prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: What is the sticking point in the political showdown over the budget?

Read the following text and answer briefly.

Context 1: CNN com - Transcripts
Tensions Boil Over possible government shutdown; New trouble targeting Gadhafi; Libyan Rebels in Panicked Retreat; Should U S  Recognize the Rebels?; Meeting With Gadhafi; Washington, D C  to Feel Burden of Shutdown; Religious Leaders Fast to Protests Cuts for Poor
WOLF BLITZER, HOST: Don, thanks very much 
Happening now, the top U S  general in charge of the military mission in Libya now expressing doubts that the opposition has the manpower to topple Moammar Gadhafi, as deadly new air strikes force rebel fighters into another retreat  This hour, I'll speak with a former Republican Congressman who's in Tripoli right now trying to get Gadhafi to step down 
Also, growing outrage across the United States, amidst new signs tomorrow's potential government shutdown may -- repeat may be unavoidable  Why one lawmaker is telling Congress -- and I'm quoting right now -- "go straight to hell "
And possible presidential hopeful, Donald Trump, on a mission to tell President Obama, "you're fired " We're fact checking his controversial investigation into the president's birth 
Up first, the political showdown over the budget, as tensions reach a boiling point about 31 hours until impending government shutdown  Just hours from now, President Obama will meet with Republican House speaker, John Boehner, and the Democratic Senate majority leader, Harry Reid, for further negotiations  Those talks scheduled to begin 7:00 p m  Eastern 
Hundreds of thousands of people across the country will be impacted by the shutdown  And we'll be bringing you examples throughout the next two hours 
One place it would be felt heavily is right here in Congress' backyard, the city of Washington  Washington, DC -- its spending is tied to the federal budget  And this major metropolitan area could lose millions of dollars while a number of critical services, like trash collection, for example, would be suspended for at least a week 
Today, an enraged Eleanor Holmes, the delegate representing Washington, DC, lit into Congress over the stalemate 
(BEGIN VIDEO CLIP) ELEANOR HOLMES NORTON (D), D C  DELEGATE: It's one thing to beat up on the District of Columbia  It's another thing drop a bomb on the city  And that's what this Congressional -- C R  does  It takes the route of authoritarian governments and dictatorships by dictating to a local government how it may spend its local funds  And it may force the District of Columbia government to shut down, although our government had a balanced budget 
BLITZER: And get this -- the members of Congress charged with reaching a deal, they'll still be receiving a paycheck if there's a shutdown, despite the hundreds of thousands of government employees who won't be receiving any paychecks  The current Congressional salary, by the way, $174,000 a year 
Our CNN senior Congressional correspondent, Dana Bash, is up on Capitol Hill with the latest developments -- Dana, specifically, where are the sticking points right now?
DANA BASH, CNN SENIOR CONGRESSIONAL CORRESPONDENT:
Well, look, Wolf, this is effectively a bill to fund the government  And the sticking points certainly are about how much spending to cut  That's what this whole issue has been about 
However -- however, one of the main issues, I am told, that were just -- that was discussed at the White House meeting this afternoon with the president, the House speaker and the Senate majority leader, was over not necessarily spending measures, but over lightning rod issues like regulating greenhouse gases and abortion 
BASH (voice-over): One of the biggest disagreements is not over government spending, but policy 
REP  JOHN BOEHNER (R-OH), SPEAKER OF THE HOUSE: Some 40 or 50 policy restrictions that were attached to -- to our bill 
BASH: So-called policy riders Republicans call essential and Democrats call nonstarters  The most divisive is over abortion  A GOP plan to cut all federal funding for Planned Parenthood, which provides abortion procedures in addition other women's health services 
SEN  HARRY REID (D-NV), MAJORITY LEADER: This is a budget  This is to keep our country running  This is not a woman's health bill 
BASH: Planned Parenthood staged a rally outside the Capitol to protest 
CECILE RICHARDS, CEO, PLANNED PARENTHOOD: They don't want to allow Planned Parenthood to serve the three million women that we see every single year  Ninety-seven percent of the services Planned Parenthood provides are preventive care 
UNIDENTIFIED MALE: I certainly don't think that taxpayers should subsidize abortions  It's -- if a woman chooses to have an abortion, it's legal to do that in this country  But I don't think taxpayers should be put in a position to have to pay for those abortions 
BASH: Another major sticking point -- how much spending to cut  A Democratic source tells CNN they have finally tentative agreement on slashing $34 5 billion from the rest of this year's budget  But a Republican source says there's no deal 
BOEHNER: There is no agreement on the number  There are no agreement on the policy issues that are contained with it 
BASH: Then there's the critical issue of what programs and agencies to cut  Democrats say they're trying to find spending cuts with the least impact on those who need it most  So they're pushing for things like temporary one year cuts in programs  Some examples, cuts in wetlands protection and Pell grants for summer school and graduate students 
Republicans call that smoke and mirrors 
BOEHNER: And our goal is to make real spending cuts 
BASH: Some examples of what Republicans want to cut -- money for food inspectors, Head Start education programs and funding for housing 
BASH: This afternoon, House Republicans did pass a bill to keep the government running for one week past tomorrow's midnight deadline  It has $12 billion in cuts  It would fund the Defense Department for the rest of the year  But Democrats, including the president of the United States, call it a distraction and they say that they really want to keep the focus on what they're negotiating, which is a bill that would keep the government open -- keep the government functioning and funded for the rest of the year 
BLITZER: And the president's playing hardball  He's saying he'll veto that legislation --
BASH: He was, yes 
BLITZER: -- if it were to pass the Senate and come to his desk  I hear, Dana, that some employees already are getting furloughing notices 
BASH: It's true  This is just preventive  But all across the Capitol here today, people in offices and -- and -- well, really, everywhere -- were told whether or not, if, in fact, it does come to a government shutdown, if they're going to be here or not  And this is an example  We obtained one of the furlough notices  And I'll just read you a line  This -- imagine if this came across your desk  It says: "Because your services are not needed for the orderly suspension of operations and you're not engaged in one of the accepted functions, you're being placed on furlough effective Saturday, April 9, 2011 "
Now, again, of course, this is just protective  The government is still open  But interesting that they're already getting ready for a government shutdown and telling people who will come to work and not 
One more note  Even people who are here, who are called essential, they're not going to get paid, either 
BLITZER: All right, Dana 
Don't go too far away 
We'll be in close touch 
The impact of the potential government shutdown is even being felt on the front lines of combat in Afghanistan  And Iraq  The Defense secretary, Robert Gates, is in Iraq right now  And he's telling U S  troops they will feel a pinch 
ROBERT GATES, SECRETARY OF DEFENSE: I hope they didn't have you standing out here in the sun too long
If -- if the government shutdown starts on the 8th and goes for a week, you'd get a half a check  If it goes from the 15th to the 30th, you wouldn't get a paycheck on the 30th but you would be back paid for all of it  So that's -- that's the deal 
BLITZER: Not great deal 
Gates also told the troops this would likely be his last trip to the country as Defense secretary and he wanted to say thank you 
He's expected to retire later this year 
Now to the deadly stalemate in Libya  New signs the military operation in the region is facing some tough new challenges 
Our Pentagon correspondent, Barbara Starr is here 
She's watching the story 
She's got more 
What are you learning? BARBARA STARR, CNN PENTAGON CORRESPONDENT: Well, Wolf, there was very dramatic, very hard-nosed testimony today on Capitol Hill from the top U S  commander responsible for the U S  involvement in Libya, saying that Gadhafi forces are becoming increasingly difficult to target, as they are using civilian vehicles, mixing in with local populations, moving next to mosques, schools, hospitals -- all the same tactics we saw for years in Iraq 
And now, all of this today leading to a very dramatic exchange between General Carter Ham and one of the most vocal administration critics, Senator John McCain 
SEN  JOHN MCCAIN (R), ARIZONA: Hearing your testimony, General Ham, is almost an Orwellian experience for me  The fact is that if we had imposed the no-fly zone three weeks, four weeks ago, Gadhafi would not be in power today 
The fact is that the situation on the ground is basically a stalemate 
Would you say that the situation on the ground is a stalemate or an emerging stalemate?
GEN  CARTER HAM, COMMANDER, U S  AFRICA COMMAND: Senator, I -- I would agree with that if present on the ground 
MCCAIN: So the goal -- our policy objective of the removal of Gadhafi is further from being achieved than it was three or four weeks ago 
HAM: Senator, I -- I don't know that I would agree with that  What I -- because that, again, was not a military mission  The military mission of protecting, I think, was not wholly achieved, but achieved in large part 
STARR: General Ham also acknowledging another problem -- a key U S  aircraft, the AC-130, that flies low and slow to target on the ground, is facing what he called "a significant threat" from surface to air missiles, which he said remain effective and operational in some cases 
And, Wolf, get this  General Ham says there were about 20,000 of those surface to air missiles when the campaign started and they are concerned that an awful lot of them are still out there -- Wolf 
