text:
Chelsea Wolfe Debuts Two New Singles
Chelsea Wolfe has shared two new songs from her Birth of Violence sessions
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Chelsea Wolfe has shared two new songs from her Birth of Violence sessions, including her version of Joni Mitchell's single, "Woodstock" and the never before heard, "Green Altar."
From Chelsea Wolfe: "While preparing for the 'Birth of Violence' tour, I was watching a lot of Joni Mitchell videos. A 1966 Canadian performance that I found of hers ended up inspiring the video for my song 'Highway.' One night after working on the live set, Ben and I were hanging out and I was just letting the Joni videos roll.. 'Woodstock' came on and I started singing along. After that I simply asked Ben if he'd be into covering it with me for the tour, and we just went back into the studio and started working it out. The cover came together quite naturally and it was a treat to play on stage every night. Joni is obviously such a big inspiration to this side of my music, so it felt right to pay tribute to her."
"'Green Altar' is a cherished song that unfortunately didn't make it onto the album. It's a love song I wrote after finding out that my dear friends (artist) Bill Crisafi and (designer) Hogan McLaughlin were engaged. I envisioned them getting married in a lush, green outdoor space outside of some majestic castle ruins."
Wolfe has also shared an official documentary of her 2019 'Birth of Violence' Tour which unfortunately came to a halt with the onset of the pandemic. The piece is beautifully shot by photographer/director Bobby Cochran who joined Wolfe at the tail end of the North American leg. Cochran documents the show, stage, and captures moments behind the scenes. The two also sat down to discuss the creation of the album, Birth of Violence, about what it's like being on tour and her rituals.
Wolfe tells, "It's not my natural inclination to want cameras around when I'm in my head or doing vocal warmups before a show, or when I'm with friends or family backstage, but Bobby asked, and in the spirit of pushing myself to document that era of my musical life, I welcomed him along. Then, after the COVID-19 pandemic hit and I had to fly home from the European acoustic tour before I got to play a single show of it, I was so grateful that he had this footage and was putting it together. I wanted to share this documentary for that reason as well, for those who had tickets to cancelled shows (I love you!), and as a sort of wave goodbye to the time I spent focused on 'Birth of Violence', as I'm now making plans for and in the headspace of the next new album."
Chelsea Wolfe Live Dates:
11/26: Los Angeles, CA – Substance LA at The Belasco (Tickets)
Order Birth of Violence by Chelsea Wolfe HERE
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AAT warns of dramatic rise in self-assessment filing
Lockdown restrictions and mounting pressure on businesses could combine to cause a 'dramatic rise' in self-assessment filing this tax year, according to the Association of Accounting Technicians (AAT).
Almost a million self-assessment tax returns were filed late in the last financial year, but the situation has been worsened by the coronavirus (COVID-19) pandemic. The chances of late filing increased dramatically once a second national lockdown was announced, the AAT said.
In responding to the concerns of its members, the AAT identified three potential solutions and brought them to the attention of the senior leadership team at HMRC. These include a two-month deferral on filing and payments; the waiving of penalties for late filing; and increased use of HMRC's Time to Pay.
Phil Hall, Head of Public Affairs and Public Policy at the AAT, said: 'There has been a raft of government assistance to mitigate the worst of the economic problems caused by coronavirus, so it doesn't seem unreasonable to ask what could be done to reduce the chances of millions of people being landed with at least a £100 late filing penalty, and in many cases much more, to add to the growing financial problems many are currently enduring.
'For now, it's important that we all do everything we can to be ready to meet the 31 January 2021 deadline, whilst recognising that's very much easier said than done.'
Please contact us if you require any assistance with self-assessment.
Supreme Court backs small firms on business interruption claims
The UK's Supreme Court has found in favour of small firms receiving payments from coronavirus (COVID-19) business interruption insurance policies.
IMPORTANT UPDATE FROM THE TEAM AT PGT ON COVID-19
In our continuing commitment to protecting the health and well-being of our team, our clients and the wider community generally, we have taken the decision to only have skeleton staff working in our office w.e.f Tuesday 24th March, but
DON'T PANIC, IT'S BUSINESS AS USUAL(Well almost!)
We are committing our best endeavours to keep our business operating as near to normal as possible with a continuing focus on helping our clients access the practical financial help notified by the Chancellor.
Please continue to contact us by phone using the office phone line (01452 308153) and the Partner's mobile phone numbers as detailed below:
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Q: Issue Testing after IdentityServer3 Deploy After going through walkthroughs I had a test mvc app, test web api, and identityserver3 all working perfectly on my machine.  I deployed IdentityServer3 to our servers in AWS behind a load balancer.  I followed all the instructions in the Deployment wiki.  I am able to hit the .wellknown configuration fine after deployment from a browser on my machine.
I changed the authority url for the mvc and api test apps to point to the aws deployment.  Clients, Scopes, users, etc are all configured identically as they are hitting the same database as it was when running on local machine.
I can get an access token using RequestResourceOwnerPasswordAsync just fine so I think ids is installed fine.
However, both the API and the MVC app just trying to use implicit flow are now failing.  FOr instance, when I try to hit a mvc controller action marked with [Authorize] I get an error stating "An invalid request URI was provided. The request URI must either be an absolute URI or BaseAddress must be set".
If I try to hit the webapi from the mvc app (both running locally on my machine) after a successful RequestResourceOwnerPasswordAsync call, I get the error "Response status code does not indicate success: 401 (Unauthorized)." after what seems like a timeout.
Any help would be greatly appreciated.

A: Figured out the problem.  When specifying PublicOrigin, it has to be a full URL and not just the domain.  I had left off https:// prefix.
The web api issue was related to connectivity to the identity server.  There was some incorrect proxy settings for the app.

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text:
\section{Introduction}
The advent of quantum computers has opened
a significant turning point for exponentially
speeding up computing tasks that classical computers need thousand years to execute~\cite{Arute2019, ChinaSupremacy}.
Although mankind has witnessed tremendous development in this field theoretically and experimentally in the last few years, most state-of-the-art quantum computers still rely on noisy intermediate-scale quantum computers NISQ.
Noises and qubit-number constraints prevent
to build high-fidelity quantum computers capable of
substantially implementing quantum algorithms
\cite{Preskill2018quantumcomputingin,7927034,
Wang285,Kandala2019}.
To bypass these constraints, various hybrid quantum-classical algorithms that use classical computers to optimize quantum circuits
have been proposed \cite{Cerezo2021, PhysRevA.101.010301, PhysRevA.103.L030401}. Among these, variational quantum algorithms (VQAs) may be the most promising ones in the NISQ era.

VQAs generally consist of three essential steps: (i) initializing quantum states for a given wavefunction ansatz, (ii) measuring a cost function suitable for problems being considered, and (iii) minimizing the cost function and updating new parameters. The self-consistency is performed until convergence.
VQAs have been extensively employed to tackle numerous tasks,
including the variational quantum eigensolvers (VQEs)
\cite{Peruzzo2014,
PhysRevResearch.1.033062,
Kirby2021contextualsubspace,
Ryabinkin2019,
PhysRevA.101.052340,
Gard2020,
PRXQuantum.2.020337},
quantum dynamics simulation
\cite{PhysRevX.7.021050,McArdle2019,
Nishi2021,PRXQuantum.2.030307,
zhang2020lowdepth,
PhysRevResearch.3.023095},
mathematical applications
\cite{PhysRevA.103.052425,
huang2019nearterm,
PhysRevLett.122.060504,
PhysRevA.103.052416,
bravoprieto2020variational,
xu2019variational,
PRXQuantum.2.010315,
Lloyd2014,
LaRose2019},
quantum machine learning (QML)
\cite{PhysRevA.98.032309,
farhi2018classification,
PhysRevLett.122.040504,
Havlicek2019,
PhysRevA.101.032308,
farhi2018classification,
Cong2019,
pesah2020absence,
zhang2020trainability,
Beer2020},
and new frontiers in quantum foundations
\cite{Arrasmith2019,wilde_2017,
Cerezo2021,
PhysRevA.101.062310,Koczor_2020,
PhysRevLett.123.260505,
beckey2020variational,
Meyer2021}.

Typically, VQAs employ variational quantum circuits to measure the cost function on a quantum computer and outsource its optimization to a classical computer. While one can manipulate gradient-free optimizers, such as Nelder-Mead simplex \cite{Mead}, to minimize the cost function, using gradient-based methods like gradient descent can help us speed up and guarantee the convergence of the optimization. Several quantum algorithms have been proposed to evaluate the cost function gradient measured on quantum computers \cite{10.1145/3385412.3386011,Sch_fer_2020,Stokes2020quantumnatural,lopatnikova2021quantum,yamamoto2019natural,PhysRevLett.126.140502}. Among those methods, quantum differentiable programming (QDP) has been introduced and utilized extensively
\cite{10.1145/3385412.3386011,Sch_fer_2020,guerreschi2017practical,
bergholm2020pennylane,
PhysRevLett.118.150503,
PhysRevA.98.032309,PhysRevA.99.032331,
Banchi2021measuringanalytic}.
It relies on a technique called
the parameter-shift rule that evaluates
the derivative of any differentiable function
using quantum circuits
\cite{guerreschi2017practical,
bergholm2020pennylane,
PhysRevLett.118.150503,
PhysRevA.98.032309,PhysRevA.99.032331,
Banchi2021measuringanalytic}. Therefore, this method is beneficial for
developing "on-circuit" gradient-based
optimization techniques, especially for
quantum machine learning (QML) applications
where various methods like quantum neural networks
(QNNs) demand the derivative information of the cost function.

