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Cards Against Humanity Guide - Games like Cards Against Humanity AD
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Cards Against Humanity Guide – Games like Cards Against Humanity AD
by Cary Grant 11 months ago 2 weeks ago
Games like Cards Against Humanity
Cards Against Humanity is the weird game ever created in history. Read about other Games like Cards Against Humanity with a similar theme.
"Cards Against Humanity" is a party game in which players complete fill-in-the-blank statements using words or phrases printed on playing cards that are usually considered offensive, indecent, or politically incorrect. Each player draws ten white cards to start the game, and there are set rules to play the game.
Each player in the game draws ten white cards to begin the game. The person starts as the Card Czar, who most recently pooped and plays a black card. He has to read the fill-in-the-blank phrase on the black card out loud, and every other player fills in the blank by passing one white card, face down, to the Card Czar.
The Card Czar shuffles almost all of the possible answers and shows each card combination with the group. Card Czar should probably again read the black card before presenting each solution.
Then he picks the funniest play, and its giver gets one Awesome Point. The round is completed here, a new player becomes the Card Czar, and other players draw back up to ten white cards.
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What are 20 Games like Cards Against Humanity?
Other games like Cards against Humanity are described below to guide readers regarding choosing their favorite games.
Sheets & Giggles Game
The Sheets & Giggles Game is another fantastic party game that puts a spin on the classic parody for adults with four rounds having hilarious, inappropriate, action-packed wordplay, almost considered offensive. The team describes terrible words and phrases, acts them, gives a hint of 1 info, and then acts them under a sheet.
Utter Nonsense
It's a card game where you have to read in accents your cards on which written stupid phrases. You must have few friends who are genuinely willing to look silly to play this one, though. Players take turns. The nonsense judge is considered to be the winner. The player who gets the accent card for the round becomes the nonsense judge for the round.
KinderPerfect
This is an adult party game for parents, and this is inspired by Cards Against Humanity, where the player pair cards into hilarious parenting confessions or stereotypes. It consists of 400 CARDS.
Disturbed Friends
Disturbed Friends is a party game and offensive also, that was made to figure out how disturbed your friends are and at the same time, very importantly, how disturbed they think you are. The player is faced with difficult situations and unethical debates that will surely want you to reconsider your friendships.
Go Fish Yourself
Go Fish Yourself is a party game in which players try to get one another to make pairs of dirty-sounding, naval-themed cards. Each team has a ridiculous rule that must be followed to continue the game. Each card has a challenge, so by making more pairs by the player, the more challenges he must face. The last player left in the game wins as all players standing on chairs have socks on their hands and cards on their heads, so a player fails and can't perform a challenge and is out of the game.
Exploding kittens is a beautiful card game for adults, teens, and kids; the player is into kittens and booms, laser beams, and sometimes goats. This game is disordered and having hilarious conclusions at the end.
We Didn't Playtest This At All.
The purpose of the game is to win. It happens when every other has lost. To start the game, shuffle the cards and deal two to each player. To maintain the balance in-game, every player has an equal chance of drawing a Star Card from the deck when their turn comes. Players have to follow the card rules.
Joking Hazard
Joking Hazard is a party game, this hilarious game in which players compete to finish excellent and terrible comic strips with their friends. The Player has to make a 3-panel comic by playing cards and then decide which one is the best.
Urban Dictionary Game
This game is based on a popular website where people define millions of slang words as fun. In Urban Dictionary words, there are hashtags, phrases, and pictures to which players compete to impress the judge. Playing Players can exemplify words as well to win the round. By this game, players get to know who knows how much insane internet slang.
The Voting Game
The Voting Game is a party game that searched for the hilarious truth that is behind your friendships. To find your friends to single each other out. Gameplay changes depend on who you're playing with. Personal stories are outside the box after a revealing vote.
Never Have I Ever is considered the oldest drinking party game, and it puts it into cards to get you thinking. Players ask other players about things they have not done in every turn, and the players who have done this thing answer by taking a drink, a drinking game!
The Game of Nasty Things
The Game of Things is a popular, hilarious series where every player writes in their response, It can be anything that comes to mind, regardless of right or wrong answer, and the person must guess which person said what phrases or words. This may have adult prompt cards to choose from.
Drunk, Stoned, or Stupid
In a party game, in each round, a card is drawn, and the group of players decides who in the group would be most likely to do what is written on the menu. First, a player announces themselves to the judge and reads a card aloud. And Every other player votes for who's most likely to do that is written on the card.
What Do You Meme?
This is a game for the internet generation based on popular memes. Everyone plays a card each round, and it is a popular meme image, and the player plays the caption. It includes all 360 Caption Cards, 45 Photo Cards.
Apples to Apples Party Box
Apples to Apples and Cards Against Humanity has a similar gameplay style. It is a family-friendly game. The player needs to play a similar description to the card on hand as close as possible that is comparing them like apples to apples, so the name of the game.
Red Flags is not recommended for children in the one player is the Single, and he works as a type of Judge. The other players draw four White (Perk) cards and three Red cards (Red Flags). Each player read aloud the cards that they have chosen. Each player, not the Single, takes one of the Red Flag cards from their hand and puts it to the player to their left.
The Single selects which date they would likely choose, that winner would keep red Flag as a symbol of One winning point. All cards are then disposed of, so players re-draw up to four Perks and three Red Flags, and the player to the left of the Single will now the new Single.
READ ALSO: Club Penguin Guide – Most Popular Games Like Club Penguin – Answer Diary
A card-based party game can be best enjoyed with three or more people. Players use qualifications to form a resume, and the players compete with one another to be hired for a job. Players create a story using their capabilities to explain how they are suitable for the job. The employer decides which applicant to be hired for the job.
Million Dollars But
Rooster Teeth made this game; it has one player getting a million dollars. The game is that there is a catch and everyone plays a scenario card to add to the net. So, everyone has to promote or underestimate each one. In the end, the card they wouldn't do for a million bucks would be a winner card.
Spaceteam
In this game, you have to work together to repair the crashing spaceship. Some tools are available to fix the problems. It will be bad if all cards are non-sense, so shout at your friends to help or suffer your death.
Secret Hitler
Secret Hitler is a social deduction game in which around 5-10 people can search and stop the Secret Hitler. Players are either the liberals, who are in the majority of the fascists, who are hidden.
What is Cards Against Humanity Examples?
Sure other games that can be taken as an example of Cards against humanity are;
Cards Against Humanity: Period Pack.
Cards Against Humanity: Geek Pack.
Cards Against Humanity Design Pack.
Cards Against Humanity: Sci-Fi Pack
Cards Against Humanity: Green Box.
Cards Against Humanity: College Pack.
Cards Against Humanity: World Wide Web Pack.
Is there any Cards Against Humanity App?
The iOS and Android apps are available for free, and this is a word-for-word copy of the official version. It can work on smartphones, tablets, and computers; also, it can be played with a group of friends at the same place.
Can we Play Cards Against Humanity Online Multiplayer?
There's a free version of "Cards Against Humanity" that allows you to play with your friends online. The games allow everyone to see the game; at that time, your hand is kept independent.
What is Cards Against Humanity Secret Card?
According to Buzzfeed, people are eager to discover a hidden Card in their Card's Against Humanity box that could be the trump card many times. It is less based n intelligence and choice but rather more on luck.
Where to Buy Cards Against Humanity?
It can be brought from Cards Against Humanity store also from Amazon as well. It can be bought from the Amazon store for 2508€. Further, it can be downloaded from their official website as well.
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Is Cards Against Humanity Good for Kids?
The manufacturing company says this version of the game is designed "for people ages eight and up" and that the content is "PG-rated" as they also tested it with families. But because Many of the regular Cards Against Humanity cards are not relevant for most children, it may not be appropriate for them to play.
What is Cards Against Humanity Cards List?
There are two sets of cards: black cards with questions or fill-in-the-blank statements and white cards with noun phrases that fill those blanks and answer those questions. At the start of each round, one player, called the "car czar," deals with a black card from the deck, and others will answer it with the white card they drew from the deck earlier.
What are Popular Incoherent Games?
A few of the top popular incoherent games apart from Cards against Humanity are:
Xenoblade Chronicles X
Tactics Ogre PSP
What are Popular Cards against Humanity Rules?
To answer, Pick two cards. Each player plays two white cards in combination.
If any of the players play a black card with more than one white card, he could win, bet one of his Awesome Points to play, and an additional white card. Players may trade in Awesome Points to draw up to ten cards by returning white cards to the deck at any point of the game.
When everyone has answered the question, players take turns removing one card each. The last remaining card is announced the funniest. Every round, pick one white card randomly and use it into play to the name of an imaginary player named Rando Cardrissian. If he wins the game, all players will be left with never-ending shame.
What are Popular Cards Against Humanity Expansions?
This game made card games fun, and everyone who plays it loves them. Almost everyone's played it so many times, so it may appear too old to start. For this reason, expansion packs gained importance.
There are some following famous expansion packs: Cards Against Humanity: Green Box contains 300 brand-new cards (245 white and 55 black), Cards Against Humanity: Red Box includes 300 cards (230 white and 70 black), Cards Against Humanity: Blue Box having 300 cards (220 white and 80 black), Cards Against Humanity: Fifth Expansion includes 100 completely NEW cards (75 white cards and 25 black cards), Cards Against Humanity: Sixth Expansion have 100 completely NEW cards (75 white cards and 25 black cards) to add to the game.
Cards against humanity is a popular party game that goes against political opinions and all. It is a fun game to play with a little chill of childishness and thrilling cognition of adulthood. This game has specific alternatives which can be played as per player choice. It tickles on players' funny bones and chills throughout the whole game mood.
I hope this article would have been a great help to you in terms of knowledge and assistance. Hope you love reading "Games like Cards Against Humanity"
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Paragraph 218 makes abortion practically illegal – Scrap it!
Kate Cahoon from the Bündnis für sexuelle Selbstbestimmung on the chances of law reform, international solidarity and why abortion is still illegal in Germany
The Bündnis für Sexuelle Selbstbestimmung demonstrating in Berlin in September 2021
Hi Kate. Thanks for giving us your time. Could you start by introducing yourself, and saying a little about the Bündnis für Sexuelle Selbstbestimmung, where you are active?
I've been living in Germany for 12 years. At some point, I realised that abortion is technically still a crime in this country. I couldn't believe it and have been involved in the pro-choice coalition Bündnis für sexuelle Selbstbestimmung ever since. We're a broad coalition of activists and representatives from political parties, NGOs, health providers, unions and other civil society groups.
In addition to the protests against the anti-choice "Marsch des Lebens" every September and regular campaigns for abortion rights, we also helped to build a nationwide network of pro-choice groups and initiated protests around Safe Abortion Day (28 September) in Germany.
What is paragraph 219? Maybe you can start by explaining the background to this law. Why was it introduced and how has it been used?
Paragraph 219a of Germany's criminal code prohibits doctors from advertising abortion services or providing information about abortions on their websites. The law was introduced by the Nazis in 1933 and lay dormant for decades, until anti-choicers started to use it to initiate lawsuits against practitioners, like the well-known case against doctor Kristina Hänel. She was fined for providing information on her website in 2017 but refused to accept the verdict, promising to take the matter to Germany's constitutional court. Hänel's response was accompanied by nationwide protests and media reports, helping to re-ignite the movement for abortion rights in Germany.
Germany, and particularly Berlin, has a reputation for having liberal laws on sexual freedom, and yet abortion is still illegal here. Can you explain?
Religion has a much stronger influence on German politics and the wider society than many people realise. Parts of the country are still deeply conservative; Christian fundamentalists and right-wing actively oppose the existing regulations on abortion and push for even more restrictive laws. That's despite the fact that the vast majority of people in Germany is evidently in favour of abortion.
Many people, especially young people, are shocked when they find out about the current legislation or encounter the deliberate hurdles placed in the path of those in need of abortion services, like mandatory counselling and the three day waiting period before an abortion can be performed.
What do the various political parties in Germany say about abortion rights?
The CDU/CSU have staunchly opposed any attempt to reform Germany's abortion laws in the past decades. They are explicitly anti-choice and consider the current legislation to be an ideal "compromise" between the interests of those facing an unwanted pregnancy and "unborn life". Leading AfD politicians like Beatrix von Storch are vocal on abortion and meet openly with the leaders of Germany's anti-choice movement. Their party platform often combines racist and anti-choice messaging, demanding a "Wilkommenskultur für Ungeborene", meaning unborn (white German) babies should be welcomed into the country instead of refugees.
The Left party (die LINKE) is the only political party to have consistently demand the full legalisation of abortion from the outset. The Greens and the Social Democrats are broadly pro-choice and have become more explicit about the need to remove abortion from the criminal code in the lead up the recent election. Despite claiming to be liberal, the FDP is not in favour of fully legalising abortion and frequently refers to the Constitutional Court rulings of 1975 and 1993 which assert a right to life for every individual embryo.
How strong is the Anti-Choice movement in Germany? Who goes to the "Marsch für das Leben" (March for Life)?
The anti-choice movement in Germany is well funded and closely connected to religious fundamentalist groups and organisations from other European countries and other parts of the world, in particular the US. Prominent members of the AfD have been known to march in the front row of the March for Life in Berlin and CDU parliamentarians often send official greetings to participants.
A few years ago, the march was attracting large numbers of participants, around 7,000-8,000 people who mainly came in on buses from other parts of the country and neighbouring Poland. The organisers tried to attract young people by organsing a weekend of "pro-life" activities in the capital city. It's a strange mix of church goers enjoying a family outing and right-wing fanatics with signs referring to the "Babycaust".
Thankfully – and perhaps as a result of the loud and disruptive protests organised by our coalition and other radical left groups – the number of participants has decreased significantly in recent years.
This year sees the 150th anniversary of paragraph 218. What is this paragraph, and what are its effects?
Abortions are regulated by paragraph 218 of the criminal code, in the chapter on "Crimes against Life" next to murder and manslaughter. These laws were introduced back in 1871, and while they didn't apply in East Germany, where abortion on demand was legal from 1972 onwards, they were reinstated for the Federal German Republic in the early 1990s.
Aside from criminalising abortion per se, the law stipulates that pregnant women are required to seek counselling services by state accredited authorities in order for them to be able to terminate a pregnancy. An abortion can be performed if certain conditions are met, however, the act remains unlawful. The wording of the law is clearly paternalistic and intended to discourage those with an unwanted pregnancy from seeking an abortion. It contributes to social stigma around abortion and creates considerable barriers to abortion access.
Some counselling services run by church institutions will provide counselling without issuing the certificate needed, intentionally misleading clients. The number of doctors and public hospitals willing to perform abortions in this uncertain setting has plummeted in recent years, particularly in regional areas. Medical students do not routinely learn how to perform an abortion as part of their studies, which has led to young doctors organising workshops to practice on papayas. The costs of an abortion are also not covered by statutory health insurance, although individuals with a low income can wade through endless paperwork to get costs reimbursed by federal states.
The new German government has promised to abolish paragraph 219. That's great news, isn't it?
In 2018 it also looked like paragraph 219a was about to be scrapped and it didn't happen, because the FDP side-stepped and the SPD ultimately changed their minds, not wanting to risk their chances of becoming coalition partners with the CDU. Now the Greens, SPD and FDP have promised to do it, but it's still yet to happen.
Why do you think that the incoming government has promised to abolish paragraph 219 at this time?
Basically it's long overdue; the SPD and Greens in particular would have lost credibility if they didn't make it happen. I think the coalition partners are keen to appear progressive and were happy to find something they could agree upon so easily. The real issue that needs to be tackled is paragraph 218.
Some people have suggested that the upcoming reforms might weaken our case for legal abortion. I don't agree. The fact that paragraph 218 and the need for abortion to be covered by statutory health insurance is mentioned in the coalition paper at all is a direct result of our protests in the last few years and our efforts to set the agenda in the lead up to the election. No government is ever going to hand our rights to us on a plate – we will have to keep fighting for it and we're one huge step closer than we were before.
Abortion rights aren't just an issue in Germany. In recent years, abortion has been legalised in Ireland and Argentina. What can the movement here learn from these successes?
Abortion rights are contested in many parts of the world, and in countries like Poland and Argentina hundreds of thousands of people have taken to the streets in recent years to demand safe and legal abortion. We don't have these kinds of mass mobilizations in Germany at this point in history, perhaps because the situation here is perceived as being less urgent, but there's still a lot we can learn from other struggles.
In Berlin, we have particularly strong links with the movement in Poland across the border. Many Polish women live in Germany or come over here to get abortions. Although they are facing massive repression, they are also showing great resilience.
The examples of Ireland and Argentina give us hope – if the fight for legal abortion can be won after such a long battle, we are bound to succeed in the end as well.
Finally, how can someone who wants to fight for Choice get more involved in Berlin?
Join die LINKE and make sure our party stays at the forefront of the struggle for legal abortion! But aside from that, follow the Bündnis für sexuelle Selbstbestimmung on social media and support our protests. International activists and groups are also encouraged to get in touch and potentially help plan activities for International Safe Abortion Day on September 28.