BLITZER: Barbara, thanks very much for that report 
Panicked rebels are once again on the retreat from Gadhafi's forces  Just today, at least three people were killed, another 10 injured, in new air strikes  And there are mounting questions about whether NATO could be responsible for the attack 
Our senior international correspondent, Ben Wedeman, is joining us now from Benghazi 
Ben's watching all of this closely 
You just heard General Ham, who is the commander of the U S  military's Africa Command  He was in charge of the mission before handing over complete control to NATO  You just heard him say there could be a stalemate out there 
What's the sense on the ground?
BEN WEDEMAN, CNN SENIOR INTERNATIONAL CORRESPONDENT: Well, the sense was a few days ago that it was, indeed, a stalemate -- sort of a seesaw battle that went back and forth between Ajdabiya and Brega 
But what we saw today was that that seesaw was tipped over  And it was a general retreat by the opposition forces from somewhere near Brega to almost the other side of Ajdabiya  This, after this air strike, which almost everybody on the ground believes to be NATO leaving not three, but four people dead  And many others are still unaccounted for 
That set off this general retreat whereby we saw all their heavy -- all of the opposition forces' heavy equipment -- multiple rocket launchers, tens and tens of these pickup trucks mounted with heavy machine guns streaming through Ajdabiya to the other side, the far side of the city  Some of them going all the way back to Benghazi, according to the head of the rebel forces in the eastern part of the country, Abdul Fatah Younis  He says that the Gadhafi forces were approaching Ajdabiya from three different directions 
I would not call that a stalemate -- Wolf 
BLITZER: Ben, you got a close-up look at some of the casualties today out on the front lines 
WEDEMAN: It's very bad, very bad  I mean it wasn't just fighters  It was also medics who had gone to the scene of this reported air strike, which then got hit again  So one of them was a doctor, one of them was a medic  And we were in the hospital  And there was real anger at NATO, anger at the fact that when they needed those air strikes on the Gadhafi forces, they weren't getting them  And now, for the second time in a week, there's been another strike  Now, of course, we must stress that NATO says that they -- because they don't have enough boots on the ground, they can neither confirm nor deny this was a NATO strike  But certainly, speaking to eyewitnesses in the hospital, it certainly sounded like an air strike  And there are no other planes in the skies of Libya other than NATO planes -- Wolf 
BLITZER: Ben Wedeman in Benghazi for us 
The U S  says Moammar Gadhafi is no longer the legitimate leader of Libya 
So why not recognize the rebels?
Why one U S  official says it raises serious concerns 
And a former U S  Congressman in Libya armed with a message for the Libyan dictator 
Will he get to meet with him face-to-face?
My interview with Curt Weldon, that Republican former Congressman -- that's coming up, as well 
BLITZER: Let's get right to Jack 
He's got some nuclear concerns on his mind with The Cafferty File -- Jack 
JACK CAFFERTY, THE CAFFERTY FILE: Well, they had another little temblor in Japan -- a 7 1 magnitude earthquake hit Northeastern Japan today, the strongest aftershock since that massive 9 0 quake and tsunami that followed devastated that nation four weeks ago  And this one today was in roughly the same area 
One of the big concerns, of course, is possible further damage to the Fukushima Daiichi nuclear power plant  The Tokyo Electric Power Company, TEPCO, which operates the plant -- or what's left of it -- said there were no serious incidents as a result of today's aftershock 
So they say  Radioactivity from that plant has poisoned the surrounding land, air and ocean  Millions of people have been exposed  Millions more could be, as radioactivity has been picked up in food and drinking water and detected in faraway places, like California 
This week, workers plugged a crack in the plant that had been gushing contaminated water into the ocean for weeks  As a result, TEPCO says now radiation levels in the ocean waters off the coast there have dropped dramatically 
Yesterday, the head of the United Nations' scientific committee on the effects of atomic radiation said the Fukushima accident is not expected to have any serious impact on the health of the Japanese people  He said, quote: "We have seen traces of iodine in the air all over the world, but they are much, much, much lower than traces we have seen at similar distances following Chernobyl," unquote 
Well, not everybody is convinced  In South Korea, more than 130 primary schools and kindergartens ordered closed today outside of Seoul  People there were worried that windy, rainy weather could be carrying radioactive material from Japan 
North Korea aired warnings on television for its people to stay indoors during that rain storm and to take a full shower if they were caught outside in the storm 
Even here in the United States, some chefs are now using sensors to test levels of radiation in the fish they plan to serve in restaurants 
Here's the question -- do you think you're being told the truth about the nuclear accident in Japan?
If your -- if your trout is he glowing, Wolf --
BLITZER: Yes?
CAFFERTY: -- you might want to send it back and get a ham sandwich 
BLITZER: You want it well done, but not necessarily that well done 
CAFFERTY: No 
BLITZER: All right, Jack 
Not a laughing matter 
BLITZER: Serious stuff 
CAFFERTY: Right 
BLITZER: See you in a few moments 
New questions this hour about the capabilities of the rebels in Libya and whether they have the power to overthrow Moammar Gadhafi 
Should the United States -- should the United States have a hand in helping arm the rebels?
Let's bring in our foreign affairs correspondent, Jill Dougherty, with this part of the story 
What are you hearing over at the State Department -- Jill  JILL DOUGHERTY, CNN FOREIGN AFFAIRS CORRESPONDENT: Well, you know, Wolf, other countries have done it, other countries like France and Italy have done it -- recognizing the opposition  And supporters say now, with the rebels in retreat, the U S  shouldn't wait 
But what would it really change anything?
DOUGHERTY (voice-over): The U S  says Moammar Gadhafi is no longer the legitimate leader of Libya 
Secretary of State Hillary Clinton is full of praise for them 
HILLARY RODHAM CLINTON, SECRETARY OF STATE: These were not soldiers  These were not trained military forces  They were doctors and lawyers and university professors and economists and, you know, young men who were students  And they are being attacked by mercenaries, by ruthless forces that Gadhafi is utilizing to show no mercy against his people  And they are courageous  They are moving as fast as they can to try to form themselves into a military operation 
DOUGHERTY: Clinton has met with the rebel leaders personally, but the administration still is cautious  The president authorized the CIA to send in agents to learn about the rebels and assess their needs  Clinton's special representative, the State Department's Christopher Stevens, seen here in 2008 in Tripoli, is on the ground in Benghazi, scoping them out 
MARK TONER, U S  STATE DEPARTMENT SPOKESMAN: We sent somebody in to get that kind of on the ground assessment of the -- of -- of their identity, of their leadership structure, to talk with them firsthand and to see what direction we think they're moving in  We've seen some positive signals 
DOUGHERTY: Recognizing the rebels, a senior official tells CNN, raises serious issues  It would acknowledge that Libya is now a divided country 
And could the U S  be sure the group represents the whole opposition movement?
It's a bit early, this official says  Maybe they turn out not to be the right folks 
But Secretary Clinton knows the timing is urgent 
CLINTON: What NATO is doing is buying time, buying space 
DOUGHERTY: So far, the U S  is providing what's called non- lethal humanitarian aid  The administration hasn't yet decided to arm them or provide financial assistance 
DOUGHERTY: But a senior U S  official tells CNN there's a lot the United States could be doing right now without going so far as to recognize the rebels, pointing out that the U S  funds political groups and other organizations around the world  But this official says you want to be careful about who they are 
So, so far, caution seems to be winning out over urgency -- Wolf 
Jill is at the State Department 
The House speaker, John Boehner, may be doing double duty if the government shuts down this weekend  You're going to find out why he could be cleaning up a lot of trash in his own backyard 
And a former U S  Congressman now on a mission to meet with Moammar Gadhafi in Tripoli in person  Curt Weldon, he's here  He'll join us in THE SITUATION ROOM from Tripoli  You're going to find out who he says would be a good replacement for the embattled Libyan leader 
BLITZER: Military leaders have a message for Congress about "don't ask/don't tell "
Well, military leaders say preparations for repealing "don't ask/don't tell" are going better than they expected  They testified before a House committee today about getting rid of the policy that bars openly gay service members  They caution, though, that it will take time and training to implement the repeal  And it must still be certified by President Obama, the Defense secretary and the chairman of the Joint Chiefs of Staff 
Well, your Smartphone just got a little smarter  The FCC is requiring that wireless carriers provide access to the mobile Internet anywhere it's available, even when it's offered by a competing provider  And that could be a huge -- make a huge difference to smaller carriers, who told the FCC they just can't compete otherwise against industry heavyweights like Verizon and AT&T 
New York City school chancellor, Cathie Black, is stepping down after only three months on the job  Mayor Michael Bloomberg says her short stint just didn't work out as either of them had expected or hoped  Her approval rating has plunged to 17 percent 
Black chaired "First" magazine before overseeing the nation's largest school system  Deputy Mayor Dennis Walcott will replace her 
