text:
3 dead in helicopter crash in New York, National Guard says
Three National Guard members on a routine training flight have been killed in a helicopter crash in a western New York town.
Podcast explores what community means through diverse voices
Columbus Peyton Furtado - January 20, 2021 6:14 PM 0
A local podcast is telling a community's story from perspectives who don't often get a voice.
Home Local Wilmington ranked top 15 best US cities for beer drinkers
Wilmington ranked top 15 best US cities for beer drinkers
WILMINGTON, NC (WWAY) — Over the last few years, the beer industry has been overflowing in the Wilmington area. A new report released shows the Port City may also need to be named Pint City for beer lovers.
According to SmartAssest.com, Wilmington has ranked in the top 15 best cities in the country for beer drinkers.
The report shows Wilmington is the home of 15 breweries with the average price of a pint costing customers $4.00.
One of those breweries is Wilmington Brewing Company. Since opening in 2014, they have expanded from a small homebrew shop to a 11,800 sqft facility on S. Kerr Aveune.
"Small home brew shop, we were doing great, and John's like we gotta keep going, keep moving," Wilmington Brewing Company Owner Michelle Savard said. "So then we went to this building which is 12,000 square feet, added the brewery, then we expanded the Brewhouse."
Now, they are growing even more. Wilmington City Council recently approved the business to grow by about 5,000 sqft. They are adding an event space at their S. Kerr Aveune location.
"We're just trying to keep up with demand, so we get bigger tanks, and bigger tanks to be able to brew enough beer to send out into the market," Savard said.
Edward Teach Brewery in downtown Wilmington is expanding, too. Located in the Brooklyn Arts District in an old fire engine house, the business open its door in December 2017.
"We're currently in a 10,000 sqft. space, and we're adding on an additional 30,000 sqft., space," Sholar said.
In the SmartAsset study, they analyzed data on metrics like the number of breweries, concentration of bars and price of a domestic pint to find the best cities for beer drinkers nationwide. Out of the 350 total cities we analyzed, Wilmington and Asheville cracked the top 15.
Asheville leads the way, ranking as the fourth-best city for beer drinkers nationwide. Wilmington came in as 14th overall.
Both cities rank better than average in four of the five metrics we considered: the total number of breweries, the density of breweries, the density of bars and the average price for a pint of domestic draught beer. In particular, Asheville and Wilmington stand out for their top-10 figures for the number of breweries per 100,000 residents.
According to Smart Assest, the United States beer industry sells more than $119.3 billion in beer and malt-based beverages to consumers each year and 26.5 gallons of beer and cider were consumed per person (21+) in 2018.
Edward Teach Brewing
Wilmington Brewing Company
Wilmington City Council


Driving with my family recently after a long trip away, we pondered what we would do for dinner. We spent the last several days eating restaurant meals and were craving a home cooked dinner. The problem was we were still hours away from home and too tired to stop and grocery shop. My wife suggested using online delivery from our local grocery store. I was skeptical. Would the fresh food sit out on our porch spoiling in the unseasonable Houston heat? She assured me that our retailer promised we could specify the delivery time. And so we placed the order while driving home.
An hour down the road we received a text from Kate, our personal shopper, who told us she was starting our order and asked for permission to text or call with any questions. This communication was followed with a text photo of apples to ensure they met our standards. The order delivered right after we arrived home. We were satisfied with the service and now about half of our grocery shopping has shifted online.
We are among the 52 million consumers who currently shop online and there will be many more of us in the coming months based on our recent The Virtual Grocery Store study. Like us, the majority of online grocery shoppers is satisfied with the experience and become repeat users.
Happy customers, the never-ending search for convenience, more delivery options, shipping deals, like Amazon Prime, the infinite assortment, and more aggressive online strategies being launched by major grocery retailers will drive the quick adoption of virtual grocery shopping. The tipping point will be here before you know it.
Watch, listen, and learn. Food and beverage manufacturers should monitor to ensure their products are part of the assortment where it matters. Grocery retailers should start developing e-commerce programs or to expand current services. Now is the time to act, while shoppers, like my family, are still experimenting and before virtual grocery shopping becomes an everyday reality.
Will Legal Marijuana Create New Food Opportunities?
A look at whether or not there are changes in snack food consumption in areas where marijuana has been legalized.
In today's world of social media and blogging, consumers are seeking their echo chambers of health the same way they use them for lifestyles and politics. They're finding niche or individualized plans that meet their own specific goals, as opposed to plans that work for the average person.