While quantum algorithms
should be performed
on quantum computers,
the current limitation of
NISQ computers cause challenges
in developing and testing
new quantum algorithms,
demanding the use of
virtual alternatives
called quantum virtual
machines (QVMs).
Besides,
QVMs are necessary for modeling
various noisy channels to characterize
the noises and the efficiency
of quantum error correction.
One can classify QVMs into two types according to the way to build them: (i) the matrix multiplication approach \cite{qiskit,cirq_developers_2021_5182845,smith2017practical,bergholm2020pennylane,7927034,10.1145,Villalonga2019,roberts2019tensornetwork},
and (ii) the wavefunction approach \cite{suzuki2020qulacs,Guerreschi_2020,Steiger2018projectqopensource,kelly2018simulating, Jones2019,DERAEDT2007121,DERAEDT201947}.
While the former performs matrix multiplication
for all qubits in quantum circuits,
the latter represents quantum circuits
by corresponding wavefunctions.
On the one hand, the former can significantly
reduce the memory capacity
using tensor network contraction
\cite{doi:10.1137/050644756,PhysRevLett.125.060503},
and the cost to pay is
exponentially increasing
the computational time.
On the other hand, the latter, in principle, can require less computational time in a limit of qubits number and a sufficiently large memory size that can store the total quantum wavefunction.
Therefore, both approaches exist
side by side
and a possible hybrid approach
\cite{Arute2019,markov2018quantum}
for convenient purposes.

There are several QVM's libraries
developed for QML orientation, such as
TensorFlow Quantum library
\cite{broughton2020tensorflow} implemented in Cirq
\cite{cirq_developers_2021_5182845},
Pennylane \cite{bergholm2020pennylane}
designed for photonics devices,
and TensorNetwork \cite{roberts2019tensornetwork,Huggins_2019}.
These libraries are all constructed in
the matrix-multiplication type of QVMs,
designed to submit quantum tasks
to the developed hardware conveniently.

In this work,
we develop a QVM platform
named Qsun using the wavefunction approach
towards the QML applications.
In Qsun, a quantum register is represented
by a wavefunction, and quantum gates
are manipulated directly by updating
the amplitude of the wavefunction.
Measurement results
rely on probabilities of the wavefunction. Our simple approach yields faster computation speed for a small number of qubit when compared to other QVMs such as Qiskit, ProjectQ, or Pennylane. Basing on this generic QVM,
we aim to exploit the advantages of QDP
with the parameter-shift rule as the core engine towards practical applications
in quantum machine learning. Two representative
examples of QML are demonstrated: quantum linear regression and quantum neural network. These algorithms are compared to standard progams: Qiskit, ProjectQ, and Pennylane, and classical algorithms when applicable. In these comparisons, Qsun performs slightly better for QDP, QLR, and QNN. All in all, Qsun is an efficient combination of QVM with QDP features that is oriented toward machine learning problems. In the following, we introduce the QVM platform Qsun and its performance compared to others in Sec.~\ref{secii}, followed by an introduction to the QDP implementation within Qsun in Sec.~\ref{seciii}. We then discuss some QML applications of the Qsun package in Sec.~\ref{seciv}.

\section{Quantum virtual machine implementation in Qsun}
\label{secii}
In practice, quantum computers work on quantum algorithms by  composing a quantum register, or qubits, operated by a sequence of quantum gates. Results are then traced out from quantum measurements.
We now introduce our quantum virtual machine (QVM) named Qsun, an open-source platform simulating the operation of a generic quantum computer \cite{QSUN}.
We aim the platform to the development of quantum machine learning (QML) and related problems. We develop it in Python and employ the Numpy library
for fast matrix operations and numerical computations.

\subsection{Simulating quantum computers using wavefunction basis}
Unlike widely-used approaches based on matrix
multiplication \cite{qiskit,cirq_developers_2021_5182845,smith2017practical,bergholm2020pennylane,7927034,10.1145,Villalonga2019,roberts2019tensornetwork}, our platform is developed using the class of ``wavefunction'' approach \cite{suzuki2020qulacs,Guerreschi_2020,Steiger2018projectqopensource,kelly2018simulating, Jones2019,DERAEDT2007121,DERAEDT201947}, in which a quantum register is represented by its wavefunction. The
operation of quantum gates is simulated by updating the wavefunction's amplitude, and output results are obtained by measuring  wavefunction's probabilities. We expect that working directly on wavefunction is beneficial for QML applications, especially for building and training variational quantum circuits in quantum neural networks (QNNs).
As depicted in Fig.~\ref{fig:class},  Qsun consists of three main modules \texttt{Qwave, Qgates}, and \texttt{Qmeas} for quantum register, quantum gates, and quantum measurement, respectively.

\subsubsection*{Qwave}

In general, for a quantum register with $N$ qubits, its quantum states are represented in the $2^N$-dimension Hilbert space as
\begin{align}\label{eq:Nqubit}
|\psi\rangle = \sum_{j = 0}^{2^N-1}\alpha_j |j\rangle,
\end{align}
where $\alpha_j$ are complex amplitudes obeying a completeness relation
$\sum_{j =0}^{2^N-1}|\alpha_j|^2 = 1$, and vectors $|j\rangle$ are
elements of the computational basis.
We integrate quantum state's information into the class \texttt{Wavefunction} as described in Fig.~\ref{fig:class} and Table.~\ref{t:1}.
The class allows us to access and update amplitudes directly according to
the evolution of the quantum state under the action of the unitary quantum gates.  It also measures probabilities that contain output information.

\begin{figure}[t!]
\centering
\includegraphics[width=8cm]{class-eps-converted-to}
\caption{Qsun quantum virtual machine (QVM) consists
of three main modules \texttt{Qwave},
\texttt{Qgates}, and \texttt{Qmeas},
to simulate quantum circuits with
a quantum register (qubits),
quantum gates, and quantum measurements,
respectively.
In Qsun, a quantum register
is constructed by its wavefunction through the
\texttt{Wavefunction} class and
its containing objects, as illustrated in the figure.}
\label{fig:class}
\end{figure}

\begin{table}
\small
\begin{center}
\caption {
List of methods used in the class \texttt{Wavefunction}.} \label{t:1}
    \begin{tabularx}{\linewidth}{@{}p{3cm}Xc>{\centering\arraybackslash}p{2cm}c@{}}

        \hline
        \textbf{Methods} & \textbf{Description} \\
        \hline

    \texttt{amplitude} & a NumPy array of complex numbers that stores the amplitudes of quantum states. \\
   \rowcolor[gray]{.9} \texttt{state} & a NumPy array of strings that labels the quantum states's basis. \\
    \texttt{probabilities} & return a list of corresponding probabilities for each basis vector in the superposition. \\
   \rowcolor[gray]{.9} \texttt{print\_state} & return a string representing a quantum state of the system in bra-ket notations. \\
  \texttt{visual\_circuit} & print a visualization of a quantum circuit. \\
    \hline

    \end{tabularx}
\end{center}
\end{table}

\subsubsection*{Qgates}

To manipulate a single-qubit gate $U$
$=\begin{pmatrix} a & c \\
b & d \end{pmatrix}$
acting on the $n^{\rm th}$ qubit, the nonzero elements in \texttt{amplitude} array are updated as \cite{Jones2019}
\begin{align}\label{eq:gate}
\begin{pmatrix}
\alpha_{s_i}\\
\alpha_{s_i+2^n}
\end{pmatrix}
\to U
\begin{pmatrix}
\alpha_{s_i}\\
\alpha_{s_i+2^n}
\end{pmatrix},
\end{align}
where $s_i = {\rm floor}(i/2^n)2^{n+1}+(i \text{ mod } 2^n)$,
for all $i \in [0, 2^{N-1}-1]$. Here, ${\rm floor}(x)$ is the standard floor function taking the greatest integer less than or equal to the real of $x$. We unify the implementation of single- and multiple-qubit gates into a common framework.
We outline the operation of single-qubit gates in Algorithm~\ref{al:1} and an example of the Hadamard gate in Algorithm~\ref{al:hadamard}. We emphasize that \texttt{Qgates} only update nonzero components of wavefunction amplitudes.
This way, we can avoid demanding matrix multiplications that escalate exponentially ($2^N\times 2^N$) with the number of $N$ qubits. This generic algorithm allows us to implement
arbitrary unitary gates without decomposing them into universal ones,
which may be advantageous to model a general class of neural networks using quantum circuits.
\begin{algorithm}
\SetAlgoLined
\KwResult{Wavefunction with new probability amplitudes}
 w $\leftarrow$ Wavefunction\;
 states $\leftarrow$ w.state;
 ampl $\leftarrow$ w.amplitude\;
 $N$ $\leftarrow$ size(state[$i$][0]);
 $n$ $\leftarrow$ target qubit\;
 $n$\_ampl $\leftarrow$ [0, ..., 0], size($n$\_ampl) = size(ampl)\;
 $cut \leftarrow$ $2^{N-n-1}$\;
 \For{i $\leftarrow$ 0, {\rm size(ampl)}}{
  \eIf{{\rm state[$i$][$n$] == 0}}{
   $n$\_ampl[$i$] $\leftarrow$ $n$\_ampl[$i$] + $a$*ampl[$i$]\;
   $n$\_ampl[$i+cut$] $\leftarrow$ $n$\_ampl[$i+cut$] + $b$*ampl[$i$]\;
   }{
   $n$\_ampl[$i$] $\leftarrow$ $n$\_ampl[$i$] + $d$*ampl[$i$]\;
   $n$\_ampl[$i-cut$] $\leftarrow$ $n$\_ampl[$i-cut$] + $c$*ampl[$i$]\;
  }
 }
 w.amplitude $\leftarrow n$\_ampl
 \caption
 Operation of a single-qubit gate:}
 \label{al:1}
\end{algorithm}

\begin{algorithm}
\SetAlgoLined
\KwResult{Wavefunction with new probability amplitudes corresponding to Hadamard state}
 w $\leftarrow$ Wavefunction\;
 states $\leftarrow$ w.state;
 ampl $\leftarrow$ w.amplitude\;
 $N$ $\leftarrow$ size(state[$i$][0]);
 $n$ $\leftarrow$ target qubit\;
 $n$\_ampl $\leftarrow$ [0, ..., 0], size($n$\_ampl) = size(ampl)\;
 $cut \leftarrow$ $2^{N-n-1}$\;
 \For{i $\leftarrow$ 0, {\rm size(ampl)}}{
  \eIf{{\rm state[$i$][$n$] == 0}}{
   $n$\_ampl[$i$] $\leftarrow$ $n$\_ampl[$i$] + $(1/\sqrt{2})$*ampl[$i$]\;
   $n$\_ampl[$i+cut$] $\leftarrow$ $n$\_ampl[$i+cut$] + $(1/\sqrt{2})$*ampl[$i$]\;
   }{
   $n$\_ampl[$i$] $\leftarrow$ $n$\_ampl[$i$] + $(-1/\sqrt{2})$*ampl[$i$]\;
   $n$\_ampl[$i-cut$] $\leftarrow$ $n$\_ampl[$i-cut$] + $(1/\sqrt{2})$*ampl[$i$]\;
  }

 w.amplitude $\leftarrow n$\_ampl
 \caption
 Operation of Hadamard gate:}}
 \label{al:hadamard}
\end{algorithm}