And a war of words is erupting between an emerging Republican star, New Jersey Governor Chris Christie, and his state's largest teachers' union  In a network TV interview, Christie called the union leaders, quote, "political thugs " He blames them for teacher lay-offs that he says could have been avoided if they had not opposed salary freezes  The New Jersey Education Association is firing back, accusing Christie of name-calling -- Wolf 
BLITZER: Sticks and stones will break many bones 
SYLVESTER: Sticks and stones may break my bones --
SYLVESTER: But words never hurt me 
A former U S  Congressman is in Tripoli, Libya right now  His goal -- to talk to Moammar Gadhafi  His message -- we'll talk about that  My interview with Curt Weldon coming up next 
Plus, we showed it to you earlier -- a member of Congress telling colleagues to, quote, "go to hell "
Now she's is joining us live here in THE SITUATION ROOM to explain 
HOLMES NORTON: -- of Columbia  It's another thing to drop a bomb on a city  And that's what this --
BLITZER: Former Congressman Curt Weldon is in a -- Weldon is on a mission to Libya right now to try to meet with the embattled leader, Moammar Gadhafi  But that may be easier said than done 
Joining us now from Tripoli, former Republican Congressman Curt Weldon of Pennsylvania  Congressman, thanks very much for coming in 
And joining us now from Tripoli, former Republican Congressman Curt Weldon of Pennsylvania 
CURT WELDON, FORMER U S  CONGRESSMAN: My pleasure, Wolf 
BLITZER: Let's talk about your meeting with Moammar Gadhafi  I take it it has not yet happened 
Do you expect to meet with the Libyan leader? WELDON: Absolutely  The invitation that was sent to me was from his chief of staff, Bashir Salah, who I've met on all three of my official visits here in 2004 and 2005  And the letter specifically says we want you to come over and meet with the leader and our senior leadership 
And I said it's worth me coming over to support the administration and to try to let the leader know face to face that this is facing -- it's very grave timing in the situation and they have to have some movement fairly quickly or they're not going to be happy with the -- with the alternatives 
BLITZER: What's taking so long?
Why haven't you been able to meet with Gadhafi yet?
WELDON: Well, it -- that's not unusual  I mean all three of the delegation trips that I led here in 2003 and 2004 -- or, actually, 2004 and 2005 -- they always make you wait until 30 minutes before the meeting and then you go  And some of those meetings were at 10:00 at night, some were at 5:00 in the afternoon 
As you know from the excellent reporting being done by your folks here, there's a lot of security concerns, and they are very concerned where Gadhafi is at any given moment  That's one of the issues, but we have been making ourselves available 
We have been doing a lot of back-channel meetings with friends and associates that I have here, and we have met with the chief of staff and one of the sons, and today with the prime minister, a very lengthy meeting for two hours  So, we're going to give them until tomorrow  We're not going to stay beyond that  And we have given them some suggestions, and we expect a response by midday tomorrow  And if we don't, we will done exit conversation with your people and let you know our feelings 
BLITZER: What's the major headline that you got out of these meetings with other leaders? I take it you met with Saif Al-Islam Gadhafi, one of the sons of Moammar Gadhafi  What are they saying to you?
WELDON: Well, we actually didn't meet with Saif  I have met with Saif probably 10 times over the past seven years, both in America and here in Libya  I have not yet met with Saif  I have offered, if he is available 
I have met with Saadi  And the general thrust is obviously that they want peace and they want to find a way out of this  But as I have explained to them, there's certain things that have to be done according to our president and our secretary of state, who I'm here to support 
We don't have a different agenda  There's no compromise on our part  Our only mission here is to talk face to face with them and say this is reality and this is a grave situation, and you need to do certain things that we suggest that we think will get our administration to respond to your actions  And again, we're not doing any negotiating 
They know me, they have seen my efforts  I have not taken anything from their country in the way of financial benefits, and I'm here only because I want to avoid war  I don't want to see American soldiers killed, and I don't want to see more innocence Libyans killed 
BLITZER: You wrote an op-ed in "The New York Times" this week saying that once you meet face to face with Moammar Gadhafi, you will tell him to step down  Is that still your intention?
WELDON: Absolutely, Wolf  I wrote the op-ed before the trip was planned  And I wrote it, Wolf, because back in 2004, when I led the first delegation of Americans to sit down with him in the tent in Tripoli, he said to me, "Congressman, why did it take 30 years for someone from your country to come and sit with me and tell me to my face that you believe that I'm a criminal and a terrorist  And then if you didn't believe me, bomb me?"
And I said, "Leader, I can't explain that " So I said now it's time for someone to sit in a tent face to face with Colonel Gadhafi and let him know how grave this situation is 
And I'm willing to do that  And I think I'm probably the best person because I have met with him three times, and because I sat in that tent in 2004 and listened to him tell me that  So, in effect, that's why I'm here 
BLITZER: You wrote also in "The New York Times" this -- you wrote, "Colonel Gadhafi's son, Saif, a powerful businessman, a politician, could play a constructive role as a member of the committee to devise a new government structure or constitution "
You know, a lot of people, including the opposition, the rebels, as they're called, they think Saif Al-Islam Gadhafi is just as much a killer or thug as his father is, and they say they have no interest in dealing with him either 
What do you say to that criticism?
WELDON: Well, what I said, I'm not endorsing anything anyone for any office here  What I am hoping for is what the president wants, which is a free and fair election to take place, hopefully sooner rather than later 
But having been involved with Libya for seven years, I was a witness to the work that Saif did in the Lockerbie case, the La Bella nightclub bombing  I personally witnessed through the Gadhafi Foundation the work that Saif did to free up the Bulgarian nurses who were sentenced to death twice, along with a Palestinian doctor 
I have seen the work that Saif and Dr  Salani (ph) at the foundation have done in dealing with chemical weapons destruction and with the elimination of landmines and humanitarian efforts worldwide  I have been out to (INAUDIBLE), the chemical weapons plant, and I have actually seen visibly how they have removed the chemical weapons production materials  He was behind all of that 
Believe me, Wolf, I'm not happy with some of the statements and the actions that he's made over the past month, and he knows I'm not happy  But I think in a fair election, up until now, he should be given the opportunity to seek office where he can run against other candidates, perhaps, for the presidency  And so I would at this time think that he should be allowed that opportunity 
That's not to say I condone anything that he said or his actions  He will have to be accountable for those on his own 
BLITZER: Because you make him sound like he's a decent guy when so many people think he is a killer, a murderer, especially given the statements that he recently made, that if he goes into Benghazi, if he finds these rebels, he will go and kill them all  You make it sound like he's a decent guy 
WELDON: Well, I -- you know, I haven't been with him on a continual basis  I have met with him a number of times, both in the U S  and here, under some very stressful situations, especially when it came to resolving the Lockerbie case and the La Bella nightclub  And despite what Sarkozy said about resolving the issues of the Bulgarian nurses when they were sentenced to death twice, it was Saif who played a very critical role against some very powerful forces in this country that wanted to kill those people 
You know, I don't know of any incidences where I, first hand, have seen evidence of him committing human rights violations, and if he did, he has to be held accountable like everyone else  And I have said that publicly and I will say that privately 
So my judgment is just based upon my experience with him, the fact that he is a knowledgeable person, he understands the need to interact and interface with the West  I think he could be a viable candidate  But ultimately, my opinion is hopefully going to be the opinion of the Libyan people 
BLITZER: Because you probably have seen all of the articles, the reports over the past month, month and a half, of mass murder, of killings, not only by Saif Al-Islam, but some of his brothers that have gone on, the atrocities that have been so widely reported  I hear what you're saying about his role over the recent years when the Bush administration, and later the Obama administration, was trying to improve relations with Libya, but over the past several weeks, based on all of the international reporting we have seen, it's been a brutal record that he has accomplished 
WELDON: Well, again, I don't have firsthand evidence of that  I just got here two days ago  And I fully support an international tribunal to look at human rights violations on everyone in this country  That's necessary  And if they find evidence that he has been involved in that, then he should suffer the consequences of his actions 
(END VIDEOTAPE) BLITZER: In our next hour, part two of the interview with former congressman Curt Weldon  There have been some questions raised about his motive  Is he in all of this for the money? You're going to find out his answer to that and more  Stand by 
Also, Washington, D C 's congressional delegate is telling colleagues -- and I'm quoting her now -- "Go to hell " She is joining us live in THE SITUATION ROOM to tell us why 
Plus, no budget deal, no food -- the extreme tens of thousands of people are going to as a government shutdown looms 
BLITZER: Let's get back to the outrage boiling over on Capitol Hill, only hours before a potential government shutdown 