Easter Monday 10am WOD with Coach Kierran.
We have various CrossFit memberships and pricing options based on the number of sessions you require per month.
We also have gym only memberships. The Core Performance facility spans over 10,000 square ft, with large areas for high intensity training as well as a large free weights section and many machines. Allowing you to tailor and vary your workouts as and how you please.


Trapp Town Grocery is located at the address 5680 Highway 243 in Phil Campbell, Alabama 35581. They can be contacted via phone at (205) 993-4263 for pricing, hours and directions.
For maps and directions to Trapp Town Grocery view the map to the right. For reviews of Trapp Town Grocery see below.


I CAN plan to deal with stress.
The deviled eggs are in the details!
I CAN have a yummy alternative to sweets to redirect stress eating.
so for next year, I will make plenty more.
Hard boil eggs, half the eggs and remove yolks to small bowl.
salt, black pepper, and a dash of cayenne pepper.
Fill the egg white halves with this mixture and sprinkle with paprika.
As you can see, I am falling short of my original goal.
It was that party on December 21st that threw me off a bit.
to my old way of coping with stress: eating.
I CAN allow and prepare for this next year.
so I'll be reminded when I open the container next year.
this sounds less stressful for me and possibly our guests as well.
2) More deviled eggs as per above.
3) An additional vegetable appetizer.
4) An additional lean protein appetizer.
5) An almond meal and coconut oil Norwegian waffle in addition to the traditional waffles.
The chart and my goals are a bit off track.
or just leave it as it is and focus on the red line instead of the blue?
but stayed with the 1,5 lbs per week during Christmas.
There are a few of you that have emailed me that you would like to "CANDO"
along with me starting with the New Year.
I am so thrilled to have some "CANDO" buddies!
Let me know how you would like to be included.
I can post your progress or whatever you come up with.
with a revived sense of resolution with your additional support!
Goals: 5 lb loss the first week and 1.5 lb per subsequent week.
If anyone wants this chart with the formulas, I would be happy to send the Excel worksheet.
you can customize it to your own plan.
The chart automatically updates with each entry from the data on the left.
First of all I think you are doing amazing, it is the holidays and it is so hard to stay on track. I think you should pay attention to the the red line, there will be ups and downs but getting where you need to be is the goal. You are doing great, don't forget that.
You're doing great so do not become discouraged. I still think it's going to straighten out. Make sure you stop by and see my post tomorrow. I'm doing a "Janathon" that you might be interested in participating it.
Lovely Astri I have been following you and really want to join the Cando project - I have put on so much weight over the past few weeks - combination of things such as not getting my usual exercise, eating festive foods and too many chocolates so one of my main resolutions is to get back on track so any help would be fantastic. I have really enjoyed your posts Astri and always look forward to reading your news. I am looking forward to reading all your posts in 2014, have a wonderful time and big hugs to you.
I found it very hard to eat well this holiday season - the only thing that kept me from putting on weight was stress, which kind of killed my appetite. I'm afraid I made up for it over the last few days, though - lots of potato chips and caramelcorn (my self-indulgent junk foods of choice). Ah well. Christmas comes but once a year, and a good thing too!
P.S. A very happy and healthy New Year to you, the NVO, and all the extended Apple Blossom Gang!