To mimic the actual operation of quantum computers,
we introduce noises into the wavefunctions.
In Qsun, the standard quantum depolarizing channel is implemented
as a single-qubit gate $\mathcal{E}$ that is a part of
quantum circuits acting on the wavefunctions.
For a given noisy probability $p$,
applying the gate $\mathcal{E}$
on a mixed quantum state $\rho$
will transform it to~\cite{nielsen_chuang_2019}
\begin{align}\label{eq:eg}
\rho \xrightarrow{\mathcal{E}}
(1-p)\rho+\dfrac{p}{2}I,
\end{align}
where $I$ is an $2\times2$ identity matrix.
In general, one can decompose the depolarizing channel
into the bit-flip, phase-flip, and phase-bit-flip as
\begin{align}\label{eq:noise}
\rho \xrightarrow{\mathcal{E}}
(1-p)\rho
+ p_x X\rho X
+ p_y Y\rho Y
+ p_z Z\rho Z,
\end{align}
where $p_x, p_y, p_z$ are the
probabilities of bit-flip, phase-bit-flip,
and phase-flip, respectively
\cite{nielsen_chuang_2019,7927034}.
In Qsun, we use $p_x = p_y = p_z = p/3$
and apply to every qubits in
the circuit each after the action of a quantum gate
on the circuit.

\subsubsection*{Qmeas}

The module \texttt{Qmeas} is designed
to execute quantum measurements on a single qubit
or all qubits in the quantum circuit.
For a measurement on a single qubit $n$,
the probability for that its outcome is $|0\rangle$ reads
\begin{align}\label{eq:prob}
 p(0) = \sum_{i=0}^{2^{N-1}-1}\langle\psi|j_{s_i}\rangle\langle j_{s_i}|\psi\rangle
=\sum_{i=0}^{2^{N-1}-1}|\alpha_{s_i}|^2,
\end{align}
with $|j_{s_i}\rangle$ as the basis element and the post-quantum state after the measurement
is given as
\begin{align}\label{eq:poststate}
|\psi'\rangle =\dfrac{\sum_{i=0}^{2^{N-1}-1}
|j_{s_i}\rangle\langle j_{s_i}|\psi\rangle}
{\sqrt{p(0)}}.
\end{align}
Similarly, the probability
for getting the outcome $|1\rangle$
reads
\begin{align}\label{eq:prob1}
 p(1) = 1-p(0),
\end{align}
and the post-state is
\begin{align}\label{eq:poststate1}
|\psi'\rangle =\dfrac{\sum_{i=0}^{2^{N-1}-1}
|j_{s_i+2^n}\rangle\langle j_{s_i+2^n}|\psi\rangle}
{\sqrt{p(1)}}.
\end{align}

For all-qubit measurement,
the post-quantum state will
collapse to one of $\{|j\rangle\}$
with the probability of $|\alpha_j|^2$.
In Qsun,
we build these two measurements
onto \texttt{measure\_one} and
\texttt{measure\_all}, respectively.

\begin{figure}[t]
\centering
\includegraphics[width=8.0cm]{compare-eps-converted-to}
\caption{Comparing computational time $t$ (in seconds) of different QVMs as increasing the number of qubits $N$. Inset: The testing circuit including an $H$, a $\sqrt X$, and a CNOT gates acts on each qubit. The depth is fixed at 10, and the number $N$ of qubits is varied to assess the QVM performance.}
\label{fig:benchmarking1}
\end{figure}

\subsection{Assessing the QVM performance}

Let us now assess the performance of Qsun and compare it with three existing ones in Pennylane, Qiskit, and ProjectQ.
Note that Qsun and ProjectQ  belong to the wavefunction class, while the others are in the matrix multiplication class.
We have adopted the testing circuit from Ref.~\cite{quantest} composed of the Hadamard, $\sqrt{X}$, and CNOT gates acting on each qubit.
We have fixed the depth of the circuit at 10 and varied the number of qubits $N$. The code for this test is shown in \ref{appendix:test}.

Fig. \ref{fig:benchmarking1} represents the change of computational time when the number $N$ of qubits increases. In general, there are two magnitudes of slope corresponding to two ways of QVM implementation. While the wavefunction-based approach is faster than the matrix-multiplication one for small numbers of qubits ($N < 8$), the opposite behavior is observed for larger numbers of qubits.
This observation reflects the basic properties of these two approaches as discussed above and see also Ref. \cite{suzuki2020qulacs}.
However, there are some available techniques to improve the performance of the wavefunction approach for larger numbers of qubits, such as, SIMD (single-instruction, multiple data) optimization and multi-threading \cite{suzuki2020qulacs}.
We further summarize a comparison between Qsun and other simulators in terms of
practical quantum algorithms in Table~\ref{t:2}.

\begin{widetext}
\begin{center}
\begin{table}
\small
\caption {Comparison between Qsun and other simulators} \label{t:2}
    \begin{tabular}{|c|c|c|c|c|}

        \hline
        \textbf{Algorithms} & \textbf{Qsun} & \textbf{ProjectQ} & \textbf{Qiskit} & \textbf{Pennylane} \\
        \hline

    Standard algorithms & \textcolor{green}\ding{51} & \ding{51} & \ding{51} & \ding{51} \\
   \rowcolor[gray]{.9} Quantum diferentiable programming & \textcolor{green}\ding{51} & \ding{51} & \ding{51} & \ding{51} \\
   Quantum Linear Regression  & \textcolor{green}\ding{51} & \ding{51} & \ding{51} & \ding{51}  \\
   \rowcolor[gray]{.9} Quantum Neural Network  & \textcolor{green}\ding{51} & & \ding{51} & \ding{51} \\
    \hline

    \end{tabular}
\end{table}
\end{center}
\end{widetext}

\section{Quantum differentiable programming implementation in Qsun}
\label{seciii}

Given a quantum state $|\psi(\vec\theta)\rangle$ with $\vec\theta$ as variational parameters and an observable $\widehat C$,
the task is to seek the global minimum of
the expectation value
$C(\vec\theta) = \langle\psi(\vec\theta)|\widehat C|\psi(\vec\theta)\rangle$ with respect to parameters $\vec\theta$. For example, if $\widehat C$ is a Hamiltonian, its global minimum is the ground state energy. In general, $C(\vec\theta)$ is called as the cost function, and minimizing the cost function requires its derivative with respect to parameters $\vec\theta$, $\partial C(\vec\theta) / \partial\theta$. In classical computing, if the analytical form of $\partial C(\vec\theta) / \partial\theta$ is unknown, finite difference methods are often used to evaluate the derivative approximately. Although this approximation is fast and easy to implement, its accuracy depends on discretization steps. In contrast to the classical finite differentiation, quantum differentiable programming (QDP) is an automatic and exact method to compute the derivative of a function.
QDP is thus essential for accurate gradient computation in multiple VQAs, including QML models.

\begin{algorithm}
\SetAlgoLined
\KwResult{Derivative of a function}
 $f \leftarrow$ Function;
 $c \leftarrow$ Quantum Circuit\;
 $p \leftarrow$ Params;
 $s \leftarrow$ Shift\;
 {\it diff} $\leftarrow$ [0, ..., 0], size({\it diff}) = size($p$)\;
 \For{i $\leftarrow$ 0, {\rm size($diff$)}}{
    $p$\_plus $\leftarrow$ copy($p$)\;
    $p$\_subs $\leftarrow$ copy($p$)\;
    $p$\_plus[$i$] $\leftarrow$ $p[i] + s$\;
    $p$\_subs[$i$] $\leftarrow$ $p[i] - s$\;
    {\it diff}[$i$] $\leftarrow (f(c, p$\_plus) $- f(c, p$\_subs))/(2*sin($s$))\;
 }
 \caption
 Quantum differentiable programming implementation in Qsun}
\label{al:QDP}
\end{algorithm}

The heart of QDP is the parameter-shift rule that is analytically computed using
quantum circuits. The algorithm is outlined in Algorithm \ref{al:QDP}. Let us introduce a parameterized generator $\widehat V$ independent of $\vec\theta$ such that $|\psi(\vec\theta)\rangle =
e^{i\vec\theta\widehat V}|\psi\rangle$.
The cost function is then rewritten as
\begin{align}\label{eq:cost}
  C(\vec\theta) = \langle\psi|e^{-i\vec\theta\widehat V}
    \widehat C e^{i\vec\theta\widehat V}|\psi\rangle
    ={\rm Tr}\bigl(\widehat C e^\mathcal{Z}[\rho]\bigr),
\end{align}
with $\rho = |\psi\rangle\langle\psi|$;
$\mathcal{Z} = i\vec\theta \widehat V$,
and the superoperator $e^\mathcal{Z}[\rho]=
e^\mathcal{-Z}\rho e^\mathcal{Z}$
\cite{miller_1990}.
The parameter-shift rule for each $\theta\in\vec\theta $ states that
\begin{align}\label{eq:psr}
    \dfrac{\partial C(\vec\theta)}{\partial \theta}
    ={\rm Tr}\bigl(\widehat C
    \partial_\theta e^\mathcal{Z}[\rho]\bigr)
    = c\bigl[ C(\vec\theta + s) - C(\vec\theta - s) \bigr],
\end{align}
where $c=1/(2\sin(s))$, and $s$ is determined based on the superoperator and independent of $\vec\theta$.
The values of the cost function $C$
at $\vec\theta \pm s$ are measured on
quantum computers by implementing
two quantum circuits as follows
\begin{figure}[hbt!]
    \centering
    \leavevmode
    \Qcircuit @C=0.5em @R=1em {
    \lstick{\ket{\psi}} & \gate{e^{i(\vec\theta + s)\widehat V}} & \meter{C} & \rstick{C(\vec\theta + s)} \qw \\
    & &  \langle\widehat C\rangle  \\
    \lstick{\ket{\psi}} & \gate{e^{i(\vec\theta - s)\widehat V}} &\meter{C} & \rstick{C(\vec\theta - s)} \qw \\

    }
\end{figure}\\

The derivative is finally obtained by subtracting measurement results from the two circuits. An advantage of the parameter-shift rule is that it can compute the derivative of the given function exactly while the shift $s$ can be chosen arbitrarily large \cite{quanshiftrule}.

\begin{figure}
\centering
\includegraphics[width= 8.0cm]{compare_time_QCD_projectq-eps-converted-to}
\caption{Computational time $t$ in seconds of the QDP implementation in Qsun, ProjectQ using an engine Simulator() and Pennylane using a default.qubit device when the number of qubits increases. Inset: quantum circuits used for the QDP test.} \label{fig:test_qdp}
\end{figure}

We combine the QDP implemented in Qsun
with a classical optimizer like adaptive moment (Adam) optimization
and implement quantum gradient descent,
making the optimization procedure fully quantum.
Let us now examine the performance of the QDP
in comparison with Pennylane,
another QML-oriented platform.
In this test, we measure
the computational time spent for
optimizing the ground state
of an Ising model.
The code for running this test
is given in \ref{app_QDP},
and a tutorial explaining
how to use QDP with sample codes is written
in \ref{appendix:tutorial}.