Joining us now, the Democratic delegate representing the city of Washington, D C , Eleanor Holmes Norton 
ELEANOR HOLMES NORTON (D), D C  DELEGATE: Of course, Wolf 
BLITZER: I think it's fair to say that Washington, D C , a city of a population of about 600,000 people, the only major metropolitan -- the only major city in the United States that's going to foal the direct impact of a federal government shutdown so dramatically, so powerfully, because it is a federal district 
Give me an example of what's going to happen if there's a government shutdown 
NORTON: Absolutely, although your viewers will be shocked by what they are about to hear 
They know a little bit about taxation without representation -- we pay our taxes, then we have full representation in the House and the Senate  But I bet they didn't know that our local budget, without a dime of federal money in it -- and we support ourselves almost entirely -- has to be sent to the masters in the Congress to sign off on it before we can spend our own local money 
Well, listen to this, Wolf  We passed our budget in -- last spring  The appropriators signed off on it last summer 
So, why are we in a federal budget fight over their money when it is our money I am talking about? I have put forward amendments that said the district can spend its own local funds 
BLITZER: What's going to happen in the District of Columbia Saturday, Sunday, Monday, if there is a government shutdown? Give me an example or two 
NORTON: I will give you some dramatic ones  How about the shutdown of the D C  government itself? Because since the final gavel hasn't fallen on all the federal appropriations, then the district government has now prepared to shut down on Saturday morning just because the federal government is shutting down 
We are at the height of the tourist season, the Cherry Blossom Festival  That has been severely curtailed because of the federal shutdown  That's going to -- three million people come here just in one month for the cherry blossoms  Our mayor has had to put out a list of agencies that will be open and a list of agencies that won't be open 
BLITZER: Trash collection -- will there be any trash collection in the District of Columbia?
NORTON: No trash collection, and some residents have started up a Facebook page that says if they close down the District of Columbia, we're carrying our trash to Speaker Boehner's House 
BLITZER: You don't support that do you?
NORTON: I do not 
NORTON: And let me just say right here, I do not  But let me tell you, I am only expressing a little of the rage that the taxpaying residents of the District of Columbia are feeling 
BLITZER: But let me ask you this, Congresswoman, because the Democrats were in control, they had a large majority in the House all of last year; in the Senate, a significant majority  They failed to pass a budget  Don't the Democrats deserve a lot of the blame for this current impasse?
NORTON: Absolutely not, because the Democrats would never have held our budget up here 
LISA BLOOM, CNN LEGAL ANALYST: Why didn't they pass the budget?
NORTON: Well, that doesn't have anything to do with us  This is our local money 
All it would take is -- the Democrats in the Senate are ready to agree  The president is ready to sign an amendment --
BLITZER: But they could have done this any time last year 
NORTON: Wait a minute, Wolf  Wait a minute -- an amendment that said while we're fighting it out on the federal budget, we will let the district spend its own local funds 
So that's all I'm asking  I'm not in this fight, so don't ask me why the Democrats didn't pass the Democratic budget 
I passed -- we passed our budget  Our budget is balanced  The only issue before the Senate and the House is, can we spend our local money? It doesn't have anything to do with their budget 
They can go on from now until Timbuktu  Let us spend our money and don't close down our city because the federal government can't get its act together 
BLITZER: I'm with you there  This is an outrage, the fact that there is -- if there is going to be shutdown  I'm still hoping there won't be a shutdown, but it's --
NORTON: I think there may not be 
BLITZER: -- ridiculous when you think about it, when you think about how close they are  It would be a horrible, horrible tragedy, because 800,000 people directly are going to start losing their paychecks  And the District of Columbia, which is, as you point out correctly, taxation without representation, is going to suffer a great deal more than any other city in the United States 
Good luck, Congresswoman  Thanks very much 
NORTON: Thank you, Wolf 
BLITZER: I feel your pain 
Concerns within military families over a government shutdown  Also, why they are downright scared they won't be able to put food on the table 
And tens of thousands of people on a hunger strike, including some members of Congress  We'll explain why 
CAFFERTY: The question this hour is: Do you believe you're being told the truth about the nuclear accident in January?
Fred writes, "You want the truth? You can't handle the truth "
"Just how should a government balance our right to know the truth with the perceived need to not create a panic and thus a larger problem? Can you really evacuate a million people? To where? Yes, without the truth, how can anyone try to act reasonably?"
"In the end, we do have a right to know the truth  Honesty is the best policy "
Paul in Ohio writes, "Jack, I believe they're telling what they think they know with certainty  It is most certain that they don't know everything "
Jeremy in California, "So I'm confused  Is the current California radiation level 'harmless to human health,' 'not immediately harmful to human health,' not permanently harmful to people outside the region,' or no more than an apples-to-oranges transcontinental flight?"
Craig writes, "Perspective  In Japan, they have had yet another earthquake and have lived in fear and chaos for over a month  And yet, their government hasn't shut down  Nuclear disaster, natural disaster, absolute destruction hasn't kept their elected officials from doing their duty to the people 
"Yet, in America, we get Harry Reid, John Boehner and a White House who are more concerned with the 2012 election campaign  It's times like these when we see just how far off the mark we really are "
Louis writes, "No  Just too many things going wrong  They say that the seafood will be safe  I ask this: Do fish migrate or do they set up housekeeping in one spot and then stay there? And if so, why don't I catch fish in the same place every day?"
And Jim in Colorado, "The nuclear industry telling the truth? The unicorn, garden gnome and I were talking this over just the other day, and we all agreed it could happen  Why not?"
If you want to read more about the unicorn and the garden gnome, go to CNN com/CaffertyFile 
BLITZER: We will, for sure, Jack  Thank you  See you in a few moments 
Several sticking points in the ongoing budget negotiations, but will the government shutdown come down to money or social issues?
Plus, Donald Trump, he's making allegations about President Obama's birthplace  Does Donald Trump have any grounds for any of that? We're digging deeper for answers 
BLITZER: The growing outrage over the budget crisis isn't just about Congress' failure to reach a deal, it's also about some of the cuts that are being proposed 
Lets bring in our own Lisa Sylvester once again  She has the details -- Lisa 
Well, as congressional leaders hammer away on a budget compromise, a group of religious leaders have been fasting and praying to raise awareness of cuts in the budget that they say will harm the poor 
JIM WALLIS, PRESIDENT, SOJOURNERS: Orange juice never tasted so good 
SYLVESTER (voice-over): It's been 10 days since Jim Wallis last had solid food  The president of Sojourners, a Christian group that advocates for the underprivileged, is leading the charge among faith groups on a hunger fast to protest proposed cuts in the federal budget for the poor 
WALLIS: We're saying a budget is a moral document  And whether at your kitchen table, as a family, or a church or a nation, you make choices  What's important, what's not?
SYLVESTER: Wallis said in the last 10 days, more than 30,000 people around the country have joined in the fast in their own way  He says they have become a bit like God's lobbyists for the poor, putting a theological and moral spin on the cuts  Wallis said he is all for deficit reduction but --
WALLIS: I don't think doing this at the expense of the poorest people is a good choice, or hurting those who are already hurting the most is moral or even is smart 
SYLVESTER: Fiscal conservatives have suggested cuts in food stamps, foreign aid, and preschool programs for low-income families, that private groups can and should provide for the needy  But David Beckman of Bread for the World, who used to work at the World Bank, says the private sector can't fill the gap 
DAVID BECKMAN, PRESIDENT, BREAD FOR THE WORLD: All the private charitable feeding in the country amounts to about six percent of the food that poor people get from the national programs  So if you slash food stamps, as the House Republicans are proposing to do, there is no way that churches and charities and charitable people can make up for that 
SYLVESTER: Tony Hall was a member of Congress for years  As part of the fast, he is urging his former colleagues to reconsider cuts 
TONY HALL, ALLIANCE TO END HUNGER: When you make decisions about people's lives, be careful  You don't cut the poorest of the poor, because they didn't get you here  They didn't cause this mess 
SYLVESTER: On Wednesday, members of Congress began signing up for the fast 
REP  BARBARA LEE (D), CALIFORNIA: Several members of Congress today will be joining you in this fast 
SYLVESTER: Now, Sheila Jackson Lee, Keith Ellison and Jim McGovern are among 28 congressional Democrats who have signed on so far to join the hunger fast, and they will be doing a relay, with each taking one day to fast and then passing on the fast to their colleagues 
Wallis and Hall, they're doing it a little differently  They're fasting all the way through Easter Sunday  But they say for them, this fight for the poor is larger than just the specific budget battle -- Wolf 
BLITZER: These are committed, committed people to try to help 
We're going back to Libya in just a few moments  Rebel forces, furious with NATO right now, the R-rated message they are sending through our own Ben Wedeman 
Context 2: Paper Info