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\section{Introduction and Background}
Quantum computers function by using the unitary time evolution operators, i.e. quantum gates, described in the formalism of the standard quantum mechanics.
  Although  non-unitary dynamics can be emulated in the scope of unitary dynamics by using ancilla or measurement based quantum circuits (e.g., \cite{Wang2010Measurement, Terashima2005nonunitary,Daskin2014universal}), the success probability in these circuits diminish substantially with the size of the ancilla register.
In most cases, the small success probability can be remedied by using  the standard amplitude amplification \cite{Grover1998,Mosca1998quantum, Brassard2002}.
However, the input dependence of the amplitude amplification makes difficult to sequentially combine two or more ancilla based circuits.
In certain types of ancilla based quantum circuits, it is shown that the amplitude amplification can be done on the ancilla system independently of the input to the system register. This type of the amplification process is named as the oblivious amplitude amplification \cite{Paetznick2014repeat, Berry2014exponential}. In different contexts, it is also named as repeat untill success algorithm \cite{Lim2005RUS,Lim2006RUS} (please see Ref. \cite{Kothari2014efficient} for a broad overview of the topic).
A slightly modified version of the oblivious amplitude amplification is proven to be working also for matrices which are almost unitary: i.e., a non-unitary matrix but somehow close to a unitary matrix \cite{Berry2015Taylor}.

A Hermitian matrix, $A$, can be used along with $\sqrt{I-A}$ ($I$ is an identity matrix) to form a unitary matrix which can then be processed on an ancilla based quantum circuit.
However, finding the square root of a matrix is numerically a difficult problem when the size of the matrix is large.
 In this paper, we show how to approximate this unitary matrix formation in a way that the produced matrix is almost unitary.
In addition, we show that this type of approximate matrices can be processed on the ancilla based circuit where the success probability is maximized by the oblivious amplitude amplification.
We also present a lower bound for the fidelity of the final state obtained from the amplification process by measuring the distance of the approximate matrix to the closest unitary matrix.
Numerical simulations are done for random matrices of different sizes and it is found that independent of the system size, the final amplified probabilities are generally around  0.75 and the fidelity of the final state is mostly high and around 0.95. This makes possible to implement a product of non-unitary matrices  on quantum computers by sequentially combining two ancilla based circuits. Therefore, it may lead us to efficiently implement matrix functions represented as infinite matrix products.

This paper is organized as follows: In the following two subsections,    the ancilla based circuits considered in this paper and the amplitude amplification are introduced for the unfamiliar readers. In the next section, first, it is described how to complete a non-unitary matrix to a unitary matrix and then how to approximate it. Then, the numerical examples and the circuit design used in the examples are shown. In Sec.\ref{SecDiscus}, the algorithmic complexity of the whole framework is analysed and its possible use in the matrix product and matrix functions is discussed. Finally, the paper is concluded with the summary of the results.
\subsection{Ancilla Based Quantum Circuits}
It is well-known that using an ancilla register  eases the  complexity in the implementation of quantum gates (e.g. see \cite{Lanyon,Bary}). A particular type of ancilla based circuits can be described for the matrices represented as a sum of unitary matrices \cite{Daskin2012universal, Berry2015Taylor}:
Consider a unitary matrix, $A$, which is of dimension $N=2^n$ and represented as a sum of unitary processes, $U_i$s:
\begin{equation}
A=\sum_{i=0}^{M-1} U_i.
\end{equation}
A quantum operation can be described as a matrix vector transformation: For instance, let $\ket{in}$ represent a general input state. The application of $A$ on this input state can be described as $A\ket{in}$.  The result of this transformation can be obtained on an ancillary based circuit consisting of an ancilla and a system registers by using $U_i$s.
One way of doing this with  an acilla register composed of $m=logM$ qubits can be described as follows:
\begin{itemize}
\item First, all $U_i$s are aligned on the system register composed of $n$ qubits.
\item Then, the application of each $U_i$ is controlled  by the ancilla register.
Here,  the control scheme is determined from the binary representation of $i$ in a way that $U_i$ is applied when the ancilla is in \ket{\bf i} state. Here, \ket{\bf i} is the $i$th vector in the standard basis.
This circuit can be represented in matrix form by a block diagonal matrix, $V$:
\begin{equation}
\label{EqVgeneral}
V=\left(\begin{matrix}
U_0 & & \\
& \ddots& \\
  & & U_{M-1}
\end{matrix}\right).
\end{equation}
\item The initial state of the ancilla register  is assumed to be \ket{\bf 0} state. Then, it is put into the superposition state by the application of  a series of Hadamard gates, $H^{\otimes m}$.  Thus, the whole circuit in matrix form becomes  equal to the following:
\begin{equation}
\mathcal{U}=
(H^{\otimes m}\otimes I) V = \frac{1}{\sqrt{M}}\left(\begin{matrix}
\sum_{i=0}^{M-1} U_i & J_1\\
J_2& J_3
\end{matrix}\right),
\end{equation}
where $I$ is the identity matrix and $J_1, J_2$, and $J_3$ represent the other parts of $\mathcal{U}$.
\end{itemize}