Fig~\ref{fig:test_qdp} presents
the change of computational time
when increasing the number of qubits $N$
for three cases of Qsun, Pennylane, and ProjectQ.
As shown in the inset of Fig.~\ref{fig:test_qdp},
for each qubit, we have two variational parameters
$\vec\theta$, meaning that the number of variational
 parameters is twice of $N$.
Qsun is faster than Pennylane for
$N < 5$, whereas it is slower for larger numbers
of qubits ($N > 5$).
Among the three cases,
ProjectQ consumes the most computational time for all $N$.
Of course, the exponential growth with
the number of qubits is not inevitable.

\section{Quantum machine learning applications using  Qsun}
\label{seciv}
Various quantum machine learning models
can be developed with quantum differentiable programming (QDP) implementations
to evaluate the gradient and employ
gradient-based optimization.
This section demonstrates QML applications
using Qsun in two well-known models:
quantum linear regression (QLR)
and quantum neural network (QNN).
Its performances are compared
to other standard tools.

Before digging into detailed examples,
let us derive the QDP implementation
in derivative of a standard mean squared
error cost function:
\begin{align}\label{eq:mse}
    C(\vec \theta) = \frac{1}{M}
    \sum_{i=0}^{M-1} \Big(y_i - \widehat{y}_i\Big)^2,
\end{align}
where $\vec\theta$ is a tuple of
variational parameters, $y_i$ represents
the true value and $\widehat y_i$
stands for prediction value,
with $i\in [0, M-1], M$
the number of samples in the dataset to be trained.
Concretely, we also consider the prediction value
is a composition function of an activation function
$f(\vec\theta)$, i.e., $\widehat y_i(f(\vec\theta))$.
Then, we derive at a chain rule:
\begin{align}\label{eq:gradchain}
    \frac{\partial C(\vec{\theta})}{\partial\theta}
    =\frac{1}{M}\sum_{i=0}^{M-1}
    \frac{\partial C(\widehat y_i)}{\partial\widehat y_i}
    \frac{\partial \widehat y_i(f)}{\partial f}
    \frac{\partial f(\vec{\theta})}
    {\partial \theta},
\end{align}
where $\theta\in\vec\theta$, with
\begin{align}
\frac{\partial C(\widehat y_i)}{\partial\widehat y_i}
    =-2[y_i-\widehat y_i],
\end{align}
the derivative $\frac{\partial \widehat y_i(f)}{\partial f}$
depends on the particular form of the activation function,
and
\begin{align}\label{eq:gradxf}
\notag \frac{\partial f(\vec{\theta})}{\partial\theta}
    &=\sum_k \frac{\partial m_k(\vec\theta)}
    {\partial\theta}\\
    &=
    \sum_k c_k\Bigl[m_k(\vec\theta+s_k)
    - m_k(\vec\theta-s_k)\Bigr],
\end{align}
where $m_k(\vec\theta) = \langle\psi(\vec\theta)|
\mathcal{\widehat M}_k |\psi(\vec\theta) \rangle$
is a measurement outcome of an operator
$\mathcal{\widehat M}_k$ for a measurement set $\{k\}$.
To arrive at the second equality in Eq.~\eqref{eq:gradxf},
we have applied the parameter-shift rule \eqref{eq:psr}.

\subsection{Quantum linear regression}

We implement quantum linear regression
on a ``diabetes'' dataset \cite{diabetes}
available in the scikit-learn package \cite{scikit-learn}
with 400 samples for the training set
and 10 samples for the testing set.
We write the linear regression model in the form
\begin{equation}
    \widehat{y} = w x + b ,
    \label{classic_linear_model}
\end{equation}
where $w$ and $b$ are the slope
and intercept of the linear regression
need to be obtained.
To evaluate them on quantum computers,
we store their values in two qubits.
The values of  $w$ and $b$ now become
the expectation values of
the Pauli matrix $\widehat\sigma_z$.
The quantum version of
linear regression model
\eqref{classic_linear_model} states
\begin{equation}\label{linear_model}
    \widehat{y}(\vec\theta) =
    k\big(\langle \widehat w \rangle x
    + \langle \widehat b \rangle\big),
\end{equation}
where $k$ is the scaling factor
that transforms the output data
from $[-1, 1]$ into $[-k, k]$.
Its value should be chosen so that the R.H.S can cover
all of the true values $\{y_i\}$.
Here, $w, b$ are functions of
variational parameters $\vec\theta$,
for example $w \equiv w(\vec\theta)
= \langle \psi(\vec\theta)|\widehat\sigma_z |\psi(\vec\theta) \rangle$
with the initial state $|\psi\rangle = |0\rangle$,
(see the inset Fig.~\ref{fig:compare_linear_regression}).
The cost function is the mean squared error
as described in Eq.~\eqref{eq:mse}.

After having the model, we run the circuit
in the inset Fig.~\ref{fig:compare_linear_regression}
to find the optimized values for $w$ and $b$
via updating $\vec\theta$.
We first calculate their derivatives using
the chain rule as shown in
Eq.~\eqref{eq:gradchain} and
the parameter-shift rule in the QDP as
depicted in Algorithm \ref{al:QDP},
and then update new parameters
using gradient descent
\begin{align}\label{eq:grad-des}
    \theta_{\rm t+1} = \theta_{\rm t} -\eta
    \frac{\partial C(\vec\theta_{\rm t})}{\partial\theta},
\end{align}
where $\eta$ the learning rate,
$\vec{\theta}_{\rm t}$ is the set of parameters at time step t.
They are continuously updated
until the optimized values are found.
The quantum circuit that used to train the model
is represented in the inset
Fig. \ref{fig:compare_linear_regression},
and the code is given in \ref{appendix:regression}.

For comparison, we next provide
the analytical solution for minimizing
the cost function \eqref{eq:mse}
with \eqref{classic_linear_model}.
We vectorize:
\begin{align}
    \begin{pmatrix}
     w \\
     b
    \end{pmatrix} = (X^{T}X)^{-1}X^{T}Y
\end{align}
where
\begin{align}
    X = \begin{pmatrix}
     x_{0} & 1 \\
     \vdots & \vdots \\
     x_{M-1} & 1
    \end{pmatrix}, \quad Y = \begin{pmatrix}
     y_{0} \\
     \vdots \\
     y_{M-1}
    \end{pmatrix},
\end{align}
and $T$ the transpose operator.

The performance of Qsun is compared to those of
Pennylane, ProjectQ, and analytical solution using
the same set of parameters.
We use the maximum number of
iterations 1000 and $k = 10$.
For Pennylane, we use
GradientDescentOptimizer()
with its default configuration. For ProjectQ, we use the same optimize algorithm as we have used for Qsun, which is shown in \ref{appendix:regression}.
As we can see from Fig.
\ref{fig:compare_linear_regression},
Qsun's result is closer to
the analytical result than the Pennylane and ProjectQ one, which implies
a high performance of Qsun.
In the same case of the ``wavefunction'' approach,
Qsun has a better efficiency than ProjectQ in the speedup as shown in
Fig. \ref{fig:benchmarking1} and Fig. \ref{fig:test_qdp},
and in the optimization process.

\begin{figure}[t]
    \centering
    \includegraphics[width=8.0cm]{compare_linear_regression_projectq-eps-converted-to}
    \caption{Linear regression models trained by quantum programming using Qsun (blue), Pennylane (green), ProjectQ (orange)
    and analytical solution (dashed purple).
    We use the diabetes dataset
    \cite{diabetes} with 400 samples
    for the training set and
    10 samples for the testing set.
    The boundary $k$ = 10 with 1000 iterations.
    Inset: the quantum circuit that
    trains the quantum linear regression models.}
    \label{fig:compare_linear_regression}
\end{figure}

\subsection{Quantum neural network}

In this subsection, we show the ability of Qsun for deep learning by building and training a quantum neural network (QNN). We model the QNN as a variational quantum circuit (VQC) parameterized with multiple variables that are optimized to train the model. Fig. \ref{fig:qnn_diagram.jpg} represents
the process for building and training our QNNs. It is a hybrid quantum-classical scheme with five steps summarized as follows:

\begin{itemize}
        \item The quantum part:
        \item[]{Step 1:} Quantizing and encoding dataset into quantum states using the amplitude encoding method \cite{PhysRevA.101.032308,PhysRevA.102.032420}.
        \item[]{Step 2:} Building a QNN circuit and measurement.
        \item[]{Step 3:} Evaluating the derivative of measurement results using QDP.
        \item The classical part:
        \item[]{Step 4:}
        Deriving the derivative of the defined cost (loss) function.
        \item[]{Step 5:} Running a gradient-based optimization and updating parameters.
\end{itemize}

\begin{figure*}[hbt!]
    \centering
    \includegraphics[width=14cm]{QNN_diagram}
    \caption{\label{fig:qnn_diagram.jpg}A Quantum Neural Network framework. The blue box is the quantum part of the QNN, and the green box is the classical part of the QNN. At first, quantify and encode the dataset (training and testing) into quantum states of qubits $|\psi_i\rangle$. Each feature in the dataset encodes into one qubit.
    The employed rotation gates will parameterize the quantum circuit, and the CNOT gates cause entangled in the circuit. These gates repeat L times for L layers in the quantum neural network. After that, we measure the circuit and give the corresponding probabilities $p_k$. We employ a  QDP scheme with the pentameter-shift rule to calculate the derivative of $p_k$ and send the results to a classical computer to derive the derivative of the loss function. After that, we implement a gradient-based optimization to obtain new parameters. When the scheme is not optimal yet, we update the circuit with new parameters; when it is optimal,
    we turn it to the testing process.}
\end{figure*}