Title: Compressed quantum error mitigation
Publish Date: 10 May 2023
Author List: Maurits Tepaske (from Physikalisches Institut, Universität Bonn), David Luitz (from Physikalisches Institut, Universität Bonn)

Figure

FIG 3 The out-of-time-ordered correlator C otoc i=L/2,j (t) as a function of the operator position j and time t, for the infinite temperature initial state, for a denoised second-order Trotter supercircuit with Trotter depth Mtrot = 32 and denoiser depth M = 2 We consider evolution times t = 0 5, 1,    , 5, for the periodic L = 14 Heisenberg chain that is affected by two-qubit depolarizing noise with p = 0 01 
FIG  4  The complex eigenvalues λ of the noisy second-order Trotter supercircuit with Mtrot = 16 at time t = 1 (left), the corresponding optimized denoiser with M = 4 (center), and the denoised Trotter supercircuit (right) The Trotter circuit is for a L = 6 Heisenberg model with PBC, and all twoqubit channels are affected by depolarizing noise with p = 0 0046 The unit circle, on which unitary eigenvalues must lie, is shown in black, and the noiseless eigenvalues are shown as blue bars It is evident that the denoiser recovers all the noiseless eigenvalues from the noisy circuit 
FIG  2  The complex eigenvalues λ of the noisy second-order Trotter supercircuit with Mtrot = 16 at time t = 1 (left), the corresponding optimized denoiser with M = 4 (center), and the denoised Trotter supercircuit (right) The Trotter circuit is for a L = 6 Heisenberg model with PBC, and all twoqubit channels are affected by depolarizing noise with p = 0 036 The unit circle, on which unitary eigenvalues must lie, is shown in black, and the noiseless eigenvalues are shown as blue bars It is clear that the denoiser recovers with high accuracy the noiseless eigenvalues from the noisy circuit 
FIG  3  The half-chain channel entanglement entropy S at different two-qubit depolarizing noise strengths p, for a secondorder Trotter supercircuit with Mtrot = 16 and t = 2, for a M = 4 denoiser The Trotter circuit is for a Heisenberg model with PBC of size L = 6 The different curves correspond to the different supercircuits, i e  the noisy supercircuit, the denoiser, the corresponding denoised supercircuit, and the noiseless variant 
FIG  4  The out-of-time-ordered correlator C otoc i=L/2,j (t) as a function of the operator position j and stacked time t, for the infinite temperature initial state, for a denoised secondorder Trotter supercircuit with Trotter depth Mtrot = 32 and denoiser depth M = 2 It is optimized at t = 2 and stacked up to ten times The calculations are for the periodic L = 14 Heisenberg chain that is affected by two-qubit depolarization with p = 0 01 The denoiser is affected by the same noise 
FIG 6 The distribution of the ZZ angle α of M = 2 denoisers (top panels) and M = 8 denoisers (bottom panels), with the lightest color corresponding to the denoiser for the Trotter supercircuit with t = 0 5, and the darkest color with t = 5 As usual, we consider the Heisenberg model on a periodic chain, and second-order Trotter supercircuits with depths Mtrot = 8, 16, 32, 64, which together with the denoiser is affected by a two-qubit depolarizing noise with p = 0 01 The panels are arranged as Mtrot = 8, 16, 32, 64 for top left, top right, bottom left, bottom right, respectively 
FIG  7  The sampling overhead γ of the optimized denoisers from Fig  2 of the main text, with denoiser depths M = 1, 2, 4, 6, 8 and Trotter depths Mtrot = 8, 16, 32, 64 at times t = 0 5, 1,    , 5, for the Heisenberg model on a chain with PBC affected by two-qubit depolarizing noise with p = 0 01 The panels are arranged as Mtrot = 8, 16, 32, 64 for top left, top right, bottom left, bottom right, respectively 
FIG 8 The domain wall magnetization Z dw after evolving a periodic density wall |dw |dw * with the denoised second-order Trotter supercircuits D C from Fig 2of the main text These supercircuits have various Trotter depths Mtrot = 8, 16, 32, 64, denoiser depths M = 1, 2, 4, 6, 8, and evolution times t = 0 5, 1,    , 5, for the periodic L = 14 Heisenberg chain that is affected by two-qubit depolarizing noise of strength p = 0 01 The denoiser is affected by the same noise The non-denoised results are labelled with M = 0 and the noiseless results with p = 0 The panels are arranged as Mtrot = 8, 16, 32, 64 for top left, top right, bottom left, bottom right, respectively We see that the denoiser allows us to recover the noiseless behavior 

abstract

We introduce a quantum error mitigation technique based on probabilistic error cancellation to eliminate errors which have accumulated during the application of a quantum circuit  Our approach is based on applying an optimal "denoiser" after the action of a noisy circuit and can be performed with an arbitrary number of extra gates 
The denoiser is given by an ensemble of circuits distributed with a quasiprobability distribution  For a simple noise model, we show that efficient, local denoisers can be found, and we demonstrate their effectiveness for the digital quantum simulation of the time evolution of simple spin chains  Introduction 
-Quantum information processing has been theoretically shown to hold great promises, and quantum algorithms were developed which can in principle achieve an exponential speed-up over their classical counterparts, both for general purpose computing and quantum simulation   However, present day quantum computing prototypes still suffer from significant noise processes which hinder the execution of many potentially groundbreaking quantum algorithms  
Nontrivial quantum algorithms typically require large sequences of quantum gates, each of which introduces dissipation and hence an overall loss of coherence, eventually rendering the results useless  Until quantum error correction becomes practical, quantum error mitigation seems to be more feasible to increase the accuracy of expectation values 
Here the goal is to induce the (partial) cancellation of errors that stem from noisy quantum gates by extending the circuit corresponding to the desired algorithm with an ensemble of gates , sampled from a quasiprobability distribution  The traditional way to accomplish this is with the gatewise method from , where noise is mitigated by inverting the noise channel of each gate separately, i e  the cancellation of errors is performed for each gate on its own 
Here the local noise channel is approximated in a way such that it can be easily inverted analytically, e g  using Pauli twirling   Gates are then sampled from the inverted noise channel by interpreting it as a quasiprobability distribution  Because in this gate-wise approach every noisy gate has to be modified separately, the sign problem is exponentially large in the number of gates, limiting the practicality of the mitigation 
The success of the gate-wise approach resulted in a large body of work concerning these methods , including extensions for simultaneous mitigation of multiple gates by Pauli-twirling entire layers or variationally constructing a mitigating matrix product operator   In principle, errors during the execution of a circuit can propagate and accumulate 
These propagated errors * david luitz@uni-bonn de ≈ C

