awhile to draw and cut by hand, but with CAD, Natalie just had to copy the same shape over and over again, insetting the front curve by whatever measurement I gave. With this pile of pieces, I just had to cut a bunch of formers and uprights to connect them all together.
I decided I wanted some supports to run unbroken from the top to the bottom of the bar for strength, which meant I had to cut some notches and holes in the plywood that they could run through. If I had more time to figure the whole thing out ahead of time, I would have drawn these into the CAD. Since the pieces were already cut, I needed to measure and cut them by hand. See, even with fancy fabrication machines, you still need a solid grasp of traditional tools to build things.
I built the bar up one level at a time, marking carefully to keep the whole thing square and straight. I positioned the supports so they were nearly above the support below them; they were offset just a bit so I would be able to drive a nail in.
The supports along the front of the bar did double duty as formers, providing a nailing surface for the wiggle wood I would add later. I tried to keep the back as open as possible so it could be used as shelving to store all the props; the set was fairly open and skeletal, so the bar served as a place for a lot of the hand props to appear and disappear. The diagonal braces in the photograph above are just to keep the bar sturdy as they use it in rehearsal. Once the wiggle wood was added, I removed them, because the wiggle wood acted as one large piece of diagonal bracing.
I finished the bar onstage in between rehearsals. The curve was longer than eight feet, so I could not cover it with just one piece of wiggle wood. The center is relatively flat, so I placed a small piece directly in the center; I have found it easier to fill and sand seams between wiggle wood when they are on flat areas. The footrest also got a small strip of wiggle wood after the bar was secured to the wagon underneath it. All the faces got a thin coat of joint compound and a light sanding, and then it was on to painting.
You can see the bar is a bit rough around the edges in the photograph above since I did not have time to take a picture until after strike. The Art Deco design painted on the front was a great touch added by Natalie and her crew. As she also pointed out, despite all the climbing and dancing done on this bar, she never saw it sag or wobble.


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ewittels@juno.com
The College of the City of New York, B.S., Electrical Engineering
Emanuel Wittels
Emanuel Wittels is a legal assistant in our New York and New Jersey offices.
Mr. Wittels has experience as a legal assistant with diverse duties that include client intake, background case investigations, preparing pre-trial submissions, witness preparation, preparation of medical authorizations, retainers, and closing statements.
Prior to joining the firm, Mr. Wittels developed a broad and diversified business background. In England, he founded the Redifon Computer Division of Rediffusion, a top-ten British firm. In the United States, Mr. Wittels founded the Wordstream Division of Avionic Products. He created and designed the Wordstream Word Processing System used by major Banks, Insurance, and Fortune 500 companies. Also in the US, Mr. Wittels founded the Auragen Corp. featuring fault-tolerant computer systems. Mr. Wittels has also been associated with IBM, General Electric, and Bell Laboratories in various management and supervisory capacities including project management, software development, system design, and development.
Mr. Wittels studied theater at HB Studios in New York. He has written, produced, and directed two films, including a feature-length movie titled "Worlds on Fire." His work included playwriting, screenwriting, and acting, including scenes from Shakespeare's Hamlet, The Tempest, Richard III, Arthur Miller's Death of Salesman and View from the Bridge. Mr. Wittels earned a Bachelors of Science in Electrical Engineering from the College of the City of New York and has taken graduate courses at Columbia, Syracuse, and NYU. He is also a U.S. Navy veteran.


I think I have purchased every available brand of chai tea on the market. Our tea cupboard is packed with boxes of chai tea - and you can tell which ones we like; the empty ones. So I decided to make my own. I initially had visions of me at my day job spending hours in the kitchen slowly preparing spices and heating them up on my own portable cooking element, but they're on to me already. So, home preparation is the go.
I purchased some heat sealable teabags. Most of these I will use to infuse oils with herbs for the soaps I make, but here is another use. Of course, a mesh tea-ball will do, I just chose the bag because some of the spices will be powdered and I didn't want too much sediment in the final brew (you can always let it settle and just avoid serving the last bit, if you are strong-willed).
My partner and I went to Gaganis Bros on the weekend (if you don't know what this is, it's a magnificent, no, glorious, food wholesaler in Hindmarsh, Adelaide) and we bought up big on spices.
Put the spices in a mortar and give them a few grinds with a pestle. If you don't have a mortar and pestle, pounding the spices in a plastic bag with something hard might work!
Tip the contents and the black tea into the teabag. At this point, I also added a piece of orange peel. Iron the open side of the bag to seal it shut. And there you have your chai teabag.
In a small saucepan, I heated a mug's worth of water and a mug's worth of soy milk. To this, I added the teabag, two teaspoons of homemade vanilla essence (thanks to a lovely Christmas gift) and a couple of tablespoons of vegan cream. The vegan cream comes from a simple recipe my friend Karena (Magic Jelly) has graciously shared on her site and consists of cashews, soy milk and canola oil. It is super easy to make and is very versatile, as the recipes on Karena's site explain. The addition of vegan cream takes the chai to another level, but it really is optional.
Illustrated above, the spices, the cream, the vanilla essence and the tea bag.
I was fortunate enough to be presented today with a dozen vegan coffee cakes, again, courtesy of Karena. She has the recipe on her site and this is a modified version from a recipe for East Coast Coffee Cake found in Vegan Brunch. Delicious.
Making the chai teabag took about 10 minutes including clean-up, so it's an easy and worthwhile treat for lazy Sundays.


Lately I've been thankful for warmer weather and laying ladies.
For two good things coming together to make a great thing.
For the friendship these two tiny humans have.
And for a 27 yr old Jeep that keeps kickin.
I'm thankful for a wife who appreciates the gall bladder and liver! Hearing your enthusiasm about anatomy & physiology is such a beautiful thing to experience!
I'm thankful for friends who encourage me just when I need it, for dogfriends when I can't afford my own (yet!), & Blue Bell ice cream making a triumphant entry into grocery stores in Indy!
I'm grateful for this blog that always brings to mind the things that really count!