\subsubsection*{Data quantization and amplitude encoding}

Set $x_j^{(i)}$ as the $i^{\rm th}$ sample ($i\in[0, M-1]$) of the $j^{\rm th}$ feature ($j \in [0, N-1]$) in the dataset of $N$ features with $M$ samples for each feature.
Since we only analyze one sample (other samples are treated similarly), we can omit the indicator $i$ and
rewrite $x_j^{(i)}$ as $x_j$. We now map $x_j$ into a qubit by normalizing its value in range $[x_j^{\rm (min)}, x_j^{\rm (max)}]$ into $[0, 1]$.
Using the Min-Max normalization, we
obtain
\begin{align}
\widetilde x_j = \dfrac{x_j - x_j^{\rm (min)}}{x_j^{\rm (max)} - x_j^{\rm (min)}}.
\end{align}
Here, the normalized value $\widetilde x_j \in [0, 1]$.
We map this value into
the amplitudes of a qubit as
$|\psi_j\rangle = \sqrt{\widetilde x_j} |0\rangle + \sqrt{1-\widetilde x_j} |1\rangle.$
Then, the quantum state for $N$ features reads
\begin{align}
    |\Psi\rangle =
    \bigotimes^{N-1}_{j=0} \ket{\psi_{j}}
    =\bigotimes^{N-1}_{j=0}
    \left( \sqrt{\widetilde x_j}\ket{0} + \sqrt{1-\widetilde x_j} \ket{1} \right).
\end{align}
 %
The encoding implementation is given in Algorithms \ref{al:Encoding}:

\begin{algorithm}
\SetAlgoLined
\KwResult{Probablity amplitudes of QNN's initial quantum states}
 sample $\leftarrow$ sample\_scaled\;
 $N$ $\leftarrow$ number\_of\_features\;
 ampl $\leftarrow$ [0, ..., 0], size(ampl) = $N$\;
 \For{i $\leftarrow$ 0, N-1}{
    ampl[$i$] $\leftarrow$ [sqrt(sample[$i$]), sqrt(1-sample[$i$])]\;
 }
 ampl\_vec $\leftarrow$ $\text{ampl[0]} \otimes \text{ampl[1]} \otimes \cdots \otimes \text{ampl[$N$-1]}$\;
 \caption
 Encoding data in Qsun}
\label{al:Encoding}
\end{algorithm}

\subsubsection*{Building the QNN circuits}
The QNN model uses $N$ qubits for $N$ features
and includes multiple layers. It is parameterized through a set of variables $\vec{\theta} = \{\theta_{kjj'}\}$ with $k$ as the layer index, $j$ as qubit (feature) indices,
and $j'$ indicates the number of rotation gates implementing on each qubit.
Each layer has one $R_x$ and $R_y$
gates for each qubit followed by CNOT gates
generating all possible entanglements
between them if the number of qubits
is more than one.

\subsubsection*{Decoding probabilities into predictions}

Here, we map measurement results from the previous step into classical predictions by using an activation function.
We consider the expectation value of the projection operator $\widehat\Pi = |1\rangle\langle 1|$ as
\begin{align}
    p^{(i)}_j\equiv
    \braket{\widehat\Pi}
    = \langle\psi^{(i)}_j|1\rangle\langle
    1|\psi^{(i)}_j\rangle
    = |\langle
    1|\psi^{(i)}_j\rangle|^2.
\end{align}
Note that $|\psi^{(i)}_j\rangle$
is the final state of qubit $j$
at sample $i$.
We also emphasize that
one can choose
the projection operator
$\widehat \Pi$ arbitrarily.
We use the sigmoid function,
$S(x) = 1/(1+e^{-x})$ to transform
the measurement data into predictions.
In our concrete example below,
we have two features represented
by two qubits, i.e, $j = 0, 1$.
We use the prediction rule as
\begin{align}
     S_i(p) =
    S\bigl(\gamma(p^{(i)}_0-p^{(i)}_1)\bigr),
\end{align}
where $\gamma$ is a scaling shape for the
sigmoid function such that for large $\gamma$
then $S(x)$ becomes a Heaviside step function.
To use a soft prediction,
we introduce a label-conditional
probability for a prediction value as
\begin{equation}
\widehat{y}_{i}(l) = \left\{\begin{array}{lr}
S_i(p), & \text{for } l = 0\\
1- S_i(p), & \text{for } l  = 1
\end{array}\right..
\end{equation}

\subsubsection*{Training the QNN model}
In the current version of Qsun,
we are using a quantum-classical hybrid scheme
combining QDP and the classical Adam optimization
to train our QNN model.
The cost function is defined by
\begin{equation}
        C(\vec{\theta}) = \frac{1}{M}
        \sum_{i=0}^{M-1}
        \bigl[ 1-\widehat{y}_{i}(y_i) \bigr]^{2}, \label{eq:cost2}
\end{equation}
which is a function
of $\vec{\theta}$. Here, $y_{i} \in \{0, 1\}$ are true values,
$\widehat{y}_{i}(y_i)$ are predicted probability
conditioned on the label $y_i$.
We then evaluate the derivative of the cost function using QDP,
followed by a gradient-descent procedure to search for optimal parameters $\vec{\theta}$.

The derivative of the cost function
concerning each $\theta_{kjj'} \in \vec{\theta}$
following the chain rule \eqref{eq:gradchain}
gives
(hereafter, we omit its indices)
\begin{align}\label{eq:grad}
    \frac{\partial C(\vec{\theta})}{\partial\theta}
    =\frac{1}{M}\sum_{i=0}^{M-1}\frac{\partial C(y_i)}{\partial\widehat y_i(l)}
    \frac{\partial \widehat y_i(l)}{\partial p}
    \frac{\partial p(\vec{\theta})}
    {\partial \theta},
\end{align}
with
\begin{align}
\frac{\partial C(y_i)}{\partial\widehat y_i(l)}
    &=-2[1-\widehat y_i(l)], \\
\frac{\partial \widehat y_i(l)}{\partial p}
    &=(-1)^l\widehat y_i(l) [1-\widehat y_i(l)],
\end{align}
and
\begin{align}
\notag \hspace{-0.25cm}\frac{\partial p(\vec{\theta})}{\partial\theta}
    &=\gamma\frac{\partial}{\partial\theta}
    \Bigl(p^{(i)}_0-p^{(i)}_1\Bigr)\\
\notag   &=\gamma\Bigl\{
    c_0\bigl[p^{(i)}_0(\theta+s_0) - p^{(i)}_0(\theta-s_0)\bigr]\\
    &\hspace{0.5cm}
    -c_1\bigl[p^{(i)}_1(\theta+s_1) - p^{(i)}_1(\theta-s_1)\bigr]
    \Bigr\},\label{eq:gradx}
\end{align}
here, we have applied the parameter-shift rule \eqref{eq:psr}.
We finally update the model with new parameters using
the Adaptive Moment (Adam) optimization algorithm~\cite{kingma2017adam}
as follows. Let $g_{\rm t+1}$
be the gradient of the cost function w.r.t.
$\theta$ at time step t+1, (t starts from 0):
\begin{align}\label{eq:gt1}
    g_{\rm t+1} \equiv \frac{\partial C(\vec{\theta}_{\rm t})}{\partial \theta},
\end{align}
where $\vec{\theta}_{\rm t}$ is the set of parameters at time step t.
Next, we estimate the first and second order moments of the gradient as
\begin{align}\label{eq:fs}
    v_{\rm t+1} = \beta_{1} v_{t} + (1-\beta_{1}) g_{t+1} \\
    w_{\rm t+1} = \beta_{2} w_{t} + (1-\beta_{2}) g^{2}_{t+1},
\end{align}
and compute
\begin{align}\label{eq:vwh}
    \widehat{v}_{\rm t+1} = \frac{v_{\rm t+1}}{1 - \beta_{1}^{t+1}},
    \text {and }
    \widehat{w}_{\rm t+1} = \frac{w_{\rm t+1}}{1 - \beta_{2}^{t+1}}.
\end{align}
Here, $\beta_1, \beta_2$ and $\epsilon$ are nonnegative weights, originally suggested as $\beta_1 = 0.9, \beta_2 =
0.999$ and $\epsilon = 10^{-8}$.
Also, $v_0 = w_0 = 0$.
Finally, the parameter $\theta$
is updated to
\begin{align}\label{eq:update}
    \theta_{\rm t+1} = \theta_{\rm t} - \frac{\eta \widehat{v}_{\rm t+1}}{\sqrt{\widehat{w}_{\rm t+1}} + \epsilon},
\end{align}
where $\eta$ is the learning rate.
The implementation of Adam algorthims in a combination with QDP is given in  Algorithm~\ref{al:GD}.
\begin{algorithm}
\SetAlgoLined
\KwResult{Updated parameters}
 $c \leftarrow$ Quantum Circuit\;
 $p \leftarrow$ Params;
 $s \leftarrow$ Shift\;
 $\beta_{1}, \beta_{2}, \epsilon, \eta \leftarrow$
 Beta$_{1}$, Beta$_{2}$, Epsilon, Eta\;
 $v$\_adam, $s$\_adam $\leftarrow$ $v$\_adam, $s$\_adam\;
 $t \leftarrow$  $t^{th}$ iteration\;
 diff $\leftarrow$ zero\_matrix, size(diff) = size($p$)\;
 \For{i $\leftarrow$ 0, {\rm size(param)}}{
    \For{j $\leftarrow$ 0, {\rm size(param[$i$])}}{
        \For{k $\leftarrow$ 0, {\rm size(param[$i][j$])}}{
            $p$\_plus $\leftarrow$ copy($p$)\;
            $p$\_subs $\leftarrow$ copy($p$)\;
            $p$\_plus$[i][j][k]$ $\leftarrow p[i][j][k] + s$\;
            $p$\_subs$[i][j][k]$ $\leftarrow p[i][j][k] - s$\;
            diff$[i][j][k] \leftarrow$ QDP($p$\_plus, $p$\_subs, $c$, $s$)\;
}}}
$p$, $v$\_adam, $s$\_adam $\leftarrow$ Adam(diff, $p$, $v$\_adam, $s$\_adam, $\eta$, $\beta_{1}$, $\beta_{2}$, $\epsilon$, t) \;
 \caption{
 Adam optimization implementation in Qsun}
\label{al:GD}
\end{algorithm}