$\mathcal{U}$ can be employed to emulate the action of $A$ with the success probability $\frac{1}{M}$:  If we apply $\mathcal{U}$ to the input \ket{\bf 0}\ket{in}; in the output, for the states in which the ancilla is equal to \ket{\bf 0}, the circuit gives the action of $A$ on the system register, $A\ket{in}$.
 Since $A$ in $\mathcal{U}$ is normalized by the coefficient $\frac{1}{\sqrt{M}}$, the probability to see the ancilla in \ket{\bf 0} is $\frac{1}{M}$.

This can be also generalized to $A=\sum_{i=0}^{M-1} k_i U_i$ by using an operator $K$ whose first row and column are equal to the coefficients $k_0, \dots, k_{M-1}$ (Note that the coefficients are assumed to be normalized.):
\begin{equation}
\label{EqGeneralU}
\mathcal{U}=
(H^{\otimes m}\otimes I) V (K\otimes I)= \frac{1}{\sqrt{M}}\left(\begin{matrix}
\sum_{i=0}^{M-1} k_iU_i & J_1\\
J_2& J_3
\end{matrix}\right).
\end{equation}
$K$ can be considered as a Householder transformation  for the vector $\bra{\bf k}=\left(k_0, \dots, k_{M-1} \right)$: i.e., $K\ket{\bf k}=\ket{\bf 0}$ and $K\ket{\bf 0}=\ket{\bf k}$. The circuit representing $\mathcal{U}$ is drawn in Fig.\ref{FigCircuit1General}.
\input{FigCircuit}

\subsection{Amplitude Amplification}
As derived from Eq.\eqref{EqGeneralU},  the success probability of  emulating the unitary matrix $A$ by the circuit, $\mathcal{U}$, is   $\frac{1}{M}$. The probability depends on the size of the ancilla and decreases exponentially in the number of qubits contained in the ancilla.
This can be increased upto one by the application of the  amplitude amplification, which is the main part of the
famous Grover's search algorithm \cite{Grover1998} finding a solution encoded in a quantum state.

The amplitude amplification is described as follows  \cite{Mosca1998quantum, Brassard2002,Kaye2006}:
Let the state \ket{\psi} be defined as the linear combination of the standard basis resulted from the application of the operator $B$ to an initial zero state:
\begin{equation}
\label{EqPsiinStandard}
\ket{\psi}=  B\ket{\bf 0}=\sum_{x=0}^{N-1}b_x\ket{\bf x},
\end{equation}
where $b_x$ is the amplitude of the $x$th vector, \ket{\bf x},  in the standard basis. Let also some states in \ket{\psi} be considered as the ``good" states represented by the set $X_{good}$, and the remaining states be the ``bad" states represented by $X_{bad}$:
\begin{equation}
\label{EqPsiinGoodBad}
\ket{\psi}=  \sum_{x\in X_{good}}b_x\ket{\bf x} + \sum_{x\in X_{bad}}b_x\ket{\bf x}.
\end{equation}
The re-normalizations of  $X_{good}$ and $X_{bad}$ form a new two dimensional basis set \{\ket{\psi_{good}},\ket{\psi_{bad}}\}. \ket{\psi} can be rewritten in this new basis with coefficients represented by $sin(\theta)$ and $cos(\theta)$ with $\theta\in[0,\pi/2]$:
 \begin{equation}
\ket{\psi}= sin(\theta)\ket{\psi_{good}}+cos(\theta)\ket{\psi_{bad}}.
\end{equation}
Here, $sin(\theta)^2=P_{good}=\sum_{x\in X_{good}}|b_x|^2 $, and $cos(\theta)^2=P_{bad}=\sum_{x\in X_{bad}}|b_x|^2$.

In the amplitude amplification algorithm, the amplitude of \ket{\psi_{good}} is amplified by using the following search iterate:
\begin{equation}
\label{EqUpsiUf}
Q=U_{\psi}^{\perp} U_f.
\end{equation}
Here, when applied to \ket{\psi}, $U_f$  negates the sign of \ket{\psi_{good}} and does nothing to \ket{\psi_{bad}}:
 \begin{equation}
U_f\ket{\psi}=-sin(\theta)\ket{\psi_{good}}+cos(\theta)\ket{\psi_{bad}}.
\end{equation}
 When  $\ket{\psi_{good}}$ is known,  $U_f$ can be easily constructed in matrix form as follows:
\begin{equation}
\label{EqUfGeneral}
U_f=I-2\ket{\psi_{good}}\bra{\psi_{good}}.
\end{equation}

The other operator in the search iterate is $U_{\psi}^{\perp}$   described in matrix form as:
\begin{equation}
 U_{\psi}^{\perp}=2\ket{\psi}\bra{\psi}-I=BU_0^\perp B^{-1},
 \end{equation}
where $U_0^\perp=(2\ket{\bf 0}\bra{\bf 0}-I)$ is the reflection about the axis orthogonal to \ket{\bf 0}, and $B^{-1}$ is the inverse of the matrix $B$. When $B$ is unitary, $B^{-1}$ is equal to the conjugate transpose of $B$, $B^\dagger$.

It is easy to prove that
 when $Q$ is applied $k$ number of times to \ket{\psi}, the final state ends up in the following:
\begin{equation}
Q^k\ket{\psi} =
 sin\left((2k+1)\theta\right)\ket{\psi_{good}}
+\cos\left((2k+1)\theta\right)\ket{\psi_{bad}}.
\end{equation}
From the above equation,  the highest probability for the good states, $ sin\left((2k+1)\theta\right)^2$, can be obtained when $(2k+1)\theta \approx\frac{\pi}{2}$. This leads $O(\frac{\pi}{4\theta})$ as a bound for $k$.

\subsubsection{Application to $\mathcal{U}$ and Oblivious Amplitude Amplification}
In the circuit $\mathcal{U}$ given in Fig.\ref{FigCircuit1General}, the good and the bad states are already known: the set of good states are those where the ancilla qubit is in \ket{\bf 0} state and the rest is the set of the bad states. Therefore, the iteration operator used in the amplitude amplification can be determined.

Let \ket{\beta} be the output state of $\mathcal{U}$.
\ket{\beta} can be written in terms of the combination of the good and the bad states:
\begin{equation}
\label{EqBetaGoodBad}
\ket{\beta}=\frac{1}{\sqrt{M}}\ket{\beta_{good}}+\frac{\sqrt{M-1}}{\sqrt{M}}\ket{\beta_{bad}}.
\end{equation}
Since the good states are the ones where the ancilla register equal to zero, the normalized $\ket{\beta_{good}}$ reads the following:
\begin{equation}
\label{EqBetaGood}
\ket{\beta_{good}}=\ket{\bf 0}\sum_{x=0}^{N-1}\beta_x\ket{\bf x},
\end{equation}
where \ket{\bf x} is the $x$th vector in the standard basis.

It is shown that the amplitude amplification can be done on the first register by using the following search iterate \cite{Paetznick2014repeat, Berry2014exponential,Berry2015Taylor}.
\begin{equation}
\label{EqQ1}
 Q= -\mathcal{U}S\mathcal{U} S,
\end{equation}
where $S$ is considered in place of $U_f$ and has the same effect as $U_{0}^\perp$ in the iteration:
\begin{equation}
\label{EqSExplicit}
 S= \left(I^{\otimes^m}-2 \ket{\bf 0}\bra{\bf 0}\right) \otimes I^{\otimes^n}.
 \end{equation}
 The main difference of this iteration from the standard amplitude amplification is the independence from the input to the system register: $\mathcal{U}$  does not include the input preparation operator which converts a zero state into the desired input.

Since the amplitude of the good states is $1/\sqrt{M}$; $Q$ is applied exactly $\left \lfloor{\frac{\pi}{4}\sqrt{M}} \right \rfloor$ number of times to maximize the amplitude of  $\ket{\beta_{good}}$.

\section{Application in the Case $A$ is  Non-Unitary}
When $A$ is non-unitary; the expected output from the circuit $\mathcal{U}$ can no longer be described by the fixed amplitudes given in Eq.\eqref{EqBetaGoodBad} since it changes based on the input state to the system. This necessitates the inclusion of the input preparation  in the operator $U_{\psi}^{\perp}$ of the standard amplitude amplification:
\begin{equation}
 U_{\psi}^{\perp}=\mathcal{U} (I^{\otimes m} \otimes A_{in}) U_0^\perp (I^{\otimes m} \otimes A_{in})^{\dagger}\mathcal{U}^{\dagger},
\end{equation}
where $A_{in}$ converts the zero state into the desired input state.
To reach the maximum amplitude,  in this case, $Q$ needs to be applied $\left \lfloor{\frac{\pi}{4\eta}\sqrt{M}} \right \rfloor$ number of times, where $\eta$ is the norm of the expected output state produced from $||UU_{in} \ket{\bf 0}||$. Since $\eta$ is not known, one can apply quantum search algorithm \cite{Kaye2006}. In that case, the first register is partially measured: If it is zero, then the algorithm is stopped. Otherwise, the iteration operator $Q$ is applied again.

In the following subsections, we shall show how to extend $A$ to a  unitary matrix in order to avoid input dependence in the amplitude amplification and successfully apply the oblivious amplitude amplification.