text:
♪J. S. Bach – Concerto for Two Violins – Violinists: Arabella Steinbacher, Akiko Suwanai
March 27, 2015 by 1EarthUnited
Higher Density Blog
Klavdy B
How Americans Can Take Back The United States
Very important MUST READ post, everyone must remember the real history, how the US lost it's independence in 1871 and became an illegal incorporated gov't – "Congress committed treason when they created the 1871 corporate Constitution."
When the president takes the oath of office he is swearing to defend the Constitution of the District of Columbia, the INCORPORATED government. He isn't promising to preserve, protect and defend the original Pennsylvania Constitution of 1776. See for yourself – "I do solemnly swear (or affirm) that I will faithfully execute the Office of President of the United States, and will to the best of my ability, preserve, protect and defend the Constitution of the United States." It doesn't state – "Constitution for the United States of America" which was drafted for "We the People of the United States".

redpajama_set_name: RedPajamaCommonCrawl


The brand new Ginfall Festival comes to Victoria Hall, Helensburgh on Saturday 18th August.
On arrival, you'll receive a delicious Welcome Gin Cocktail. As well as the opportunity to try a huge variety of gins from all over the world, (including exclusive gins you wont see anywhere else), there will be live music, food stalls and a premium gin cocktail bar.
There will also be gin masterclasses and the opportunity to meet gin distillers in person , try free samples and chat about their gin.


text:
The Escapists 2 Breaks Out For Nintendo Switch January 11
Published: Saturday, January 6, 2018 - 12:15 | By: Robert N. Adams
Nintendo Switch, Xbox One, PlayStation 4
The Escapists 2, the sequel to Mouldy Toof Studios' 2014 prison simulation will be heading to the Nintendo Switch on January 11, 2018.
In The Escapists 2, you (and perhaps some of your friends) will team up to do your best at breaking out of prison. A number of options are available to you ranging from tunneling out of the prison quietly, stealing the equipment you need to make your escape, or inciting a full-scale prison riot and running out the door amidst the chaos. Overall, The Escapists 2 emphasizes player creativity in determining exactly how they will go about breaking out of the prison they happen to be stuck in. You can get an idea of what the gameplay is like in the sequel by looking at the game's trailer for its PC, Xbox One, and PlayStation 4 release:
https://www.youtube.com/watch?v=AuqQEfOueSA
The game will feature ten unique themed prisons alongside the ability to create your own con with over 300 distinct customizations. The Switch version of the game supports two-player split-screen play and up to four-player co-op and versus online drop-in, drop-out multiplayer. Players new to the series can take advantage of a tutorial that will get them used to the realities of prison life. Switch owners can use either a Joy-Con or Pro Controller to play the game.
The Escapists 2 will be available on the Nintendo Switch on January 11, 2018. If you'd prefer to pick it up on a different platform, you can get it for the PC via Steam, for the Xbox One via the Microsoft Store, or the PlayStation 4 via the PlayStation Store. Otherwise, you can pre-purchase it directly from Nintendo for $19.99 or your regional equivalent.
What do you think of The Escapists 2 heading to the Nintendo Switch? Do you think the platform is well-suited for this particular kind of gameplay? Let us know in the comments below!
Robert N. Adams
I've had a controller in my hand since I was 4 and I haven't stopped gaming since. CCGs, Tabletop Games, Pen & Paper RPGs - I've tried a whole bunch of stuff over the years and I'm always looking to try more!


text:
Charactopygus atratus är en mångfotingart som först beskrevs av Karsch 1881.  Charactopygus atratus ingår i släktet Charactopygus och familjen Spirostreptidae. Inga underarter finns listade i Catalogue of Life.