\subsubsection*{Preliminary QNN results}

\begin{figure*}[t!]
\centering
\includegraphics[width=14cm]{layer_train-eps-converted-to}
\caption{(a) Classical NN model; (b) and (c)
QNN models using Pennylane and
Qsun, respectively;
(d) and (e) are the
zoom-in of (b) and (c), respectively. Each plot shows from 1 layer (1L)
to 5 layers (5Ls). See text for more details about parameters used for each model.}
\label{fig:compare_model}
\end{figure*}

We apply the QNN model on the Social Network Ads dataset  \cite{SNA}.
This is a categorical dataset to determine whether a user purchases a particular product or not.
We consider two features $Age$ and $EstimatedSalary$
to train the model with the output $Purchased$.
We use 400 samples and split them into 323 samples
for the training set and 80 samples for the testing set.
Once the data is normalized,
we encode $Age$ and $EstimatedSalary$
into two qubits $|\psi_j\rangle, j = {0, 1}$, while $y$ = $Purchased$.
We evaluate the predicted value $\widehat y$ and minimize the loss function (\ref{eq:cost2}) to train the QNN model.
The full code is given in \ref{appendix:qnn}.

For the comparison of performance, we train the QNN model using Qsun and Pennylane. We note that while the QDP and Adam algorithm are implemented in Qsun and Pennylane separately, the QNN circuit, encoding, and decoding procedures are the same for both approaches. We also compare their results with those from a classical model to explore advantages of QNN. For the classical NN model, we use the MLPClassifier function from scikit-learn that has 100 nodes per layer with the ReLU activation function. For the QNN model, we have 4 nodes per layer with the sigmoid activation function. We fix
$s_0 = s_1 = \pi/20$ in the parameter-shift rule and $\eta = 0.1$.
For all optimization, we use
the Adam algorithm with $\beta_1 = 0.9,\beta_2 = 0.99$, and $\epsilon = 10^{-6}$.

Fig.~\ref{fig:compare_model} represents
the loss function versus iteration for different layers
as shown in the figure for three cases:
a classical NN model (a) and a QNN model trained by Pennylane (b) and Qsun (c).
In general, the loss function will reduce  and get unchanged after sufficient layers.
In our example, the loss function becomes saturated after 5 layers. As expected, the loss function of QNN model
is much smaller than the the classical one.
Interestingly, when comparing the two quantum approaches (see insets (d, e) for a zoom in), the Qsun loss is converged faster than the Pennylane one.

We next focus on our QNN model with fixed 5 layers.
In Fig.~\eqref{fig:qnn}(a),
we show the reduction of cost functions
and activation functions during the iteration
for the training and testing processes.
They both behave similarly and
become saturated after 100 iterations.
Fig.~\eqref{fig:qnn}(b, c)
represent results for the training and testing sets.
In the figure, both the true value $y$
and the predicted value $\widehat y$
are labeled as `0' and `1'
for $no-purchase$ and $purchase$, respectively.
$y\widehat y$ = `00' or `11' indicates a correct prediction,
whereas $y\widehat y$ = `01' or `10'
indicates a wrong prediction.
It can be seen from Fig. \ref{fig:qnn}
that our QNN model has a good performance,
reflected by large values of
main diagonal elements
$y\widehat y$ = `00' and `11'.
Importantly, unlike the classical
neural network \cite{SNA},
it does not require many nodes in each layer,
which is one of the main advantages of QNN.

\begin{figure*}[t]
\centering
\includegraphics[width=14.0cm]{qnn-eps-converted-to}
\caption{
Results from our QNN model with five layers
and two features on the Social Network Ads dataset.
(a) Plot of loss and accuracy versus
iteration for the training and testing process.
(b, c) The confusion matrices for the training and testing sets.
Here we use 400 samples and split them
into 320 samples for training
and 80 samples for testing
with 400 iterations.}
\label{fig:qnn}
\end{figure*}

\section{Conclusion}\label{secv}
We have developed Qsun, an open-source platform of quantum virtual machine, that simulates the operation of a real quantum computer using the wavefunction approach. For small qubit numbers, the current version of Qsun runs standard tasks significantly faster than other platforms do. The quantum differentiable programming is implemented as a built-in function of Qsun, allowing us to execute quantum machine learning applications effectively. We have employed Qsun to implement two standard models in machine learning: linear regression and neural network. For the former, Qsun yields a quantum regression model nearly overlap with the classical reference, and somewhat better than the Pennylane one. For the latter, the QNN model trained using Qsun shows a good performance with a less number of nodes in each layer than the classical neural network.
Although Qsun is aimed to quantum machine learning problems, as a generic quantum virtual machine, it can be used for multiple other purposes, such as developing and testing variational quantum algorithms for electronic structures or quantum information. It is well-fit to personal use thanks to its light weight. Qsun is under active development to cover a wide range of contents in machine learning. Our code is open source and available on GitHub \cite{QSUN}.

\begin{acknowledgments}
This work was supported by JSPS KAKENHI Grant Number 20F20021.
\end{acknowledgments}