\subsection{Extending $A$ to a Unitary Matrix}
It is known that every Hermitian positive definite matrix has a unique Hermitian positive definite square root which can be numerically  computed via Schur decomposition \cite{Bjorck1983schur, Higham1987computing}.
Using the square root of $(I-A^2)$, a non-unitary Hermitian matrix, $A$, can be extended to a unitary, $U$,  as in the following form:
\begin{equation}
\label{EqUwithsqrt}
U =\left(\begin{matrix}
A&\sqrt{I-A^2}\\
\sqrt{I-A^2} &-A
\end{matrix}\right).
\end{equation}
It is not difficult to see that $U$ is a unitary matrix: $UU^\dagger = U^\dagger U=I^{\otimes n+1}$. This can be seen easier when $U$  is written in the cosine-sine decomposition as:
\begin{equation}
U =\left(\begin{matrix}
A&\sqrt{I-A^2}\\
\sqrt{I-A^2} &-A
\end{matrix}\right)=
\left(\begin{matrix}
R&0\\
0 &R
\end{matrix}\right)
\left(\begin{matrix}
C&S\\
S&-C
\end{matrix}\right)
\left(\begin{matrix}
R^\dagger&0\\
0 &R^\dagger
\end{matrix}\right),
\end{equation}
where  the eigendecomposition of $A$ is described by $A=RCR^\dagger$, and $C$ and $S$ are the diagonal matrices with the diagonal elements cosine and sine of the eigenvalues of the matrix $A$.
{Note that this cosine-sine decomposition can also be used to generate a quantum circuit for $U$ in terms of single and two qubit gates \cite{, Tucci1999rudimentary,Mottonen,Shende2006}. }

\subsubsection{Simulation of $U$}
Computation of $\sqrt{I-A^2}$  requires the eigendecomposition  of $I-A^2$.
Since the eigenvalues of $\sqrt{I-A^2}$ and $A$ are related as cosine and sine of some values, the eigendecomposition of $A$ is enough to form the matrix $\sqrt{I-A^2}$.
Eigendecomposition of a matrix can be found through numerical methods such as power iterations and QR method.
For a Hermitian matrix whose size is reasonable for classical computers,  obtaining a kind of approximate decomposition is feasible in general.
However, when the system size is huge, this problem becomes a very heavy computational task for the classical computers so that, in some cases, decomposition may be impossible (note that the computational complexity in terms of the system size is generally $O(N^3)$.)\cite{Parlett1980symmetric}.

Therefore, when the computation of the eigendecomposition of $A$ is available;
  one can use the matrix $A$  on quantum computers as follows:
  In the circuit for $U$, the initial state of the first qubit is always set to \ket{0}.
  Thus, we apply $U$ to an initial state \ket{input}=\ket{0}\ket{in}, where \ket{in} represents the initial input desired to be applied to $A$.  This generates the following output vector:
\begin{equation}
\ket{output}=\left(\begin{matrix}
A&\ket{in}\\
\sqrt{I-A^2}&\ket{in}
\end{matrix}\right)
\end{equation}
To the above vector,  if we apply the operator $P=(\ket{0}\bra{0}\otimes I^{n})$, then the system collapses to the state $A\ket{in}$.
Therefore, at the end of circuit $U\ket{input}$, the probability to see the first qubit in zero state, determines the success probability of the simulation done by the following process.

When the eigendecomposition of $A$ is not available (because of the computational complexity, this may be the case when the system size of $A$ is large),  we shall try to estimate $U$ and process the estimated non-unitary on the ancilla based circuit described in the previous section.

\subsubsection{Estimation of $U$}
{From now on,  we assume that $A$ is a real symmetric matrix.} Then, we normalize the matrix $A$ as $A=\frac{A}{\mu}$ with $\mu=\sqrt{max_i\sum_j A_{ij}^2}$. This makes 2-norms of the columns of the matrix less than or equal to 1.
Then, instead of  the matrix in Eq.\eqref{EqUwithsqrt}, we construct the following matrix:
 \begin{equation}
 \label{EqConstructedNonUnitary}
U=\left(\begin{matrix}
A&D\\
D&-A
\end{matrix}\right),
\end{equation}
where $D$ is a diagonal matrix described by the diagonal entries $D_{ii}=\sqrt{1-\sum_j A_{ij}^2}$.
The matrix $U$ is not a unitary matrix; however,  $A^2 + D^2$  and so $UU^\dagger=U^\dagger U = U^2$ have diagonal elements equal to one. { In addition, since $A$ is normalized with $\mu$; $\rho(A^2)\leq \rho(A)\leq 1$,
where $\rho(A)$ is the spectral radius (the largest eigenvalue) of $A$. In particular cases such as $\rho(A) < 1$ or a diagonally dominant $A$, the off-diagonal entries of $A^2$ are likely to be small, and so one can expect the matrix $U$ to be close to a unitary since $A^2 + D^2$ becomes close to an identity matrix.}

We shall describe the closeness of $U$ to a unitary matrix via polar decomposition which is known to produce the closest unitary matrix to a given arbitrary matrix (e.g. see  \cite{Higham1988matrix}):
In the polar decomposition, $U=\widetilde{U}\widetilde{H}$, while $\widetilde{U}$  is the closest unitary to $U$, $\widetilde{H}$ is an Hermitian positive definite matrix.
 We define the following as a measure of the closeness of the estimated unitary $U$ to $\widetilde{U}$:
\begin{equation}
\label{Eqc}
c=\frac{||U-\widetilde{U}||^2}{||U||^2}=\frac{||\widetilde{H}-I||^2}{||\widetilde{H}||^2},
\end{equation}
{where $||.||$ represents the norm of a matrix. Also note that a similar measure, ${||U-\widetilde{U}||}$, is used by Berry et al. as an error bound in the modified version of the oblivious amplitude amplification \cite{Berry2015Taylor}.
 To bound the value of $c$, we will use the Frobenius norm:
$||.||_F$, which is also invariant under unitary transformations. Thus, $||\widetilde{H}||_F =  ||U||_F = \sqrt{trace(UU^\dagger)}=\sqrt{trace(\widetilde{H}^2)}=\sqrt{2N}$.
In addition, we can represent the term $||\widetilde{H}-I||_F$ as follows:
\begin{equation}
\begin{split}
||\widetilde{H}-I||_F = & \sqrt{trace(\widetilde{H}^2-2\widetilde{H} + I)} \\
= &
\sqrt{trace(\widetilde{H}^2)-trace(2\widetilde{H}) + trace(I))}
\\
= & \sqrt{4N-trace(2\widetilde{H})}
= \sqrt{4N - \Phi}.
\end{split}
\end{equation}
From the generalized mean equality; since the trace is the sum of eigenvalues, the following inequality holds:
 $\frac{1}{2N}trace(\widetilde{H})
 \leq \sqrt{\frac{1}{2N}trace(\widetilde{H}^2)}$.
As a consequence of this,
 $\Phi=trace(2\widetilde{H}) \leq 4N$ and so  $\sqrt{4N - \Phi} \leq 2N$.
This makes $c$ in terms of the Frobenius norms  always less than or equal to one.
When $\Phi=4N$,  $c$ becomes zero and so the matrix can be considered a unitary matrix.
Note that one can also try to maximize $c$ for different choices of $A$.}

{In the numerical examples, we shall compute $c$ by using 2-norms of the matrices instead of the Frobenious norms: Since the error also depends on the input state,  the 2-norm obtained from the maximum eigenvalue likely gives a better approximation for the possible maximum error.}
Furthermore, we shall use the following as an estimate lower bound for the fidelity of the output after the oblivious amplitude amplification algorithm:
\begin{equation}
\label{EqEstimatedFidelity}
ef =|1-c|^2.
\end{equation}
The estimated fidelity would be one for the unitary matrices. And it would be small when the closeness between $U$ and $\widetilde{U}$ is small.

When $U$ is non-unitary, it cannot be used directly on quantum computers.
Berry et al.\citep{Berry2015Taylor} have proved that a slightly modified version of the oblivious amplitude amplification works also for any arbitrary non-unitary matrix which is close to a unitary matrix. Therefore, since the constructed matrix in Eq.\ref{EqConstructedNonUnitary} is expected to be close to a unitary matrix, the modified oblivious amplitude amplification can be used for the simulation of this matrix in the ancilla based circuit. However, in the next section, the numerical results for the randomly generated matrices show that one can use the oblivious amplitude amplification given in Eq.\eqref{EqQ1} without modification  for the  matrices generated by \eqref{EqConstructedNonUnitary}.
{Note that  the modified version of the oblivious amplitude amplification would give better results; however, it requires a projection operator.
}
\subsection{Numerical Examples}
In the numerical examples, we shall use the standard oblivious amplitude amplification given in Eq.\eqref{EqQ1} along with the circuit design method described in Ref.\cite{Daskin2012universal}. The circuit design method is only included for the completeness. One can also run simulations by generating random matrices in the form Eq.\eqref{EqConstructedNonUnitary} and then writing each one of them as a direct sum of $M$ unitary matrices.

\subsubsection{General Circuit Designs}
 An ancilla-based quantum circuit design technique  is introduced in Ref. \cite{Daskin2012universal}.  A $2n$-qubit system  $\mathcal{U}$ is employed to emulate a general $n$-qubit quantum operation, $U$.
The primary
intuition of the technique is based on generating the matrix-vector product result of a quantum operation inside the new system. This intuition is conveyed in two parts: First,  the ancilla register is put into the superposition state, then  the following matrix $V$ similar to the one in Eq.\eqref{EqVgeneral} is used:
\begin{equation}
\label{EqV}
V=\left(\begin{smallmatrix}
\begin{smallmatrix}
\alert{u_{11}}&\alert{u_{12}}&\alert{\cdots} &\alert{ u_{1N}}\\
\bullet&\bullet&\dots&\bullet\\
 \vdots&\vdots&\ddots&\vdots\\
 \bullet&\bullet&\dots&\bullet
\end{smallmatrix}& & &
\\
&
\begin{smallmatrix}
\alert{u_{21}}&\alert{u_{22}}&\alert{\dots }& \alert{u_{2N}}\\
\bullet&\bullet&\dots&\bullet\\
 \vdots&\vdots&\ddots&\vdots\\
 \bullet&\bullet&\dots&\bullet
\end{smallmatrix}&&
\\&
&  \ddots  &
\\
 & & &\begin{smallmatrix}
\alert{u_{N1}}&\alert{u_{N2}}&\alert{\dots} & \alert{u_{NN}}\\
\bullet&\bullet&\dots&\bullet\\
 \vdots&\vdots&\ddots&\vdots\\
 \bullet&\bullet&\dots&\bullet
\end{smallmatrix}
\end{smallmatrix}\right),
\end{equation}
where $u_{ij}$s are the matrix elements of $U$, and  each ``$\bullet$" represents a matrix element which plays no significant role in the description.
If this matrix is applied to a quantum state in which the ancilla is in the superposition state, the desired output is obtained in the states where the system register is in \ket{\bf 0} state:
\begin{equation}
\label{EqExtendedV}
V(\frac{1}{\sqrt{M}}\sum_{x=0}^{M-1}\ket{\bf x}\ket{input})
= \frac{1}{\sqrt{M}}\left(\begin{matrix}\beta_{0}\\ \vdots\\
\beta_i\\\vdots\\ \beta_{N-1}\\\vdots\end{matrix}\right).
\end{equation}
Obviously, when we swap the ancilla and the system register, we obtain the same output as in Eq.\eqref{EqBetaGoodBad} with the good states in Eq.\eqref{EqBetaGood} (Note that here $M=N$.). As a consequence, the same amplitude amplification given in Eq.\eqref{EqQ1} can be applied to increase the probability upto one.