Källor

Dubbelfotingar
atratus

redpajama_set_name: RedPajamaWikipedia


Yesterday we spent a couple of hours wandering around Auckland taking photos then loaded up and drove to Whakapapa village and our hotel, the Tongariro Chateau.
Mountains were in the clouds but the forecast was reasonable for next day. We decided to walk the Tongariro Alpine Crossing past 2 volcanoes. We caught a bus from the hotel at 7pm and started by 7.30am. It was dull but dry. We made our way up, not too chilly but no views.
As we made our way up the clouds cleared a bit and it was good enough for photos. Not too many people either. Then we came to the bit where the volcanoes were venting gases (mainly hyrogen sulphide). Jolly smelly (bad eggs smell). There were several flat craters with snow to cross but easy enough. Lots of gases venting near Emerald Lake, which is bright blue and surrounded by gas vents. All the liquid is not water but sulphur. Then up to Blue Lake- totally frozen. Few shots until it brightend later. Nice on walk out. Down to bus shortly after 3pm. Tomorrow we visit some lakes and waterfalls.


text:
Facebook Home to be available outside the U.S. today, first big update hits in May
Sean Ludwig	 April 16, 2013 9:46 AM
NEW YORK CITY — Facebook CTO Mike Schroepfer (left) and director of mobile engineering Cory Ondrejka showed up today at the Dive into Mobile conference. Naturally, a lot of curious observers had questions about the just-launched Facebook Home skin of Android.
Facebook Home launched on select Android phones in the U.S. on Friday, including the Samsung Galaxy S III and the HTC One X. Google chairman Eric Schmidt seemed surprisingly positive about Android iterations like Facebook Home today, saying, "I love it."
One of the first major questions about Facebook Home is when Home will land outside the U.S. Ondrejka said the download of Facebook Home in the Google Play store would start rolling out internationally today.
Ondrejka also said the first major update to Facebook Home will be released in the second week of May.
The Next Web's Harrison Weber also questioned the Facebook duo about the wave of extremely negative reviews Facebook Home has received by users in the Google Play store. Ondrejka didn't appear phased by the negativity.
"There are some 5-star reviews where people are enthusiastic," Ondrejka said. "We look at lower reviews and see an opportunity to make it better."
Photo via Sean Ludwig/VentureBeat


For listening Full Audio : Dilbar Arabic Version, Fnaire Feat. Nora Fatehi, in hight quality just press the blue play button.
You can free download Full Audio : Dilbar Arabic Version — Fnaire Feat. Nora Fatehi by mp3 download 320kbs button pressing. Fast Mp3 downloading will be completed and you will get a high quality track with 320 kbit frequency.


text:
Q: Not able to upload file with form seriliaze in ajax I'm trying to submit a form with file upload but the data gets inserted into the table but with the file the error that I encounter says
Message: Undefined index: user_file

Below is my code.
HTML:
 <form id="create" method="post" action="" enctype="multipart/form-data" class="form-horizontal form-label-left">
<input type="text">
....
<input type="file" name="user_file" id="user_file"/>
<button type="submit" class="btn btn-primary" name="save" id="save">Save</button>

JS:
$("#create").submit(function(e) {

e.preventDefault();

var form = $(this);
.ajax({
       type: "POST",
       url: url,
       data: form.serialize(),
      success: function(data)
       {
        if(data.status === 'success')
        {
          //success
        }
        else
        {
          //error
        }
        $("#create")[0].reset();
       }
     });
 });

I tried the existing online but could not fix this issue.
Thanks in advance.
Edit:
The solution suggested did not solve my problem as I'm facing this issue only when the file input is part of a form where other input types are present.
However the solution suggested has only the input type file and that is not my issue.