\bibliographystyle{unsrt}

redpajama_set_name: RedPajamaArXiv


text:
Grave Matters
Carlton Stowers
| Longform |
Carlton Stowers | July 12, 2001 | 4:00am
On quiet evenings, before Malcolm X Boulevard teems with late-night life, Harold Williams climbs into an old pickup with a cranky transmission and visits the ghosts of the city's past. Caretaker of the 60-acre Oakland Cemetery, one of the oldest and most historic graveyards in Dallas, Williams takes with him the tools of his trade--a lawn mower, a gas-powered weed eater and a .38-caliber pistol.
As the 46-year-old Williams slowly winds his way through the familiar labyrinth of 30,000 headstones, many bearing the names of those who forged Dallas into a vibrant and progressive metropolis, he rarely fails to wonder at the rich history over which he is assigned to watch. Yet visitors to the all-but-forgotten resting place of bygone generations, he admits, are rare. "Some days," he says, "there might be two, maybe three. A lot of days there are none." In a silent nod to the political correctness of the day, he will offer no reason. But it is obvious.
Once proud and well-kept, located just a few blocks from the intersection of Oakland and Forest avenues when the area was populated by high-profile families like the Sangers and the Harrises, the cemetery is now guarded by a dilapidated fence and an entranceway gate that is routinely locked at sundown. Oakland and Forest have long since seen name changes to honor black icons Malcolm X and Martin Luther King, and the graveyard is now the centerpiece of a neighborhood of quick-stop liquor stores, barbecue joints and too-much-time-on-their-hands youth gangs identified by the color of their sneakers--red, yellow and green--who jealously guard nearby turf. There is an isolated spot just beyond the northern edge that is favored by young car thieves who expertly strip away quick-cash parts. Call 911, as Williams has done regularly during his five years as sexton-caretaker, and response time often will be an hour, maybe longer.
But hidden inside the cemetery boundaries are reminders both wistful and upsetting, vestiges of a time when the area danced to high society's tune and was silk-stocking white. Confederate soldiers of high rank and deeds once viewed as patriotic, even heroic, lie beneath aging, breathtaking monuments sculpted by craftsmen from as far away as Florence and Venice. Many buried there lived in a time when the nation's racial divide was wide and clearly defined; a time when the Texas State Fair, held annually in nearby Fair Park, did not wince at the idea of designating one date "Negro Day" and another "Ku Klux Klan Day." In Oakland Cemetery, deep in the heart of mostly black southeast Dallas, many of those Klansmen are buried, outnumbering by hundreds the 15 black graves--many of them nannies of prominent families--found there.
It is a landmark that mirrors the beauty and ugliness of the city's history. Although there is hope that Oakland Cemetery will soon receive monies to provide much-needed repair and updating, there are no guarantees. Even so, given its location and low profile, the cemetery most likely will continue to be at best ignored, at worst neglected.
Which is inexcusable. The stories buried there form the roots of Dallas, fast-decaying signboards that point to its successes and its failings, its moments of glory and shame. It is the final resting place of many whose money, clout and foresight helped build the city. For those reasons alone, Oakland Cemetery deserves more attention than it receives.
Wandering into its overgrown grounds, one finds many of the same honored names city fathers have assigned to the streets and byways of Dallas. There is Edwin Kiest, publisher of the Dallas Times Herald before the turn of the century; A.H. Belo, son of the founder of the media conglomerate that today includes The Dallas Morning News and WFAA-TV; members of the Caruth family who once owned much of the land that would become the Southern Methodist University campus, North Dallas shopping centers and residential showplaces; Adam Janelli, founder of the city's Salvation Army; John Armstrong, developer of Highland Park; J.F. Strickland, who started the company that is today TU Electric; engineer John O'Connor, who oversaw the building of the seawall in Galveston after the infamous hurricane that devastated it in 1915; Portugal-born insurance company owner Louis Antonio Pires, who donated almost $1 million to establish the Buckner Orphans Home.
In fact, the roll call of names familiar to Dallas historians are many: Ervay, Thornton, Akard, Miller, Record, Minyard, Grauwyler, Cabell, Armstrong, Zang and Bartos. They include ex-mayors (Winship Conner, Williams Holland, Louis Blalock), a lieutenant governor (Bennett Gibbs), wife of a former New York City mayor and an ambassador to Mexico (Sloan Simpson O'Dwyer), religious leaders (Episcopal Bishop Alexander Garrett), entertainment luminaries (B-movie actress Dorothy Brannen Exall) and patrons of the arts (Mrs. J.T. Trezevant, founder of the Dallas Shakespeare Club). Individually and collectively, they signal the prosperity and progressiveness of generations past.
Too, there are markers that remind of darker times in the city's history. More than 2,000 grave sites honor those buried in 1918 and 1919 alone, during an influenza epidemic spread by soldiers returning home from World War I. At a grave site donated by a Dallas funeral home rests Santos Rodriguez, the 12-year-old shot and killed by a rogue Dallas police officer in the backseat of a patrol car on a dark and infamous summer night in 1974 (Dallas Observer, July 16, 1992). Just a few yards away, in the canopied shade provided by a tangled grove of trees, is the headstone marking the grave of Florence Brown, daughter of a Dallas policeman whose 1913 murder has long remained a mystery (Dallas Observer, June 14, 2001). And in a section of the cemetery that is predominately Hispanic, the bodies of two 19-year-old members of rival gangs are buried side by side.
The history, ancient mixing with modern, not only tells the tale of Dallas but also speaks to Oakland Cemetery's past. By the late 1880s, with the arrival of a railroad creating rapid growth, Dallas' City, Pioneer and Greenwood cemeteries were filling quickly, leaving only small family burial grounds and those constructed by organizations like the Masonic Lodge and the Order of Odd Fellows as burial sites. George Loudermilk, a forward-thinking entrepreneur of the day, began making plans with fellow businessmen to purchase land for a new cemetery that would serve the community's needs for decades to come. "First-class" was the phrase the promoters used. Designed by well-known engineer Benjamin Grove of Louisville, Kentucky, Oakland Cemetery would be built on bounty land originally deeded to a man named Thomas Lagow who had received it from the Republic of Texas in exchange for his participation in the War with Mexico. Years later, his sons would trade away another parcel of the 4,400-acre Lagow holdings--land where Fair Park today stands--for a team of oxen and a wooden plow.
When Oakland was dedicated on December 8, 1892, it was far outside the existing Dallas city limits. Among the rules and regulations established by Loudermilk and his fellow Cemetery Company partners was that it would be the city's first perpetual-care facility. Families bidding loved ones farewell could rest assured that the final resting places of their mothers and fathers, husbands and wives, sons and daughters, would be well-kept forever.
By 1923, however, ownership of the cemetery was transferred into a nonprofit corporation known as the Oakland Cemetery Lot Owners Association, and a trust fund was set up for its long-term operation and care. A board of directors agreed that only the interest earned by the trust would be expended for salaries of cemetery employees and the facility's upkeep.
Events that the planners had not anticipated offered early signals that all would not forever be well. The stock market crash of 1929 virtually wiped out the trust fund, creating the need for sizable bank loans to keep Oakland in business. Additionally, the grand plan did not take into consideration that the time would arrive when all lots were sold and only a half-dozen burials a year could be conducted. In effect, the income meant to assure the promised "first-class perpetual care" would be drastically reduced.
Today caretaker Williams, the lone full-time employee at Oakland, operates on a budget best described as "Spartan." In addition to running the office, he lives year-round on the property, standing watch as its one-man security force. Aside from part-time mowing and general cleanup help he hires for $8 an hour a few times a month, he is responsible for most of the maintenance. Occasionally, he says, volunteer Boy Scouts, church groups and the Dallas Genealogy Society lend a hand.
When a rare burial is scheduled, it is Williams and a 74-year-old helper, who has performed the task for years, who dig the grave with pick and shovel, then stand by to fill it after the services are concluded.
"Back in 1960," Williams says, "I understand there was a full-time maintenance crew of 10. Of course, they were only being paid 50 cents a hour in those days." There has, he says, been no consideration given to providing him any kind of staff assistance in the five years since he was hired.
What, then, would it take to return the historic facility to the showplace it once was?
"The place badly needs a new fence," he says, "and, of course, we'll never get the necessary maintenance work done--mowing, edging, watering, trimming trees, cutting away vines--without the financing to hire three or four full-time people. And there are a lot of roads in the cemetery that need to be paved and even curbed if possible."
Now he is smiling, as if dreaming of hitting the lottery. "The board of directors has actually had an architect draw up plans for a new office and sexton's quarters," he says. "That would provide the place with a tremendous face-lift." Estimated cost of the new buildings, according to consulting architect Sally Johnson, would be in the neighborhood of $1.36 million. That's far more than is in the Oakland Trust. In fact, estimates for just replacing the fence surrounding the grounds would put a sizable dent in the fund, since the lowest bid has been in excess of $100,000.
With that, Williams walks behind the small counter that greets the occasional visitor to his office and points to rows of antique metal file drawers. In them are the 30,000 interment cards that provide information on each person buried in the cemetery. Virtually every modernly equipped facility today has such information on computer.
"I checked around," Williams says, "and was told that just to have the information transferred from cards to discs would cost $30,000."
That's $30,000 he doesn't have after paying for the monthly utilities, banking fees, insurance and dumping cost for the brush and limbs he clears away. "We even pay $360 per month to the city for something called storm-drain fees," he says, "and I don't even know what that is."
What he is describing, then, is a century-old business that has reached the point where there is a steadily draining financial out-go and precious little new income being generated. With no new burial plots to sell and few grave site preparations to bill for, the nonprofit Oakland Cemetery Lot Owners Association has become just that.
All that remains is the history, the legends, the countless stories that await those few who choose to visit. They, Williams says, are priceless. And with that he begins to tick off fascinating tidbits passed on to him by his predecessor, Howard Hooper, and from spare-time research he's done:
Confederate General Richard Montgomery Gano, he points out, is buried here. Grandfather of eccentric billionaire Howard Hughes, he was a minister in civilian life and is said to have successfully stolen $2 million in gold from a Union train at the height of the Civil War. It was Gano's father, historians note, who baptized George Washington. There are, in fact, 20 relatives of Hughes buried in Oakland. Family members of World War I Medal of Honor winner Sergeant Alvin York, capturer of 132 German prisoners single-handedly during the Battle of Argonne Forest and immortalized on the silver screen by a young Gary Cooper, rest in Oakland. So too, some historians insist, does the brother of John Wilkes Booth, assassin of President Abraham Lincoln. The Hobbys of Houston have relatives buried in Oakland.
In the far eastern corner of the property is a section where pets of the wealthy and eccentric were once routinely buried--dogs and cats, mostly, but also at least one horse and a chimpanzee.
Among the more colorful early-day animal rights activists to be found in Oakland is Ivor O'Connor Morgan, daughter of a Texas railroad baron-turned-banker, who, before her death 65 years ago, willed $1.5 million be used to build homes for the stray dogs and cats that roamed the city streets.
And if it's scary stories you prefer, there is the grave site of Dallas' Annie Lawther. She, according to long-standing local legend, is the white-gown-clad ghost that has "haunted" the shores of White Rock Lake for decades.
So, why, with its lure of rich history and scenic sculpture, has Oakland Cemetery been all but erased from Dallas history? Why, despite an operating trust fund of almost $1.25 million, has the property been allowed to turn into something more resembling a wildlife preserve than a perpetual-care resting place?
At least part of the problem is one only the boldest of historians and city leaders will straightforwardly address: location, location, location.
For all the claims of social maturity, the simple fact remains that many whites view the predominately black area in which the graveyard is located as a place where they are unwelcome and unsafe. They understand why the Oakland caretaker arms himself with a pistol before going out to mow. A member of the Dallas Genealogy Society says that on recent weekends as she and friends roamed the cemetery in an effort to record grave sites, they were made uneasy by the occasional sounds of gunshots from nearby residential areas.
"It is long past time to quit worrying about who lives in the houses surrounding it," says plain-speaking historian Frances James, Dallas' resident expert on cemeteries and a frequent visitor to Oakland, "and get busy restoring the place to what it should be."
Guide for several Dallas Historical Society tours to the cemetery in recent years, James has become increasingly concerned with the lack of upkeep. "There was one family I know of," she points out, "who used to go out there regularly to visit the grave of a son. The father always brought along a 300-foot-long watering hose because the only working faucet he could find was that far away from the grave site he wanted to take care of.
"And, it seems, every time I suggest bringing a tour group out, I'm met with new excuses. One year it was concern over fire ants; the next it was the danger of dead and dried tree limbs that might fall and prompt lawsuits."
She wonders also what will eventually happen to the magnificent sculpture that has weathered and begun to show signs of decay.
Sitting inside the small and cluttered structure that serves as office and sexton house, caretaker Williams is aware of the shortcomings and the criticisms. "Actually," he says, "most people who have family here are very understanding. Sure, they would like to see improvement, but they realize the problems we're facing.
"Frances James has mentioned several times that she would like to see the roads in the cemetery widened so the bus carrying her tour groups can drive through instead of parking at the entrance and having the people walk," he says. "Where does she expect the financing to come from?"
Oakland Cemetery, he says, is South Dallas' great enigma. Over the years, small donations from individuals and local businesses have trickled in but hardly enough to do more than keep the gates open.
"Most of the people who still come to visit grave sites," he says, "are families of those buried within the last 20 years or so." Generally, they are the descendants of Hispanic families who moved to Dallas in the '40s and '50s and bought up the remaining plots.
Like James, Williams is concerned about the declining condition of many of the cemetery's priceless sculptures. Standing in front of a life-sized gossamer-clad marble angel that has watched over the Armstrong family plot since it arrived here from Genova, Italy, decades ago, he points to the tiny web of cracks that are beginning to show. "Repairing the headstones and monuments here," he says, "would be like trying to raise the Titanic. In the first place, even if the money was available, permission would have to be granted from a member of each family." In the majority of cases, he laments, none is still living.
William C. "Dub" Miller can remember when they were. He grew up with many now buried in Oakland Cemetery. One day, he says, it will also be his final resting place, alongside late wife Nell, whom he married back in 1936. And he's optimistic that when that time comes he will be buried in a cemetery whose glories have been restored.
President of the Oakland Cemetery Lot Owners Association Board of Trustees, the 95-year-old former city councilman (1953-60) and still-active real estate executive does not see the current problems as unsolvable. "We're in the process of seeking out foundations and individuals with an appreciation for the importance of the city's history who might be willing to help us accomplish our goal," he says.
And while tight-lipped about any signs of progress, he hints that in the near future the financing needed for restoration and proper maintenance--an estimated $3 million--might be coming.
"One of the main difficulties we've faced in the 14 years I've been associated with the board," he explains, "is that we're now into the third and fourth generations of many of the families buried there. And times have changed. People today are too busy, too occupied with too many other things, to make a trip out to the cemetery to visit the grave of their ancestors. It's one of those American traditions that seems to have passed."
But not for Miller, who visits Oakland regularly to remember his family, who launched a realty business in 1874. "Today," he proudly notes, "we're the oldest business in Dallas."
He sees the frayed and leafless limbs of trees badly in need of trimming, the vines that have wound their way over headstones, the weeds that now hide too many of the more modest graves. Yet in his mind's eye, he sees the way it was. And the way he hopes it will be again.
"For years," he says, "our main objective has simply been to keep Oakland Cemetery going. We've shown that we can do that and have now set more ambitious goals. It is important that the people of Dallas, regardless of color or heritage, have a sense of this city's history." In fact, he says, the board has set in motion the process to file an application for a historical marker. It is something long overdue.
Another day has passed, and caretaker Williams is slowly driving along the mazelike roads that wind through the cemetery. Birds, noisy throughout the day, have settled quietly into the branches of overhanging trees. A rabbit lifts its head above the grass to stare in surprise at the passing human. A small fox, sleek and startled, dashes from its hiding place behind a tombstone and scurries across the rain-softened road.
The only visitor to the caretaker's office had been an elderly woman in search of the location of an ancestor's grave. All she knew was that his name was Peacock and he had been an Army captain during the first World War. Williams, after a careful search of his antiquated files, was able to direct her to the grave site. Another connection with history made.