Having a non-unitary $U$ does not change the circuit design. However, it changes the success probability given in the above equation. When $U$ is close to a unitary matrix, we can apply the oblivious amplitude amplification  in Eq.\eqref{EqQ1} (One can also use the modified version of the oblivious amplitude amplification given in Ref.\cite{Berry2015Taylor}).

\subsubsection{Numerical Examples}

In the numerical examples, the oblivious amplitude amplification given in Eq.\eqref{EqQ1} is applied to the non-unitary matrices constructed in the form given in Eq.\eqref{EqConstructedNonUnitary}.
The following method is used to generate random symmetric matrices:
\begin{itemize}
\item An $N\times N$ symmetric random matrix, $A$, with the elements in $[-1, 1]$ is generated.
\item Then, $A$ is normalized by $\mu=\sqrt{max_i\sum_j A_{ij}^2}$.
\item Then, the diagonal matrix $D$ is obtained: $D_{ii}=\sqrt{1-\sum_j A_{ij}^2}$.
\item Then, the matrices A and D are used to construct $2N\times 2N$ matrix $U$.
\end{itemize}

In addition, we also generate random input state to $U$ in the form: $\ket{input}=(\ket{0}\otimes \ket{in})$, where \ket{in} is a random quantum state with real coefficients.

We have run the simulations for 100 random cases with $U$  of orders $N=16$, $N=32$, $N=64$, and $N=128$ (Note that the total system sizes with the ancilla register becomes
$(2^8\times2^8), (2^{10}\times2^{10}), (2^{12}\times2^{12})$ and $(2^{14}\times2^{14})$, respectively.).  For each random case, the estimated fidelity given in Eq.\eqref{EqEstimatedFidelity}  has been computed as follows:
\begin{itemize}
\item First, to find the polar decomposition of $U$, the singular value decomposition of $U$ is computed:
$U=V_1E V_2^\dagger$, where $E$ represents the singular values and $V_1$ and $V_2$ are the right and left singular vectors.
\item Then, the closest unitary is computed from $\widetilde{U}=V_1V_2^\dagger$.
\item Then, $c$ given in Eq.\eqref{Eqc} is computed by using the 2-norms of the matrices.
\item Finally, the estimated fidelity is computed from Eq.\eqref{EqEstimatedFidelity}.
\end{itemize}
In the amplitude amplification process, the amplitudes of the first $N$ states-i.e., the states where the first register is in \ket{\bf 0}-are used to compute the success probability. Furthermore, the estimated fidelity is compared with the real fidelity which is the inner product of the collapsed quantum state (the first $N$ amplitudes) and the vector $(A\ket{in})$.

In Fig.\ref{figMatrices}, both $U$ and \ket{in} are generated randomly. And from the last iteration of the oblivious amplitude amplification (the state in which the success probability is the highest), the fidelity and probability are computed for each case. As can be observed in the figure, the mean value of the observed  fidelities is 0.9462 and the mean value of the observed success probabilities is 0.7666.

Furthermore, in Fig.\ref{figRuns}, the same matrix $U$ is tested in the amplitude amplification with  different input states in order to observe the effect of the change in the input state on the fidelity and  the validity of the estimated fidelity.
Fig.\ref{figRuns} shows that the fidelity remains high and is always above the estimated fidelity (the mean of fidelities in all subfigures is 0.9426). Therefore,  the proposed estimated fidelity may provide a good lower bound for the fidelity. As in  Fig.\ref{figMatrices}, the mean value of the success probabilities here also remain as 0.7601.

\begin{figure*}
\subfloat[16x16 Matrix]{\includegraphics[width= 3.5in]{fig216x16}}
\subfloat[32x32 Matrix]{\includegraphics[width= 3.5in]{fig232x32}}\\
\subfloat[64x64 Matrix]{\includegraphics[width= 3.5in]{fig264x64}}
\subfloat[64x64 Matrix]{\includegraphics[width= 3.5in]{fig2128x128}}
\caption{The change of the fidelity, the probability, and the estimated lowest fidelity  at the end of the amplitude amplification process for  100 random matrices of different sizes and random inputs.
\label{figMatrices}
}
\end{figure*}
\begin{figure*}
\subfloat[16x16 Matrix]{\includegraphics[width= 3.5in]{fig316x16}}
\subfloat[32x32 Matrix]{\includegraphics[width= 3.5in]{fig332x32}}\\
\subfloat[64x64 Matrix]{\includegraphics[width= 3.5in]{fig364x64}}
\subfloat[128x128 Matrix]{\includegraphics[width= 3.5in]{fig3128x128}}
\caption{The change of the fidelity, the probability, and the estimated lowest fidelity  at the end of the amplitude amplification process. In each run, the matrix $U$ is unchanged but a different random input is used.
\label{figRuns}
}
\end{figure*}

\begin{figure*}
\subfloat[16x16 Matrix]{\includegraphics[width= 3.5in]{fig16x16}}
\subfloat[32x32 Matrix]{\includegraphics[width= 3.5in]{fig32x32}}\\
\subfloat[64x64 Matrix]{\includegraphics[width= 3.5in]{fig64x64}}
\subfloat[128x128 Matrix]{\includegraphics[width= 3.5in]{fig128x128}}
\caption{The change of the fidelity and the probability in the amplitude amplification process for  the random matrix $U$ given in Eq.\ref{EqConstructedNonUnitary} of different sizes. In each figure, the vertical dashed line shows the value of $k=\left \lfloor{\frac{\pi}{4}\sqrt{N}} \right \rfloor$.
\label{figIterations}
}
\end{figure*}

In Fig.\ref{figIterations}, we also present the change of the fidelity and the probability
in the iterations of the oblivious amplitude amplification for random cases with the matrices of the same orders:  $N=16$, $N=32$, $N=64$, and $N=128$.  The required number of iterations for each case has been computed from $k=\left \lfloor{\frac{\pi}{4}\sqrt{N}} \right \rfloor$. For $N=16$, $N=32$, $N=64$, and $N=128$; respectively, $k=3$, $k=4$, $k=6$, and $k=8$ drawn  as dashed vertical lines on the figures. As seen in the figure: the fidelities in all figures remain high for a few iterations, but then start gradually decreasing while the probabilities are rising. When the probabilities reach their maximums either at the $k$th iteration or before that; the fidelities go down to around 0.95.

As a general observation, we can see that  the numerical results presented in   Fig.\ref{figMatrices}, Fig.\ref{figRuns}, and Fig.\ref{figIterations} remain mostly similar despite  the change in the system size.  This indicates the independence of the results from the system size.

\section{Discussion}
\label{SecDiscus}
\subsubsection{The Total Circuit Complexity}

Quantum circuit design methods can be broadly categorized into stochastic and non-stochastic approaches \cite{Daskin2014Diss}.
In terms of stochastic approaches, generally genetic and evolutionary algorithms are used to obtain a circuit which minimizes an optimization function measuring the closeness of the found circuit to the given operator (e.g. \cite{Daskin2011decomposition}). {
Note that instead of designing a quantum circuit implementing a specific matrix,
one can also consider the quantum control approach using optimization to find a way to implement the operator directly, without gates( e.g. \cite{Stojanovic2012quantum}).
This can also be done for non-unitary processes.}
On the other
hand, non-stochastic deterministic methods are generally based on matrix decomposition techniques: for instance, methods based on the Cartan decomposition \cite{Love2008}, the cosine-sine decomposition \cite{Shende2006}, the QR decomposition \cite{Cybenko2001reducing} are presented. It is shown that a circuit for a general unitary matrix  requires at least $(2^{2n-2}-3n/4-1/4)$
number of two-qubit quantum gates \cite{Shende2006}.

The combination of the circuits for each $U_i$ forms a binary coded network controlled by the ancilla register. These types of networks can be decomposed into single and two qubit quantum gates by using a simple decomposition technique described in Ref.\cite{Mottonen}.
The decompositions of the networks for the circuit design in Ref. \cite{Daskin2012universal} yield a circuit with $O(N^2-N)$ number of CNOT gates if $M=N$ (For  the complete complexity analyses, please refer to Ref.\cite{Daskin2012universal}.).  Therefore, the quantum complexity of the circuit $\mathcal{U}$ is $O(N^2-N)$. The amplitude amplification requires $O(\sqrt{N})$ repetitions which makes the total complexity $O(\sqrt{M}N^2-\sqrt{M}N)$.

If each $U_i$ can be efficiently simulatable: i.e. each requires only $O(poly(n))$ gates; the total circuit complexity for $\mathcal{U}$ can be bounded by $O(poly(n)M)$:
Since there would be $O(poly(n))$ number of quantum gates for each $U_i$, they are likely to compose $O(poly(n))$ number of binary coded networks.
The decomposition of such networks produce, in total, $O(poly(n)M)$ number of quantum gates. On the other had, the amplitude amplification would require $O(\sqrt{M})$ repetitions yielding $O(poly(n)M\sqrt{M})$ number of  CNOT and single quantum gates.  When $M=N$, this becomes $O(poly(n)N\sqrt{N})$.