C

FIG  1  An example of the quantum error mitigation procedure used in this work for the time evolution of the wave function of a spin chain  The ideal second-order Trotter supercircuit C of depth Mtrot = 1 (light blue) is approximated by applying a denoiser D of depth M = 1 (red) to the noisy Trotter supercircuit C (dark blue) 
Because the denoiser is applied after fully executing the noisy Trotter supercircuit, it represents an approximate inverse of the global noise channel with a precision tunable by the depth of the denoiser  can potentially blow up and lead to large errors for the circuit as a whole   Here we introduce a mitigation technique that takes into account the propagation of errors, can be performed with a tunable number of extra gates, and works for non-Clifford local noise channels since the inversion of the accumulated global noise channel is implicit 
We first execute the targeted noisy circuit completely, letting the noise propagate and accumulate, and only afterwards we apply an extra random circuit sampled from a quasiprobability distribution  We call the corresponding ensemble of random circuits a denoiser, and we construct it such that upon averaging the accumulated errors cancel 
Essentially, the denoiser inverts a global noise channel  Since we will construct it as a local brickwall circuit, following the classical preprocessing approach from , we call this compressed quantum error mitigation  Method  -Due to the inevitable coupling of a quantum processor to its environment, every qubit operation is affected by noise 
Therefore, the simplest technique to minimize the impact of the resulting noise is to minimize the number of operations when performing a quantum algorithm  In we showed that many-body time evolution operators can be efficiently compressed into brick-wall circuits with high fidelity per gate  In this Letter, we consider the noise explicitly by treating quantum operations as (generally non-unitary) quantum channels, corresponding to completely positive and trace preserving (CPTP) maps  
For example, instead of a noiseless two-qubit gate G, which acts on a quantum state |ρ in superoperator form as G|ρ = G⊗G * |ρ , we get the noisy channel G = N G, where the noise channel N implements the two-qubit noise   These channels are used to construct a "supercircuit" C = N G i=1 Gi , consisting of N G channels, which is affected by multi-qubit accumulated noise 
This supercircuit encodes an ensemble of circuits   For simplicity, we assume that the noisy channels Gi in each half brickwall layer are lattice inversion and translation invariant, such that we can construct a denoiser with these properties, limiting the number of variational parameters  The purpose of quantum error mitigation is to modify the ensemble of circuits described by C in a way that we can use it to obtain the noiseless expectation values 
In superoperator language, we do this by following the supercircuit C with a denoiser supercircuit D, such that D C is as close to the noiseless supercircuit C = C ⊗ C * as possible  Here C is the target unitary circuit  Because the noise channel N is non-unitary, hence making the supercircuit C non-unitary, we need to use a non-unitary denoiser to retrieve the unitary C 
We illustrate the mitigation procedure in Fig  , where a denoiser with one layer is used to mitigate errors for a second-order Trotter supercircuit with one layer  This circuit architecture is commonly used to simulate the time evolution of a quantum many-body system, until some time t, with controllable precision , and we will use it to benchmark the denoiser 
In practice, we cannot directly implement a supercircuit, and so we have to utilize its interpretation as an ensemble of circuits  Essentially, after executing a shot of the noisy circuit we sample the denoiser and apply it  The goal is to construct the denoiser in a way that averaging over many of its samples cancels the accumulated errors and gives us a good approximation of the noiseless expectation values 
It should be noted that our approach requires more gate applications on the quantum processor than with the gate-wise scheme, since there each sample from the mitigation quasiprobability distribution can be absorbed into the original circuit, whereas our approach increases the circuit depth  We take this into account by imposing the same noise on the denoiser 
Furthermore, within our scheme, the dimensionality of the quasiprobabilistic mitigating ensemble can be controlled, in contrast to the gate-wise approach where it is equal to the gate count  To facilitate the stochastic interpretation we parameterize each two-qubit denoiser channel G i as a sum of CPTP maps, such that we can sample the terms in this sum and execute the sampled gate on the quantum processor 
Concretely, we use a trace preserv-ing sum of a unitary and a non-unitary channel  For the unitary part we take a two-qubit unitary channel U( φ i ) = U ( φ i ) ⊗ U * ( φ i ), with U ( φ i ) a two-qubit unitary gate parameterized by φ i   For this we take the two-qubit ZZ rotation exp(−iα(σ z ⊗ σ z )) with angle α, which can be obtained from native gates on current hardware , and dress it with four general one-qubit unitaries, only two of which are independent if we want a circuit that is space inversion symmetric around every bond 
The resulting gate has 7 real parameters φ i   For the non-unitary part, which is essential because D has to cancel the non-unitary accumulated noise to obtain the noiseless unitary circuit, we use a general onequbit measurement followed by conditional preparation channel M( , with V a general one-qubit unitary and each κ i a 3-dimensional vector, resulting in a real 9-dimensional ζ i  
This yields the two-qubit correlated measurement M( With these parts we construct the parameterization with coefficients η i ∈ R that satisfy η 0 + η 1 = 1 because G i is trace preserving  Note that here the tensor product symbol corresponds to combining two one-qubit channels to make a two-qubit channel, whereas in most of the paper it is used to link the column and row indices of a density matrix 
We construct the denoiser from the noisy channels Gi = N G i   With this parameterization one denoiser channel has 17 independent real parameters, such that a denoiser of depth M , i e  consisting of M brickwall layers, has 34M real parameters (we use one unique channel per half brickwall layer)  For reference, a general channel has 544M parameters 
To determine the mitigated expectation values we use the full expression where |ρ 0 is the initial state and |1 is the vectorized identity operator on the full Hilbert space  To evaluate this on a quantum processor, we use the stochastic interpretation of (1) to resample   In particular, from each channel (1) we get a unitary with probability p 0 = |η 0 |/γ and a measurement followed by conditional preparation with probability p 1 = |η 1 |/γ 
Here γ = |η 0 | + |η 1 | is the sampling overhead, which characterizes the magnitude of the sign problem from negative η i   For quasiprobability distributions, i e  with γ > 1, every denoiser sample has an extra sign sgn(η) = N G g=1 sgn(η g ), 2  The normalized distance between the denoised Trotter supercircuit D C and the noiseless Trotter supercircuit C (top panels), at evolution times t = 0 5, 1,    , 5, and the twopoint z-spin correlator C zz i=L/2,j=L/2 (t) of a spin on the middle site at times 0 and t (bottom panels), for the infinite temperature initial state 
We consider denoisers with depths M = 1, 2, 4, 6, 8 and second-order Trotter circuits with depths Mtrot = 16, 32, 64  In the top panels we use a Heisenberg chain with L = 8, and in the bottom panels with L = 14, both with periodic boundary conditions  All gates are affected by two-qubit depolarizing noise with p = 0 01
Context 3: Football Club Urartu (, translated Futbolayin Akumb Urartu), commonly known as Urartu, is an Armenian professional football team based in the capital Yerevan that currently plays in the Armenian Premier League  The club won the Armenian Cup three times, in 1992, 2007 and 2016  In 2013–2014, they won the Armenian Premier League for the first time in their history 

In early 2016, the Russia-based Armenian businessman Dzhevan Cheloyants became a co-owner of the club after purchasing the major part of the club shares  The club was known as FC Banants until 1 August 2019, when it was officially renamed FC Urartu 

History

Kotayk
Urartu FC were founded as FC Banants by Sarkis Israelyan on 21 January 1992 in the village of Kotayk, representing the Kotayk Province  He named the club after his native village of Banants (currently known as Bayan)  Between 1992 and 1995, the club was commonly referred to as Banants Kotayk  During the 1992 season, the club won the first Armenian Cup  At the end of the 1995 transitional season, Banants suffered a financial crisis  The club owners decided that it was better to merge the club with FC Kotayk of Abovyan, rather than disband it  In 2001, Banants demerged from FC Kotayk, and was moved from Abovyan to the capital Yerevan 

Yerevan

FC Banants was relocated to Yerevan in 2001



ground_truth: The sticking point in the political showdown over the budget is how much spending to cut.

prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: Can the denoiser be applied to circuits with non-Clifford noise?

Read the following text and answer briefly.