A: You can try this.
$("#create").submit(function(e) {

    e.preventDefault();

    var form = $(this);
    .ajax({
           type: "POST",
           url: url,
           data: new FormData(this),
           processData: false,
           contentType: false,
          success: function(data)
           {
            if(data.status === 'success')
            {
              //success
            }
            else
            {
              //error
            }
            $("#create")[0].reset();
           }
         });
     });

redpajama_set_name: RedPajamaStackExchange


Towbar cycle carriers supplied by the Towbar Specialists have only been manufactured by the most established industry brands with a proven track record of excellence and longevity. You can rest assured knowing that your bikes are fully safe and secure when mounted on the back of your vehicle.
For more information about our service, please do not hesitate to get in touch today.


text:
The Podium Lounge celebrates 10th anniversary this 2018 Formula 1 Season
By Aaron Kong, September 10, 2018
Hosted by ex-Formula 1 Driver and TV Celebrity Alex Yoong and E! News Asia's Yvette King
The Podium Lounge entertainment line up over the three evenings (to late) include first ever Boyzlife performance in Singapore, special guest Celebrity DJ Joel Madden and celebratory Race Night performance by Taboo from the Black Eyed Peas
The Podium Lounge Singapore after-parties taking over the 2018 FORMULA 1 SINGAPORE AIRLINES SINGAPORE GRAND PRIX weekend extend beyond music performances towards lifestyle, fashion and charity.
The 2018 edition will see the launch of the "Cosmic 108" clothing line by Lisa S. Johnson, in collaboration with Haus of M. Photography. The clothing line takes inspiration from yoga philosophy, elements of a rock'n'roll and the yogi lifestyle. Each piece will carry the cosmic frequency of number 108 in combination with the sri yantra.
Art Works, a fine art investment gallery, will present an exhibition by British contemporary artist Lincoln Townley who is known for his expressive figurative paintings. Collected by the likes of Charlie Sheen, Al Pacino and Russell Brand and affectionately known by Michael Caine and others as 'the next Andy Warhol'.
"Drawn from the artist's subconscious, the dark and often tormented imagery of Lincoln's work seeks to evoke the chaos bubbling just below the surface of our lives, which drive our desires to succeed and win in life."
The Podium Lounge weekend will see a series of live auctions of authenticated and exceptionally rare F1 memorabilia with all proceeds going to a local charity. Outstanding and not-to-be-missed include a Lewis Hamilton signed race glove showcasing the multiple Formula 1 World Champion, a Niki Lauda signed and framed 8 x 12 inch photo, capturing the highly sought after signature of the 3-time Formula 1 World Champion who famously survived a fiery crash at Nürburgring in 1976 and returned to racing only six weeks later.
We spoke with Robbie Hoyes-Cock, CEO & Founder, The Podium Lounge about his background leading The Podium Lounge and where he goes to enjoy a drink to unwind after all that glamorous work.
Spirited Singapore (SS): What's your background and how did you come to helm 10 years of The Podium Lounge?
Robbie Hoyes-Cock (RHC): I grew up in Singapore and have lived here since I was just six months old, back in 1982. I studied law at university, worked in Citibank in their management associate training programme thereafter and then eventually decided, given the extraordinary network I'd built up as an expat here over the year, to start hosting super premium club nights for Singapore's wealthy party elite.
I was invited by the GM of The Ritz-Carlton, Millenia Singapore – Peter Mainguy (who's still the GM all these years later) to host a world-class motorsport themed event at his hotel over the 2009 Singapore Grand Prix; given they accommodate the vast majority of the Formula 1 Drivers, Teams and Team Owners. I jumped at the opportunity and enjoyed it so much that I thought I'd dedicated at least six months a year to making The Podium Lounge the most spell-binding events that anyone could ever hope to attend in Singapore.
SS: What's a key highlight from the many years at The Podium Lounge that you find a personal achievement?
RHC: I expanded The Podium Lounge brand internationally in 2013 together with my best friend and former Executive Director of Marketing & Entertainment at Pangaea (at Marina Bay Sands), Steve Yallop, and we hosted four Podium Lounge events around the Formula 1 calendar that year. It culminated in Abu Dhabi at the end of the 2013 Formula 1 Season and we were asked to host an extraordinary celebration for Red Bull Racing's Sebastian Vettel, who became a living legend by winning his fourth consecutive Formula 1™ World Driver's Championship and victory at the Abu Dhabi Grand Prix with Infiniti Red Bull Racing.