\subsection{The Circuit Simulation of a Matrix Product}
Let $\mathcal{U}_1$ and $\mathcal{U}_2$ are the universal circuits for the unitary matrices, respectively, $W_1$ and $W_2$.  Then, the circuit for the product $W_1W_2$ can be implemented as $Q_2^{k}\mathcal{U}_2Q_1^{k}\mathcal{U}_1$, where $\mathcal{U}_j$ represents the universal circuit, $Q_j$ is in the form of Eq.\eqref{EqQ1} and $k=\left \lfloor{\frac{\pi}{4}\sqrt{M}} \right \rfloor$. This can be generalized to the product consisting of $r$ number of matrices, $\prod_{j=1}^{r}W_j$ by the following:
\begin{equation}
\label{EqGeneralProduct}
\prod_{j=1}^{r}{ Q_j^{k}\mathcal{U}_j}.
\end{equation}
Here, if each $U_j$ requires $O(N^2)$ quantum gates, the obtained circuit implementation for the matrix product requires $O(r\sqrt{M}N^2)$ quantum gates or $O(\sqrt{M}N^2)$ for $r<<N$. When $U_j$ can be efficiently implementable, e.g. $O(poly(n))$, the matrix product requires  only $O(poly(n)M\sqrt{M})$ number of quantum gates.

  \subsubsection{Non-Unitary Matrix Product}
  When the standard amplitude amplification is employed; the amplitude amplification in the second circuit requires the whole amplitude amplification process in the first circuit to be applied again in every iteration. Because of this input dependence, this results in a recursion which makes the whole thing very inefficient.

  However, when $U$ is non-unitary but close to a unitary, one can apply the oblivious amplitude amplification. In that case, the complexity of the matrix product becomes the same as the unitary case.

\subsection{ Quantum Circuits for the Functions of a Matrix}
Many trigonometric functions can be represented in the forms of infinite products (Please see the first chapter of Ref.\cite{Zwillinger2014BookSeries}). Some of the infinite product formulas are also valid for matrices. For instance, formulas for the  exponential  and the cosines are as follows:
 Let $A\in C^{\otimes n}$, then the product formula for the exponential of this matrix is defined as \cite{Bernstein2009matrix}:
 \begin{equation}
 \label{EqExpFunc}
e^{A} = \lim_{k \rightarrow \infty}  \left(1+\frac{A}{k}\right)^k
= \lim_{k \rightarrow \infty} W_k^k.
 \end{equation}
 This can be simply proved by the binomial expansion:
 \begin{equation}
 (I+\frac{A}{k})^k=\sum_{j=0}^k \frac{1}{k^j}\frac{k!}{j!(k-j)!}A^j.
 \end{equation}
If we plug this into Eq.(\ref{EqExpFunc}), then we attain the Taylor expansion of the matrix exponential and complete the proof:
  \begin{equation}
\lim_{k\rightarrow \infty}(I+\frac{A}{k})^k
=\lim_{k\rightarrow \infty}\sum_{j=0}^k \frac{1}{k^j}\frac{k!}{j!(k-j)!}A^j=\sum_{j=0}^\infty \frac{1}{j!}A^j=e^A.
 \end{equation}
In a similar fashion, the cosine representation of $A$ can be defined in the product form as:
\begin{equation}
  \begin{split}
cos(\pi A)&=
\prod_{j=1}^{\infty} \left(I-\frac{4A^2}{(2j+1)^2}\right)\\
&= \prod_{j=1}^{\infty} \left(I-\frac{2A}{2j+1}\right)\left(I+\frac{2A}{2j+1}\right)
=\prod_{j=1}^{\infty} W_{j1}W_{j2}
\end{split}
\end{equation}

As in the matrix product case discussed in the previous section, first each $W_j$ in the product formulas is extended to the form of $U$ given in Eq.\eqref{EqConstructedNonUnitary} where $W_j$ replaces $A$. Then, we generate the circuit designs $\mathcal{U_j}$ for each $W_j$ by either writing $U$ as a sum of simple unitary matrices or following the circuit design in Ref.\cite{Daskin2012universal} used in the numerical examples.
Then, the same product formula given in Eq.\eqref{EqGeneralProduct} is applied.
\section{Conclusion}

In this paper, after extending a non-unitary matrix to a unitary matrix, we have  described a method to approximate this unitary extension.
It is  shown that in most cases the approximation gives a non-unitary matrix sufficiently close to a unitary matrix. Therefore, this matrix can be simulated on an acilla based circuit where
the success probability is increased by the oblivious amplitude amplification.
Since the oblivious amplitude amplification does not depend on the input to the system register, using the proposed framework one can implement a matrix product for non-unitary matrices by combining two ancilla based quantum circuits.
This allows quantum computers to  implement the approximation of the matrix functions represented as infinite matrix products.
A non-unitary matrix can be written in terms of sums of unitary matrices: when each unitary matrix in the summation can be efficiently implementable, then one may also implement the non-unitary  matrix efficiently. Therefore, one may also implement the matrix product and so the approximations of matrix functions efficiently.
We have run numerical simulations for random matrices and shown how the fidelities and the probabilities change in each random case.

redpajama_set_name: RedPajamaArXiv


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Home » Apps » Business » Asian Le Mans Series Messaging
Asian Le Mans Series Messaging
Business | 6.2MB
ABOUT THE ASIAN LE MANS SERIES
Launched in 2013 by the Automobile Club de l'Ouest (ACO), the Asian Le Mans Series is the embodiment of Le Mans endurance racing for the Asian continent. Initially operated by a third party company, the ACO took over management, organisation and promotion of the Series at the end of 2014. The Series features five categories of sports cars - LMP2, LMP3, GT, GT Cup and CN.
As part of the Le Mans Endurance Racing Pyramid, it complements the European Le Mans Series and Weather Tech Sports Car Championship. The FIA World Endurance Championship caps this ensemble while the Le Mans 24 Hours, the ultimate challenge that all the teams and drivers want to win, is the summit of excellence of this pyramid. Champions of the LMP2, LMP3 and GT categories of the Asian Le Mans Series earn invitations to participate in the following year's Le Mans 24 Hours.
The official messaging app of Asian Le Mans Series. If you are a Team or Driver this is a valuable at-track resource for you.
- Get to know other Teams and Drivers
- Stay informed about Race Schedules and Important at-track announcements
- Submit Technical Support Requests
ABOUT THE ACO
The Automobile Club de l'Ouest (ACO) founded in 1906 is the creator and organiser of major motor sporting events including the first grand prix in the history of motor racing in 1906 followed by the Le Mans 24 Hours in 1923. The ACO's aim is to develop long-distance racing and since 2012 it has been the organiser and promoter of the FIA World Endurance Championship (FIA WEC). The club is also the creator of the continental series: the WeatherTech SportsCar Championship, former American Le Mans Series (1999), the European Le Mans Series (2004), and the Asian Le Mans Series (2013). On its own circuits at Le Mans, the ACO organises the 24 Heures Motos, the 24 Heures Karting, the 24 Heures Camions and the French Motorcycle Grand Prix. But above all the ACO is a club made up of enthusiasts who defend the rights of car users on a daily basis, and it gives its members a privileged welcome to enable them to live their passion for motor sport at the events it organises.
The ACO also has a driving school, Le Mans Driver, a leisure and kart competition complex and simulators, an Enterprise department for the organisation of seminars, a team of guides providing tours of the installations of the Le Mans circuits, two official boutiques in Le Mans and Paris as well as eight regional agencies.
What's New Asian Le Mans Series Messaging
* Add group visibility option
* Record videos directly in-app
* Upload files like PDFs or videos
* 500 characters limitation increased to 2000
* Add pictures in comments
* Share shouts and events on social networks
* Better cal interface with user cal integration
* Admin and company badges
* Many new in-app facilities for admins (edit any event and member profile fields)
* Direct messages
* Open links in external browser
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Graduate, Professional and Adult Council By-Laws
Please view the GPAC Bylaws here
The purpose of the Graduate, Professional and Adult Council (the Council) is to effectively represent all graduate, professional, and adult students of Loyola University Chicago (the University), to promote and encourage interaction among graduate students at the University, and to provide a cohesive voice for the entire professional, graduate, and adult student population within the larger student body at the University. This shall be done through activities including, but not limited to, correspondence with University administration, the sponsorship of social and service events, and participation with the University Senate.
Article I – The Council
Section 1 – Purpose and Formation
A. The Purpose of the Council shall be to legislate for the betterment of the entire graduate, professional, and adult student body of Loyola University Chicago, and to bring concerns of individual Institutes and Schools to the attention of the University Senate and the University
B. All Schools and Institutes shall have two seats.
C. Each member of the Council's constituents shall be defined as the population of students enrolled in a program within the Institute or School said member represents.
Section 2 – Membership and Voting
A. Membership on the Council shall be divided among each of the University's Institutes and Professional Schools, including the Graduate School; the Institute of Pastoral Studies; the School of Business; the School of Communication; the School of Continuing and Professional Studies; the School of Education; the School of Law; the School of Medicine; the School of Nursing; the School of Social Work; the School of Health Sciences and Public Health; the School of Environmental Sustainability; and any other current or future graduate Institutes or Schools as the University may create.
B. Each member of the Council shall have one vote.
C. The Council may appoint ad hoc liaisons as needed. They shall hold no voting privileges.
D. Members of the Council shall have the following responsibilities:
1. Attend Council meetings.
2. Vote conscientiously on issues reflecting the interests of their constituents.
3. Disseminate information to students through the administration or student representative body of their Institute or School.
4. Serve as an active member of a Council committee.
5. Represent the student community by bringing issues that have emerged as concerns among their constituents to the attention of the Council.
E. Proxies and Vacancies
1. A member of the Council may assign their vote to a valid proxy from within their Institute or School by notifying the Chair or Co-Chairs at least 48 hours prior to the meeting in which the vote will take place.
2. A seat shall be considered vacant if:
i. A member voluntarily vacates their seat, or
ii. A member, who has already been provided adequate warning by the Chair or Co-Chairs after one (1) absence per semester without excuse from the Chair or Co-Chairs, fails to attend or assign a proxy to a meeting without excuse from the Chair or Co-Chairs a second time during the same semester.
3. Vacant seats shall be nominated by each Institute or School's respective administration, student government body, or current Council member of the Institute or School.
Section 3 – Meetings and Internal Governance
A. A meeting is defined as a set time established by the Officers of the Council conducted either in person, by video conference, or both.
B. There shall be no less than four (4) Council meetings each academic semester. The Chair or Co-Chairs shall convene extraordinary meetings of the Council upon the petition to the Chair or Co-Chairs of five (5) members of the Council.
C. Quorum, required to conduct official business, shall be a majority of the voting members of the Council.
D. A main purpose of Council meetings is to discuss and vote on matters that come before the Council in person or via video conference. However, voting may be conducted in the manner most convenient to the Council, such as voting via video conference, Sakai, email, third-party online survey, or other methods, as long as the methods are conducted transparently, honestly, and in good faith. These alternative voting methods shall only be utilized if voting during meetings in person or via video conference is unfeasible.
Article II – Officers and Committees
A. The Council shall have the power to elect the Officers of the Council. The Officers may include a Chair and Vice-Chair or two (2) Co-Chairs, determined by the voting members of the Council during the election. Any candidate for Chair, Vice-Chair, or Co-Chair must be in good academic and disciplinary standing with the University.
B. The Officers of the Council shall be elected by a simple majority vote no later than the end of the Spring semester. If there is no candidate for the position of Chair, the election shall be postponed until the first meeting of the Fall semester. The Vice-Chair and any additional officers may be elected at the same time as the Chair or Co-Chairs, or during the first meeting of the Fall semester.
C. Elections shall be facilitated by the sitting Chair or Co-Chairs. The Chair or Co-Chairs shall take nominations and conduct the election. If no candidate for a given position receives a majority vote in the first ballot, a run-off between the two leading candidates shall be used to determine the officer.
D. The Chair or Co-Chairs shall have the following Roles and Duties:
1. Serve as Executive Officer(s) for the Council, which includes serving as the ex officio and non-voting member of all committees, and be responsible for the execution of all decisions of the Council.
2. Appoint chairs of standing committees and non-elected officers with the consent of the Council
3. Consult with and advise Staff and Administration on matters of concern to the graduate student body.
4. Schedule and chair no less than four (4) meetings per semester.
5. Create an agenda in cooperation with Committee Chairs, Council members and other parties for each meeting.
6. Ensure all vacant seats on the Council are filled.
7. Meet once during the Fall semester with all Institutional and School student representative bodies to increase the awareness of the Council on campus.
8. Contact all Institutional and School administrations and student representative bodies prior to the end of the Spring semester to select representative(s) for vacant seats, if any.
E. The Vice-Chair or Co-Chairs shall have the following Roles and Duties:
1. Assume the duties of the Chair of the Council in the event of absence or resignation of the Chair.
2. Prepare and distribute, or delegate the task, of taking and keeping minutes at each Council meeting.
3. Monitor the enforcement of Council by-laws.
4. Verify quorum at each meeting and notify the Chair when quorum is reached or lost.
F. The Chairs of each standing committee shall:
1. Schedule meetings for the committee.
2. Create, keep, and distribute a written record of all committee business.
3. Have the power to create subcommittees to focus on special topics, with the consent of either the Chair and/or the Council.
G. Impeachment of an Officer or Council Member
1. Any voting member of the Council may charge an officer with neglect of duties or disrespecting the office, or charge a Council member with neglect of duties, by presenting a formal charge before the Council. A majority vote shall determine whether a hearing will occur.
2. Impeachment HearingsThe call for a Hearing shall constitute impeachment.
i. The call for a Hearing shall constitute impeachment.
ii. The Hearing shall be closed, or public, at the wishes of the accused.
iii. The Hearing shall take place at an emergency Council meeting within seven (7) days.
iv. The member bringing the charges will have five (5) minutes to present the charges, and the accused shall have five (5) minutes to present their defense.
v. The Council shall have fifteen (15) minutes to debate, at the end of which a secret-ballot vote shall immediately occur to determine if the officer or member is to be removed. A simple majority is required to remove the officer or member. The Chair or Co-Chairs shall oversee the counting of the ballots and summarily destroy the ballots after the vote is announced. In the event the Chair or a Co-Chair is the member bringing the charges, the Vice-Chair or other Co-Chair shall assume these duties. In the event the Chair or a Co-Chair is the accused, and the Vice-Chair or other Co-Chair is bringing the charges, the Chair of the Standing Committee on Advocacy shall assume these duties.
A. Membership on all Standing Committees shall be open to any members of the Council. All Standing Committee members must remain in good academic and disciplinary standing with the University or are subject to removal by their Institute or School.
B. The Council shall establish membership in all Standing Committees for the Academic Year no later than the second meeting of the Fall semester.
C. The Council may establish ad-hoc committees at any time with a simple majority vote. These committees will cease to exist at the first meeting of the following Fall Semester.
D. A Committee Chair will be assigned by the Chair of the Council and approved by the remaining Council members.
E. All Committees shall keep records of their proceedings and attendance of members.
F. The Advocacy Committee shall:
Investigate professional, graduate, and adult student concerns brought to the attention of the Council by contact with administrators and students, as appropriate.
Propose the best course of action with regards to a student concern.
Formulate Council policies with regard to general student issues
G. The Service Committee shall:
Investigate and develop opportunities for community service in furtherance of the University's Jesuit mission.
Promote and advertise service opportunities to the student body as a whole.
Coordinate across Institutes and Schools to encourage broad student involvement.
H. The Events Committee shall:
Organize and run at least one (1) Council social event per semester.
Create a calendar of events for each semester by the second meeting of the semester and submit it to Council approval.
I. The Finance Committee shall:
Oversee cash flow and other money management issues.
Receive and receipt all moneys due to GPAC.
Prepare needed budgets for approval by the Council.
Perform other duties assigned by the Council.
Article IV – Amendments
The Council establishes these by-laws by a two-thirds (2/3) majority vote.
Amendments to these by-laws may be presented by any member of the Council and approved by a two-thirds (2/3) majority vote.
At no time may these by-laws contradict the Student Code of Conduct or policies governing student organizations set forth by the University.
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Cataract-aapb v1.42 (Fix) is a large font version of the 3_eye_jack-aapb theme. Most of the screens are the same. Some screens have been changed to accommodate larger fonts. Menu browser was design for 27 size fonts (default is 18). Large font in the SBS and WPS is set to size 21 however, it can be change up to 27 in the SBS or WPS file. Reboot after installing and removing. Require font set.