Core updates have been popping out from everywhere lately these past few years. Like little hidden land mines, they've eliminated quite a number of websites and businesses that haven't been following guidelines to an exact T.
This year's very first Google confirmed core update did not fail to very same thing as well.
Various SEO and SEM agencies and companies all over the world, even here in Singapore at this point is now very familiar with all of these kinds of updates.
The start of 2019 was filled with a few mysterious things. February had a couple of deadly fluctuations in search that weren't confirmed. But now, it seems that all that was just the newest core update being set up behind the scenes.
This new Google core update was rolled out on the 12th of March 2019. This is the first core update that was officially confirmed after last year's August "Medic Update". And while that first one had a somewhat cool name, this very recent one had a more creative one. "March 2019 Core Update".
While its older brother, 2018's Medic update mainly targeted health, fitness and wellness themed sites, this year's first official update has been observed to reverse all of these effects like an evil sister.
Well, reversed in to a certain degree. Websites last year that had benefited from the extreme core changes from Google Medic seems to have all dipped in performance this year. And all of the ones that had negative experiences and performance last year seem to be doing better because of this March 2019 update.
It has been determined by a whole slew sites out there that the main beneficiaries are those sites that has a strong brand profile and a broad focus on topics. This means that the sites and businesses out there that over focus on their niche has fallen in performance.
This is a big thing since, there are still businesses out there that build their notoriety by over focusing themes on the niche their campaigns are in. What most of them do not realize is that the whole campaign starts to look a little bit more unnatural. Having topics that can be a bit broader and can cover a more diverse set of topics are deemed more natural. Which makes sense. This was the whole point from the beginning but, over specialising on these things can be a bit tempting.
This means that if you happen to be currently shopping for agencies out there to help you out with your business online, always look for ones that can offer SEO services that gives you a more natural and broader type of approach.
Google has said that the March 2019 update is worth confirming but it doesn't mean that this is the biggest update it has done. Which might scare you if you're doing something to cheat your way up the ranks.
Generally, the only next step is that websites and businesses continue to pool all their efforts on building trust and authority. Producing and sharing content that's actually valuable and authoritative.
These businesses and websites can also try to update all of the elements on their websites that contribute to good user experience. Imagine a website that has really slow loading speed, or has parts where the pages won't load. The level of trustworthiness there won't be too good. Users will instead get the idea that the site is shady or has something bad happening behind the scenes.
It would not matter that much even if you have all of the best and most compelling authoritative content. If you are running a website that performs badly, it would all be a very sad waste.


text:
Assistant Professor of Computer Science Dr. Christian Roberson, left, and senior Katarina Sperduto collaborated on a research challenge involving artificial intelligence. Together, they produced a scholarly paper based on the card game Birds of a Feather (a variation of Solitaire) that brought an invitation to present their findings at a major national conference.
Computer Science Project Sends Researchers to Aloha State
by FSC Staff
An educational research challenge based on a game of cards inspired Florida Southern's Dr. Christian Roberson to apply for a summer 2018 collaboration grant with student Katarina Sperduto.
Their resulting work in the areas of artificial intelligence (AI), algorithms, and machine learning led to the submission of a scholarly paper and an invitation for the student/faculty duo to present their findings at a major AI conference in Honolulu, Hawaii.
What's the deal? It's deceptively simple. A variation on the card game Solitaire, called Birds of a Feather, was at the heart of their research. Played with just 16 randomly selected playing cards, laid out in a four-by-four grid, the game was specially created to afford computer science researchers with a new, untested area of study.
Dr. Roberson, assistant professor of Computer Science and the department's chair, collaborated on the Birds of a Feather research challenge with Katarina, who will graduate in May 2019 with a double major in Mathematics and Computer Science. The focus of their work involved the development of an AI player that could effectively determine the solvability of any configuration of cards.
"The objective is to reduce the 16 cards to a single pile of cards," Dr. Roberson explained, by moving the cards individually to cover similar suits or ranks. According to the rules of the game, cards may only be stacked within a shared row or column. "As you reduce the number of cards, you lose places where the cards can be moved. So we developed code to identify states that are unsolvable."
The pair developed a computer program that played through a large number of simulated games, keeping track of each possible move to determine whether or not a game could be solved, and to identify a possible sequence of winning moves. They found that by simulating 400 games and tracking each possible move, the AI player was able to win roughly 95 percent of the time. Boosting the number of simulated games to 4,000 increased the player's effectiveness, improving its win rate to 99.8 percent.
Dr. Roberson and Katarina submitted their research paper, "A Monte-Carlo Tree Search Player for Birds of a Feather Solitaire," to the Ninth Symposium on Educational Advances in Artificial Intelligence (EAAI-19). It was accepted for presentation at the Honolulu conference in late January 2019, where Katarina gave a 13-minute presentation of their findings. The duo also received the Best Paper Award (Runner-Up) in the research challenge track.
"I thought the entire experience was amazing!" Katarina said. "It was great to get involved in undergrad research, which helped with my programming, problem-solving, and professional paper-writing skills, and attending and presenting at the conference helped with my presentation skills, as well."
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Greitens lands another $1 million, and ethics complaint
A top Missouri Democrat says Greitens failed to report a valuable donation.
Greitens lands another $1 million, and ethics complaint A top Missouri Democrat says Greitens failed to report a valuable donation. Check out this story on news-leader.com: http://sgfnow.co/2etFOCt
Will Schmitt, WSCHMITT@NEWS-LEADER.COM Published 5:04 p.m. CT Oct. 19, 2016 | Updated 5:24 p.m. CT Oct. 19, 2016
Missouri Gov.-elect Eric Greitens(Photo: AP file photo)
A top Missouri Democrat has filed an ethics complaint against Eric Greitens, alleging that the Republican gubernatorial candidate did not report the use of a list of donors as an in-kind contribution to his campaign.
The Associated Press reported Oct. 10 that donors who previously supported The Mission Continues, the nonprofit charity for veterans Greitens founded, gave $2 million to the Republican's campaign. Greitens has denied using the charity's list of donors for his campaign's benefit.
Roy Temple, chair of the Missouri Democratic Party, said in his complaint to the Missouri Ethics Commission that Greitens' campaign "did not pay for the list or report it as an in-kind contribution received on its disclosure report" and "violated Missouri's campaign finance law by failing to report in-kind contributions received from the non-profit organization."
Campaigns are allowed to rent such lists from nonprofits, but only if the nonprofit makes the list available to all candidates. Temple's complaint argues that the list "appears to have been very valuable to the Greitens Campaign."
Greitens' campaign manager Austin Chambers characterized the complaint as a distraction and attempted to use it to attack Democrat Chris Koster, who is opposing Greitens in the governor's race.
"We always comply with all campaign finance laws," Chambers said. "Campaigns start filing bogus ethics complaints when they start losing and want to change the subject."
The list obtained by the Associated Press mentions that it was last opened and saved by Michael Hafner, a former Greitens campaign worker who later worked for John Brunner's gubernatorial campaign.
Hafner told the News-Leader he could not comment on his involvement with Greitens' campaign, including whether and how The Mission Continues' list came into his possession.
"In January 2015 in contemplation of a possible engagement, I entered into a confidentiality agreement with Eric Greitens, thus preventing me to comment on any confidential information disclosed to me," Hafner said in a statement.
"I was not fired for cause," Hafner continued. "My contract was simply not renewed due to a change in political strategies by Mr. Greitens and his office."
Humphreys continues to support Greitens
Greitens continued his prodigious fundraising efforts with another $1 million tied to David Humphreys, the CEO and president of Joplin-based TAMKO Building Products.
Greitens on Wednesday reported receiving $500,000 from Sarah Atkins (Humphreys' sister) and another $500,000 from a political action committee that lists Humphreys and Atkins as its sole donors in 2016, according to the ethics commission.
This comes on top of the $500,000 Humphreys gave Greitens in September.
Humphreys has spent millions backing Republicans who support "right-to-work" legislation, which Greitens' has said he would sign if elected governor.
Koster, the Democrat, opposes "right-to-work." The issue is one of the clearest policy differences between him and Greitens.
The election is Nov. 8.
Read or Share this story: http://sgfnow.co/2etFOCt


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export enum AdResult {
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    NotInitialized,
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}

export interface IFullScreenAd extends IAd {
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}

redpajama_set_name: RedPajamaGithub


(2) whether he can arrange that workmens' tickets on the railways should be available for fire-watchers proceeding to their duties in the evening?
My right hon. Friend is waiting a full report from the Railway Executive Committee upon the issues raised. If my hon. Friend will repeat his Question later, he hopes to be in a position to reply.
Back to LONDON WORKERS (SATURDAYS).
Forward to SPEED LIMIT (PROSECUTIONS).


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