Context 2: 
The non-denoised results are labelled with M = 0, and the noiseless values with p = 0  where sgn(η g ) is the sign of the sampled coefficient of the gth channel  γ = 1 means that all signs are positive  Observables Ô p=0 for the noiseless circuit are then approximated by resampling the observables from the denoiser ensemble
where γ = N G g=1 γ g is the overall sampling overhead, with γ g the overhead of the gth gate  Clearly, a large γ implies a large variance of Ô p=0 for a given number of samples, with accurate estimation requiring the cancellation of large signed terms  The number of samples required to resolve this cancellation of signs is bounded by Hoeffding's inequality, which states that a sufficient number of samples to estimate Ô p=0 with error δ at probability 1 − ω is bounded by (2γ 2 /δ 2 ) ln(2/ω)  
Since γ scales exponentially in γ g , it is clear that a denoiser with large M and γ 1 will require many samples  We observed that decompositions with γ > 1 are crucial for an accurate denoiser  Restricting to γ = 1 leads to large infidelity and no improvement upon increasing the number of terms in or the depth M of the denoiser 
Simply put, probabilistic error cancellation of gate noise introduces a sign problem and it is crucial to find optimal parameterizations (1) which minimize γ to make the approach scalable  This issue arises in all high performance error mitigation schemes , because the inverse of a physical noise channel is unphysical and cannot be represented as a positive sum over CPTP maps 
This is clearly visible in the spectra of the denoiser, which lies outside the unit circle (cf  Fig  )  This makes the tunability of the number of gates in each denoiser sample a crucial ingredient, which allows control over the sign problem, because we can freely choose the η i in   For the parametrization (1) of denoiser channels, we try to find a set of parameters for error mitigation by minimizing the normalized Frobenius distance between the noiseless and denoised supercircuits
which bounds the distance of output density matrices and becomes zero for perfect denoising  We carry out the minimization of on a classical processor, using gradient descent with the differential programming algorithm from   Instead of explicitly calculating the accumulated global noise channel and subsequently inverting it, we approximate the noiseless supercircuit C with the denoised supercircuit D C, effectively yielding a circuit representation D of the inverse noise channel 
Results  -To benchmark the denoiser we apply it to the second-order Trotter circuits of the spin-1/2 Heisenberg chain with periodic boundary conditions (PBC) where is the Pauli algebra acting on the local Hilbert space of site i  A second-order Trotter circuit for evolution time t with depth M trot consists of M trot − 1 half brickwall layers with time step t/M trot and two layers with half time step  
We consider circuits that are affected by uniform depolarizing noise with probability p for simplicity, but our approach can be used for any non-Clifford noise  The two-qubit noise channel is which acts on neighboring qubits i and i + 1 and is applied to each Trotter and denoiser gate, and p = 0 01 unless stated otherwise 
We study circuits with depths M trot = 16, 32, 64 for evolution times t = 0 5, 1,    , 5, and denoisers D with depths M = 1, 2, 4, 6, 8  In the top panels of Fig  we show (4) for a chain of size L = 8 as a function of time t  Here it can be seen that even for M trot = 32 a denoiser with M = 1 already improves by roughly an order of magnitude at all considered t 
Depending on M trot and t, further increasing M lowers , with the biggest improvements occurring for high precision Trotter circuits with large depth M trot = 64 and short time t = 0 5, where the Trotter gates are closer to the identity than in the other cases  At the other extreme, for M trot = 16 the improvements are relatively small upon increasing M > 2  In all cases the denoiser works better at early times than at late times, again indicating that it is easier to denoise Trotter gates that are relatively close to the identity 
To probe the accuracy of the denoiser on quantities that do not enter the optimization, as a first test we consider the two-point correlator between spins at different times where we have chosen the infinite temperature initial state, and C(t) is the Trotter supercircuit for time t  In the bottom panels of Fig  we show C zz i=L/2,j=L/2 (t) for the supercircuits from the upper panels, now for a L = 14 chain 
Here we see that at M trot = 16 we can retrieve the noiseless values already with M = 1, but that increasing M trot makes this more difficult  At M trot = 64 we see larger deviations, and improvement upon increasing M is less stable, but nonetheless we are able to mitigate errors to a large extent  As a further test, we compute the out-of-time-ordered correlator (OTOC) ]
In Fig  we show the results for i = L/2, for a Trotter circuit with depth M trot = 32 and a denoiser with depth M = 2  Here we see that a denoiser with M M trot is able to recover the light-cone of correlations, which are otherwise buried by the noise  In the Supplementary Material we consider how the denoiser performs at different noise levels p, and how the denoised supercircuits perform under stacking 
There we also calculate domain wall magnetization dynamics, and show the distribution of the optimized denoiser parameters and the sampling overhead associated to the denoiser as a whole  In Fig  we show the eigenvalues of the noisy supercircuits for a noisy second-order Trotter supercircuit with M trot = 16 at t = 1 (left), the corresponding optimized denoiser with M = 4 (center), and the denoised supercircuit (right) 
The eigenvalues λ of a unitary supercircuit lie on the unit circle, and in the presence of dissipation they are pushed to the center  We see that the spectrum of the denoiser lies outside the unit circle, making it an unphysical channel which cures the effect of the noise on the circuit, such that the spectrum of the denoised circuit is pushed back to the unit circle 
The noiseless eigenvalues are shown as blue bars, making it clear that the denoiser is able to recover the noiseless eigenvalues from the noisy circuit  In the Supplementary Material we show the spectra for a p = 0 036 denoiser, where we observe a clustering of eigenvalues reminiscent of Refs    There we also investigate the channel entropy of the various supercircuits  
Conclusion  -We have introduced a probabilistic error cancellation scheme, where a classically determined denoiser mitigates the accumulated noise of a (generally non-Clifford) local noise channel  The required number of mitigation gates, i e  the dimensionality of the corresponding quasiprobability distribution, is tunable and the parameterization of the corresponding channels provides control over the sign problem that is inherent to probabilistic error cancellation 
We have shown that a denoiser with one layer can already significantly mitigate errors for second-order Trotter circuits with up to 64 layers  This effectiveness of low-depth compressed circuits for denoising, in contrast with the noiseless time evolution operator compression from , can be understood from the non-unitarity of the denoiser channels 
In particu-lar, measurements can have non-local effects, since the measurement of a single qubit can reduce some highly entangled state (e g  a GHZ state) to a product state, whereas in unitary circuits the spreading of correlations forms a light-cone  To optimize a denoiser with convenience at L > 8, the optimization can be formulated in terms of matrix product operators or channels , which is convenient because the circuit calculations leading to the normalized distance and its gradient are easily formulated in terms of tensor contractions and singular value decompositions  
This provides one route to a practical denoiser, which is relevant because the targeted noiseless circuit and the accompanying noisy variant in (4) need to be simulated classically, confining the optimization procedure to limited system sizes with an exact treatment or limited entanglement with tensor networks 
Nonetheless, we can use e g  matrix product operators to calculate (4) for some relatively small t, such that the noiseless and denoised supercircuits in (4) have relatively small entanglement, and then stack the final denoised supercircuit on a quantum processor to generate classically intractable states 
Analogously, we can optimize the channels exactly at some classically tractable size and then execute them on a quantum processor with larger size  Both approaches are limited by the light-cone of many-body correlations, as visualized in Fig  , because finite-size effects appear when the light-cone width becomes comparable with system size 
1  The normalized distance (left) and z spin correlator C zz i=L/2,j=L/2 (right), for a second-order Trotter supercircuit of depth Mtrot = 16 for time t = 1, affected by various twoqubit depolarizing errors p  We compare the values obtained with and without a denoiser, i e  M > 0 and M = 0, to the noiseless values (p = 0) 
The denoiser is affected by the same noise as the Trotter circuit  We consider denoisers with depths M = 1, 2, 4, 6, 8, and we use a L = 8 Heisenberg chain with PBC for the normalized distance, while for the correlator we use L = 14  * david luitz@uni-bonn de to observe that even for larger noise strength p, the local observable C zz improves significantly even with denoisers of depth M = 1 
For large noise strengths, we generally see that the optimization of the denoiser becomes difficult, leading to nonmonotonic behavior as a function of p, presumably because we do not find the global optimum of the denoiser  It is interesting to analyze the spectra of the supercircuits considered in this work 
As mentioned in the main text, the spectrum of the ideal, unitary supercircuit C lies on the unit circle  The comparison to this case is therefore instructive  In the main text, we showed an example of the spectra in Fig  for moderate noise strength  Here, we show additional data for stronger noise p = 0 036 in Fig  for a denoiser with M = 4 layers, optimized to mitigate errors for a second-order Trotter supercircuit with M trot = 16 layers at time t = 1 
The eigenvalues λ of the noisy supercircuit C are clustered close to zero, far away from the unit circle (except for λ = 1), showing that the circuit is strongly affected by the noise  To mitigate the impact of the noise, the denoiser consequently has to renormalize the spectrum strongly  If it accurately represents the inverse of the global noise channel, its spectrum has to lie far outside the unit circle, which is the case 
Interestingly, we observe a clustering of eigenvalues which is reminiscent to the spectra found in   By comparison to these works, we suspect that this is due to the local nature of the denoiser, and warrants further investigation  The right panel of Fig  shows the result of the denoiser, pushing the eigenvalues back to the unit circle, nearly with the exact same distribution along the circle as the noiseless eigenvalues (blue bars) 
Due to the strong noise, this is not achieved perfectly, and it is clear that this cannot work in principle if the global noise channel has a zero eigenvalue  The complexity of an operator can be quantified by its operator entanglement entropy   Here we calculate the half-chain channel entanglement entropy S of the noiseless C, noisy C, denoiser D, and denoised D C supercircuits 
We define S as the entanglement entropy of the state that is related to a supercircuit C via the Choi-Jamio lkowski isomorphism, i e  ψ C = χ C /N , where the process matrix χ ab,cd C = C ac,bd is simply a reshaped supercircuit and N ensures normalization  Then we have S = −Tr [ψ C ln ψ C ]  This entropy measure is a particular instance of the "exchange entropy", which characterizes the information exchange between a quantum system and its environment  
In Fig  we plot the various S for a second-order Trotter circuit with M trot = 16 at t = 2, for a denoiser with M = 4, both affected by two-qubit depolarizing noise with p ∈ [10 −3 , 10 −1 ]  The Trotter circuit is for a Heisenberg model with L = 6 and PBC  We see that at large p, the noise destroys entanglement in the noisy supercircuit, and that the denoiser S increases to correct for this, such that the denoised supercircuit recovers the noiseless S 
Here we investigate how denoised supercircuits perform upon repeated application  We optimize the denoiser for a Trotter supercircuit for a fixed evolution time t  Then, to reach later times, we stack the denoised supercircuit n times to approximate the evolution up to time nt: In Fig  we stack a denoised t = 1 supercircuit up to n = 20 times and calculate the correlation function, defined in the main text, for the middle site 
We consider Trotter depths M trot = 8, 16, 32, 64 and denoiser depths M = 1, 2, 4, 6, 8, for a L = 14 Heisenberg chain with p = 0 01 depolarizing two-qubit noise  The noisy results correspond to M = 0 and the noiseless results to p = 0  In Fig  we calculate the OTOC, defined in the main text, with stacked time evolution for a denoised t = 2 supercircuit with M trot = 32 and M = 2, stacked up to ten times 
We see that the stacked supercircuit performs very well, and the additional precision obtained by using deep denoisers (M = 8) pays off for long evolution times, where we see convergence to the exact result (black dashed lines in Fig  ) as a function of M   FIG    The two-point z-spin correlator C zz i=L/2,j=L/2 (t) of a spin on the middle site at times 0 and t, for the infinite temperature initial state, for denoised second-order Trotter supercircuits that are optimized at evolution time t = 1 and then stacked up to twenty times 
We use Trotter depths Mtrot = 8, 16, 32, 64 and denoiser depths M = 1, 2, 4, 6, 8  The calculations were performed for a periodic Heisenberg model with L = 14 and PBC, affected by two-qubit depolarizing noise with strength p = 0 01, which also affects the denoiser  The non-denoised results are labelled with M = 0, and the noiseless results with p = 0 
The panels are arranged as Mtrot = 8, 16, 32, 64 for top left, top right, bottom left, bottom right, respectively  The costliest and most noise-susceptible operation is the two-qubit ZZ rotation with angle α, which is the foundation of the unitary piece in our channel parameterization, defined in the main text 
For completeness, we here present the α angles of the optimized denoisers  The results are shown in Fig  , which contains histograms for the channel count N G versus α  The histograms are stacked, with the lightest color corresponding to the angles of the denoiser at t = 0 5 and the darkest at t = 5  The top four panels are for a denoiser with M = 2 and the bottom four with M = 8 
We consider M trot = 8, 16, 32, 64  We see that in both cases the distribution widens upon increasing M trot , indicating that the unitary channels start deviating more from the identity  Moreover, while the M = 2 denoisers in all cases except M trot = 64 have ZZ contributions close to the identity, this is clearly not the case for M = 8 
For simplicity, we did not focus on obtaining denoisers with the smallest sampling overhead γ, which is required to minimize the sign problem and hence ease the sampling of mitigated quantities  Instead, we let the optimization freely choose the η i in the denoiser parameterization, as defined in the main text 
In Fig  we show the sampling overhead of the denoisers from Fig  of the main text  We see that for M = 1 and M = 2 the sampling overhead is relatively small and uniform across the different t, whereas for M > 2 the optimization sometimes yields a denoiser with large γ and other times with small γ  This could be related to the difference in α distributions from Fig   
The large fluctuations of γ appears to stem from the difficulty in finding optimal deep denoisers, and our optimization procedure likely only finds a local minimum in these cases  Here C(t) is the Trotter supercircuit for time t  In Fig  we show Z dw for the circuits from Fig 
Context 3:  At the beginning of 2003, Banants merged with FC Spartak Yerevan, but was able to limit the name of the new merger to FC Banants  Spartak became Banants's youth academy and later changed the name to Banants-2  Because of the merger, Banants acquired many players from Spartak Yerevan, including Samvel Melkonyan  After the merger, Banants took a more serious approach and have finished highly in the league table ever since  The club managed to lift the Armenian Cup in 2007 
Experience is making way for youth for the 2008 and 2009 seasons  The departures of most of the experienced players have left the club's future to the youth  Along with two Ukrainian players, Ugandan international, Noah Kasule, has been signed 