This will be Beo's first performance at the 2017 Charlotte New Music Festival and will feature works composed by the participants and faculty of CNMF. Located at the NoDa Brewing Company in Charlotte, some of the contemporary works will be world premieres. Additionally, Beo will feature Max Duykers' "Glass Blue Cleft" for string quartet, which was selected as the winner of the second annual Charlotte New Music and Beo String Quartet National Composition Competition. Perhaps most exciting of all, each of the composers will be present at this performance! Also included in the performance will be pieces by Craig Bove, Marc Mellits, Jenny Clinard, Xinyan Li, Tyler Waters, Logan Rutledge, and Adam Strawbridge.


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The new Chelyabinsk Trams diagram
Over ten years ago I made the diagram of Chelyabinsk trams and trolleybuses. That design turned out to be very successful: dozens of designers used it as a reference for building their own diagrams. It wouldn't be as good if not for Artem Gorbunov's generous help.
Three years ago, together with Alexander Karavaev we made a new version of the diagram. It had a lot of design inventions: the "pencil-drawn" layer for buses and trolleybuses, the "watercolour" rivers and lakes, 3D terminals, the new shape of the stops' ticks. With that diagram, a logo for chelyabinsk trams was born: the city's coat of arms decorated with a pantograph.
Then Polina Lesnikova joined the team. She re-drew the map to account for the changes in routes. Together with Alexander, they changed a lot of details after testing the legibility of the previous version. Thus we arrived at the new diagram:
Some landmarks were added. The bus-and-trolleybuses layer gave the previous version some visual richness, and it was interesting to scrutinise. Unfortunately, it didn't provide any notable utility, so we decided to remove it. This helped to simplify the geometry of lines and make the fonts bigger. The new diagram looks stronger.
Designed by Polina Lesnikova and Alexander Karavaev, art-directed by myself.
154 2018 projects release transportation
The fourth version of Moscow metro map
I made my first Moscow metro map in 2007. The official map was disgusting then, but nobody cared. My work inspired many designers to try to design their own map
Jouele 2.1
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The takedown of the Hansa dark web marketplace, done live on national TV by Dutch police, was possible because officers had been running the site themselves – and on Thursday they detailed how they did it.
In 2016, security shop Bitdefender tipped off the Dutch plod that Hansa, one of the most popular dark web markets, was being hosted in the Netherlands. Hansa's popularity was largely down to its multi-signature Bitcoin handling, which stopped buyers getting ripped off by not releasing payment until an order arrived.


In 2016, 20,000 youth aged out of foster care nationwide without being adopted. Meanwhile, 2 million LGBTQ adults want to become adoptive parents but are prevented by discriminatory policies.
Texas, Michigan, North Dakota, and South Dakota have policies that allow agencies to refuse to place children with potential foster or adoptive parents who are LGBTQ based on religious beliefs. Kansas and Oklahoma just passed such laws in the last two weeks. Colorado's legislature is currently considering a similar one.
In 2016, a legislative bill was considered in the Nebraska unicameral similar to those in the aforementioned states, but the bill did not advance on the floor. However, the Nebraska Supreme Court made progress for the LGBTQ community in 2017 when it upheld a district court's decision that the statewide ban on gay and lesbian individuals and couples from fostering children was unconstitutional. This meant that LGBTQ individuals and couple would have equal rights be licensed foster parents.
In today's podcast, we hear how this applied to one family, the Retzlaffs, in northeast Nebraska, as well as how the renewed implementation of the Strengthening Families Act allowed them to reverse some of the social delays their adopted children suffered in their early childhood.
We also hear from a Nebraska agency director on LGBTQ discrimination, caseworker turnover, her foster son's experience with the legal system, and more.