F1's record-breaking four-time World Champion chose our star-studded party, held on the Marina Rooftop Pool of the Yas Viceroy Abu Dhabi, to continue celebrations after winning the title in New Delhi the previous week which was unbelievably cool.
The post-race party that we organized hosted the racing community's most powerful celebrities with Vettel's team of mechanics, engineers, management and friends from The Paddock Club including racing legends Damon Hill, David Coulthard, Rubens Barrichello, Eddie Jordan, Gil de Ferran (IndyCar Indianapolis 500 Champion) and other personalities including Sky Sports F1 presenters Simon Lazenby and Natalie Pinkham, Chairman of Sky Nicholas Ferguson (CBE), Princess Deborah Murrat, HI&RH Archduchess Eleonore of The House of Habsburg, English television presenter Vanessa Feltz, and soccer legend Diego Maradona all revelling in the post-race celebrations of the 2013 Formula 1 Etihad Airways Abu Dhabi Grand Prix.
SS: In your time leading The Podium Lounge, how have you seen our Singapore Grand Prix evolve?
RHC: I think Singapore GP does a wonderful job of planning the event and building hype for the Marina Bay Street Circuit around the world. For many motorsport and Formula 1 enthusiasts in particular, the Singapore Night Race has become a bucket-list destination for so many and this is something that together with the Singapore Tourism Board should be protected and harnessed for maximum potential.
The Singapore Grand Prix continues to attract scintillating trackside entertainment and racing and world class music acts. Recently, we're seeing more multi-national corporations from around the globe hosting events to coincide with the Singapore GP and flying their clients in to entertain them in style. It was a huge result for Singapore to extend the Formula 1 by another four years and hopefully we can emulate the success that Monaco has had over the ages in making the event a must-attend spectacle tens of thousands each year.
SS: What are some milestones from the past 10 years of The Podium Lounge that you personally enjoyed?
RHC: As a massive Game of Thrones fan, I was so excited to book Hodor (the giant in Game of Thrones) to DJ at The Podium Lounge Singapore in 2015. Kristian Nairn (his real name) is 6ft 11 and looked terrifying with multiple tattoos of stars on his face which are obviously concealed with make-up in the series. He's a real softy at heart though and still lives with his mum and his dogs in Ireland. I was also surprised by what a brilliant DJ he was, and everyone was going absolutely crazy for his set.
That same year, we also booked SKY BLU from LMFAO. Given how viral 'Party Rock Anthem' had become with over 1.5 billion views, it was pretty powerful watching him shuffle down The Podium Lounge runway with a bottle of Grey Goose in hand.
SS: If the Singapore Grand Prix is symbolised by the winner and champagne, what type of alcohol would The Podium Lounge be and why?
RHC: The name "The Podium Lounge" was of course modelled on the Formula 1 Winner's Podium; and champagne is very much our #1 seller at the event each year. It is indeed all about champions, success and bubbles, so perhaps whereas the Grand Prix is symbolised by the spraying of Jeroboams (3L) Champagne bottles, The Podium Lounge is more about Methusalahs (6L) and enjoying the bubbles on your VIP Table in the company of some of the most powerful and successful people on the planet.
SS: What's your favourite spirit, drank in which fashion and where in Singapore?
RHC: I'm a single malt drinker and quite partial to a Lagavulin 16, double, served on ice at The Masonic Club Bar, 23a Coleman Street. As an active member of the Freemasons in Singapore it's a wonderful, member's bar where you can imbibe a wee dram together with your 'brothers' within the quiet confines of the beautiful heritage building Freemasons Hall, which was built in 1879.
SS: What should we expect this year at the 10th year anniversary of The Podium Lounge?
RHC: Formula 1 Drivers & Teams, Formula 1 Legends, celebrities, Royalty, ambassadors, supermodels, world class musicians (including Keith Duffy from Boyzone, Brian McFadden from Westlife, Joel Madden from Good Charlotte and Taboo from The Black Eyed Peas), sensational fashion shows staged by three of LA's top designers and a guest list that always features the who's who of the racing community.
Pictures are provided courtesy of The Podium Lounge
More information about The Podium Lounge can be found at their website.
Categories: Lifestyle
Tagged: The Podium Lounge
Maracatu Cachaça picks Distilled LLP as exclusive Singapore distributor
Five Michelin-starred venues with kickass drinks programmes