The club headquarters are located on Jivani Street 2 of the Malatia-Sebastia District, Yerevan 

Domestic

European

Stadium

The construction of the Banants Stadium was launched in 2006 in the Malatia-Sebastia District of Yerevan, with the assistance of the FIFA goal programme  It was officially opened in 2008 with a capacity of 3,600 seats  Further developments were implemented later in 2011, when the playing pitch was modernized and the capacity of the stadium was increased up to 4,860 seats (2,760 at the northern stand, 1,500 at the southern stand and 600 at the western stand) 

Training centre/academy
Banants Training Centre is the club's academy base located in the Malatia-Sebastia District of Yerevan



ground_truth: Yes, the denoiser works for non-Clifford local noise channels.

prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: When did the club win the Armenian Premier League for the first time?

Read the following text and answer briefly.

Context 3:  In addition to the main stadium, the centre houses 3 full-size training pitches, mini football pitches as well as an indoor facility  The current technical director of the academy is the former Russian footballer Ilshat Faizulin 

Fans
The most active group of fans is the South West Ultras fan club, mainly composed of residents from several neighbourhoods within the Malatia-Sebastia District of Yerevan, since the club is a de facto representer of the district  Members of the fan club benefit from events organized by the club and many facilities of the Banants training centre, such as the mini football pitch, the club store and other entertainments 

Achievements
 Armenian Premier League
 Winner (1): 2013–14 
 Runner-up (5): 2003, 2006, 2007, 2010, 2018 

 Armenian Cup
 Winner (3): 1992, 2007, 2016 
 Runner-up (6): 2003, 2004, 2008, 2009, 2010, 2021–22

 Armenian Supercup
 Winner (1): 2014 
 Runner-up (5): 2004, 2007, 2009, 2010, 2016 

Current squad

Out on loan

Personnel

Technical staff

Management

Urartu-2

FC Banants' reserve squad play as FC Banants-2 in the Armenian First League  They play their home games at the training field with artificial turf of the Urartu Training Centre 

Managerial history
 Varuzhan Sukiasyan (1992–94)
 Poghos Galstyan (July 1, 1996 – June 30, 1998)
 Oganes Zanazanyan (2001–05)
 Ashot Barseghyan (2005–06)
 Nikolay Kiselyov (2006–07)
 Jan Poštulka (2007)
 Nikolay Kostov (July 1, 2007 – April 8, 2008)
 Nedelcho Matushev (April 8, 2008 – June 30, 2008)
 Kim Splidsboel (2008)
 Armen Gyulbudaghyants (Jan 1, 2009 – Dec 1, 2009)
 Ashot Barseghyan (interim) (2009)
 Stevica Kuzmanovski (Jan 1, 2010 – Dec 31, 2010)
 Rafael Nazaryan (Jan 1, 2011 – Jan 15, 2012)
 Volodymyr Pyatenko (Jan 17, 2013 – June 30, 2013)
 Zsolt Hornyák (July 1, 2013 – May 30, 2015)
 Aram Voskanyan (July 1, 2015 – Oct 11, 2015)
 Tito Ramallo (Oct 12, 2015 – Oct 3, 2016)
 Artur Voskanyan (Oct 3, 2016 – Aug 11, 2018)
 Ilshat Faizulin (Aug 12, 2018 –Nov 24, 2019)
 Aleksandr Grigoryan (Nov 25, 2019 –Mar 10, 2021)
 Robert Arzumanyan (10 March 2021–24 June 2022)
 Dmitri Gunko (27 June 2022–)

References

External links
 Official website 
 Banants at Weltfussball de  

 
Urartu
Urartu
Urartu
Urartu



ground_truth: In the 2013-2014 season.