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SA: Stop prostitution – and crime – from growing
Vic: Oppose "the most anti-free speech law ever proposed"
Urge your leaders to support the Born Alive Bill
TAS: "Offence" shouldn't make speech illegal
SA: Stop prostitution – and crime – from growing Vic: Oppose "the most anti-free speech law ever proposed" Urge your leaders to support the Born Alive Bill TAS: "Offence" shouldn't make speech illegal
Vaccines: a matter of individual conscience
Martyn Iles | February 04, 2021
I am constantly asked, so here are some thoughts and explanations on vaccines.
First, I'll be upfront about the fact that I support vaccines, am grateful for the technology that makes them possible, and accept that they are generally safe. But there are qualifications.
The main one relates to those vaccines which had an association, during their development, with foetal cell lines. In Australia, this includes the MMR, Chickenpox, Hepatitis A, and Rabies vaccines. A person's attitude to these vaccines is a matter of individual conscience that ought to be respected.
You may wonder which way your conscience ought to go – the following information may help:
Vaccine development requires a cellular environment.
Companies buy cells "off the shelf" for this purpose, called "cell lines." They have names which are combinations of letters and numbers.
The cells are not ingredients in the vaccine; they are tools used during the research and development process.
But some have raised the question – where did these cell lines come from?
In each case, they descended from an original cell. That cell was replicated once, twice, three times… and to infinity, over many years. These replicated cells, descended from an original cell at some point in history, are the "cell line".
In some cases, the original cell was from plant matter. In others, from an animal. Sometimes, they come from human tissue. Then, there are cases where the original cell was from an aborted foetus.
There are two or three popular foetal cell lines which originated from abortions in or around the 1960s. They each came from a single abortion. Their use does not result in more abortions. The abortions were not for the purpose of creating the cell line.
These cell lines are used so extensively in biotech and medicine that they are ubiquitous. We will all encounter and probably use multiple products developed with their help during our lifetimes.
Most theologians, Christian bioethicists, and all church denominations which speak to the matter, do not consider it sinful to use products, including vaccines, which have had an association with these foetal cell lines. They make that deduction because it does not amount to complicity in abortion, nor endorsement of abortion. In other words, taking these vaccines does not cause or support abortions.
Whilst I have accepted this view for a while, I must confess to harbouring uncertainty in more recent times, along – I think – with anyone who really cares about the pro-life cause. Taking an affected vaccine may not be sinful per se, but I can see that it is a serious matter of individual conscience. On the one hand, the association is incredibly remote – materially and historically. On the other hand, an abortion is a serious matter.
The situation becomes more complex, because there is no completely 'ethical' COVID-19 vaccine. (Some time ago, we indicated that the Prime Minister's office had confirmed there would be an 'ethical' alternative vaccine. Sadly, this was the UQ candidate which was abandoned during the testing phase.)
Pfizer's is the best from an ethical standpoint, but not perfect. (Because it does not rely on a foetal cell line for its development or manufacture... they only made use of a foetal cell line to conduct some trials.) I believe that this is reason enough not to make the COVID-19 vaccines compulsory.
This conscience issue is not fanciful or baseless. It should be respected in cases where it is genuine.
abortion vaccines foetal cells
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Vic: Andrews Government at war with faith communities
Time and time again, the Andrews Government has declared war on faith communities by dismantling their religious freedom.
Get equipped to influence the state of our nation, on issues that matter:
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Racers pop TSU bubble
Posted: Monday, March 5, 2012 7:00 pm
By TERESA M. WALKER
NASHVILLE (AP) — Somewhere, a bubble team can breathe a little easier for the NCAA tournament thanks to the 12th-ranked Murray State Racers.
Jewuan Long drove the baseline for a layup with 4.4 seconds left, and Murray State rallied from seven points down in the final 5:28 to beat Tennessee State 54-52 for the Ohio Valley Conference tournament championship Saturday and the automatic NCAA tournament berth.
Had Tennessee State won it, the Racers would have probably received an at-large bid, bursting another team's tournament bubble.
The Racers just considered this comeback a final tuneup for the NCAA tournament in their first trip back since finishing the 2010 season 31-5 and beating Vanderbilt in the first round. Senior guard Donte Poole said the finish just shows how focused the Racers are as they held Tennessee State without a point in the final 3:45.
"Down the stretch, we were down we just tried to put a number of stops together to give ourselves the best chance to come down and get a shot," Poole said.
The final shot didn't go off as planned. Isaiah Canaan was supposed to take the shot, but the Tigers smothered him so he passed off to Long for the floater. Tennessee State coach John Cooper thought M.J. Rhett got his feet set to draw a charge on Long with no call.
Long finished with six points.
"I got a lot of confidence in him," Murray State coach Steve Prohm said. "He hadn't made a lot of shots all night, but that's his shot."
Canaan then stripped Tigers guard Patrick Miller of the ball driving to the basket, and Long guarded Robert Covington on his 3-pointer at the buzzer to preserve the win, getting the Racers to 30-1 and avoiding a second loss to the only team to beat them this season.
Prohm said the finish shows just how resilient his Racers are and congratulated the Tigers.
"They had a great game plan today," Prohm said. "Slow you down in the offensive end. They really made it tough on us on the offensive end, and they made us work for everything so congratulations to them."
Covington led Tennessee State (20-12) with 14 points, and Kellen Thornton had 11. These Tigers were 9-23 in Cooper's first season three years ago.
"Murray State did everything they needed to do down the stretch of the game," Cooper said. "Maybe didn't play their best game of the year, but they made plays down the stretch when they needed to make plays. That's what good teams do. Hats off to them and hats off to everything they've been able to accomplish."
Canaan and Poole each scored 14 points for the Racers.
Fittingly, because the Tigers are the only team to beat Murray State, this game couldn't have been much tighter with 10 ties and 11 lead changes. Murray State led 29-27 at halftime, then came out and looked early as if it was trying to help the OVC put two teams into the NCAA tournament.
Most of the fans at Municipal Auditorium dressed in Racers' blue and yellow, but the Racers were sloppy as they started the second half missing their first six shots. They didn't hit their first field goal until 14:27 was left on a 3 by Long. That was part of a 12-2 run as the Racers rallied from a 38-31 deficit, and Jackson's layup put the Racers up 43-40 with 8:28 left. Tennessee State answered with 10 straight points to go back up 50-43 on Rhett's jumper with 5:28 left.
That set up a furious finish.
Tennessee State last led 52-48 when M.J. Rhett dunked with 3:46 left for its final bucket. Ivan Aska answered, then Ed Daniel hit two free throws with 1:01 left for his only points of the game tying it up.
Miller had another turnover with 30 seconds left for Tennessee State. That allowed the Racers to run out most of the rest of the game before Canaan found Long in the left corner. Long drove the baseline and scored, giving him six points for the game.
Cooper said Miller was his best driver, while Covington was his best jump shooter.
"We come up 0-for-2. We'll live with that," Cooper said.
Tennessee State twice led by seven in the second half. The Racers came back each time.
The Tigers outshot Murray State 46.8 percent (22-of-47) compared to 37.5 percent (18-of-48). They also outrebounded Murray 34-24. But the Racers scored 15 points off Tennessee State's 18 turnovers and had a big edge at the free throw line, hitting 14-of-16 while the Tigers hit 5-of-10.


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...player version. I want all types of ads to be implemented in to the app. (banner, interstitial ads and video ads.) So as a result, I want the same game but with different design and UI. I will publish them on both ios and android. My main concern is graphics so they have to be really good. Other than that levels of the original game can be copied.


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2021 Brown Arch Brick Award Winners Announced
By Sam Oleson
From left to right: Shay Family, Larry Huber, Dr. Stephen Leonard, Bob McLaughlin, Lee and Paula Crevier
Larry Huber
Bob McLaughlin
Lee and Paula Crevier
Dr. Stephen Leonard
Shay Family
Top Air Show Performers Commit to EAA AirVenture Oshkosh 2022
WomenVenture T-Shirt Design Contest Winner Announced
Early Commitments for AirVenture Oshkosh 2022 Air Shows
EAA AirVenture Oshkosh 2022 to Celebrate 75th Anniversary of U.S. Air Force
Tickets Now on Sale for EAA AirVenture Oshkosh 2022
July 30, 2021 – Every volunteer who contributes to making EAA AirVenture Oshkosh the World's Greatest Aviation Celebration deserves thanks, but the Brown Arch Brick Awards exist to give special attention to a few people who go above and beyond.
The 2021 Brown Arch Brick Award recipients are Larry Huber, Bob McLaughlin, Lee and Paula Crevier, Dr. Stephen Leonard, and the Shay family. The recipients were honored at a ceremony on Friday morning at the Brown Arch.
Beginning in the 1980s, Larry, EAA 285890, started volunteering as a flightline volunteer in the Vintage area. Currently, he's the vice chairman of showplane aircraft and camper registration, helping to coordinate and assist arriving pilots.
"It's an honor," Larry said of receiving the Brown Arch Brick Award. "I'm not a person that likes the notoriety, but I consider it quite an honor. I've put a lot into EAA, and EAA has given me far more than I've put into it."
Bob, EAA 188831, has been a longtime volunteer at Kermit Weeks Hangar: EAA Flight Research Center in Oshkosh, as well as at AirVenture. He became the workshops chairman in 1989 and transitioned to co-chairman of the Builders Education Center & Workshops in the early 2000s, a position he held until 2016. He's also an A&P/IA mechanic and those skills have helped immensely at the Weeks Hangar.
"I was very honored and always amazed over the years that you get recognition for doing what you love," Bob said of receiving the award. "The reward is doing what you're doing and being around the people you volunteer with."
Lee, EAA 355459, and Paula, EAA 477989, began volunteering with EAA in 1991 and have helped out in a variety of areas, including Pioneer Airport, Ultralights, Convention Headquarters, and basically anywhere else needed. Having been involved as volunteers for three decades now, Lee and Paula have developed strong friendships, which, along with genuine enjoyment of their duties, has kept them coming back to Oshkosh.
"Good people," Lee said. "We have a lot of friends … I mean there was just a lot of people that we met that we knew, and we didn't know they were up there like that until we went up there. Then we ended up with the camping group and it's like, 'Okay, you go there, you get to camp, you get to see the friends that you made from Canada.' It's like an annual thing to go up there and touch base with people you've made friends with for years and years."
Stephen, EAA Lifetime 286293, joined the EAA Aeromedical Advisory Council in the 1980s and has been assisting EAA members and pilots, as well as the organization, with medical-related issues ever since. As part of the council, he's been an active participant in shaping aviation medical policy as well as personally assisting fellow members.
"[The Aeromedical Advisory Council] was initially formed to provide aviation medical advice to Paul Poberezny so he could take informed positions when working with the FAA to help shape regulations," Stephen explained. "That role has expanded, and because the FAA medical team regularly attends AirVenture, the council members have had the chance to develop mutually productive, personal relationships with them. They trust us, and we are able to provide important input into their policy decisions. The greatly expanded the Special Issuance program, and the development of criteria for AMEs to verify qualifications and issue certificates on the spot for a number of conditions that previously required deferrals, are direct results of ideas and input from our council. Finally, we are available as a resource to EAA members to guide them toward resolution of certification problems that they have had."
Finally, the Shay family — which includes husband and wife team Bill, EAA 292424, and Margaret, as well as daughters Raquel and Sophia, EAA 1051870 — were honored with a Brown Arch Brick Award for their service as volunteers with EAA's business development team since 2009. Since the Shays began volunteering, they've had the chance to meet a variety of new people each and every year — a key factor in why they love coming back each year.
"[I enjoy] the interaction I have with other people and the ability to show people who have never been to Oshkosh before the experience and show them my passion," Bill said. "The girls have enjoyed the people they've been able to meet through the volunteering, to where they've been keeping in touch with people year-round. … They keep connections going for the past 11 years they've been volunteering."