SAP S/4 HANA on-premise or cloud: which one is right for you?
Home / Discover / Blog / SAP S/4 HANA on-premise or cloud: which one is right for you?
SAP S/4 HANA is available in two editions: on-premise and in the public cloud. Both have their pros and cons, but how should they be compared? And how will this choice impact your organization? In fact, several aspects come into play when you are considering implementing one or the other – or both, if a hybrid cloud environment would fit your company's needs best.
To bring some clarity to the on-premise versus cloud debate, we have listed 3 key areas that will be affected by your choice.
Let's start by zooming in on the impact on your IT infrastructure. Certainly the most obvious difference between the on-premise and cloud edition is the fact that with SAP S/4 HANA in the cloud you no longer need to invest in internal technical support capabilities. At all? That might be a bridge too far, since your IT support engineers probably also guarantee smooth and stable operation of other IT applications. But moving to the cloud should in any event allow you to scale down your internal support activities considerably.
Another important aspect to take into account concerns upgrades. With S/4 HANA on-premise you opt in – or not – to a yearly upgrade, while the cloud edition automatically enrolls you into a quarterly upgrade cycle. There are two time slots to choose from, and that is about the only freedom of choice there is. First you upgrade your testing environment, and then two weeks later the upgrade of your production environment inevitably follows. That means all flows need to be re-tested every quarter. So if you are considering downsizing your functional support team, keep the upgrades in mind to avoid overburdening the key users of the system with the frequent testing cycles.
SAP S/4 HANA in the cloud is a slimmed-down version of the on-premise solution. The deployment is faster, but the offering is far more limited. It is a template-based solution, focusing on a limited number of key processes, with only a reduced set of customization options. Choosing the cloud edition is in fact a decision to adapt your processes, such as procure-to-pay and order-to-cash, to the way in which they are defined in the tool. Any additional functionality you want should be developed on a separate development platform for subsequent connection. S/4 HANA on-premise, on the other hand, offers the full range of functionality. Anything you require can be provided. If you pay for it, that is.
These two clearly distinct functional paths also demand a completely different approach to project management, affecting both the job of the implementation consultants and their counterparts on the customer side. In the cloud edition, the focus lies on the end goal that the process pursues. The path towards that goal is mapped out in the software. Therefore the role of the implementation consultant should be much more that of a change agent. An experienced transformation consultant who combines project management skills with strong change management capabilities. So make sure you select a partner who is well aware of the challenges that may come your way and who can offer the capabilities to counter them.
Instead of choosing between on-premise or the cloud, there is a way of getting the best of both worlds. We expect a growing number of large enterprises to implement a hybrid cloud environment, rolling out the on-premise edition at headquarters and the cloud edition at satellite offices. In that way they take advantage of the same database structures – allowing easier interfacing – and avoid the complexity of having to roll out the corporate template worldwide. And with BO Cloud and The Digital Boardroom, SAP now has the tools to combine data from both systems real-time in one report.
So which solution suits your organization? Or should the question be: is your organization ready to consider the cloud? The agility and flexibility – with much smaller risks of vendor lock-in – that the cloud offers are definitely benefits worth considering. Having an agile organization, capable of easily adjusting its business model to a rapidly evolving market, is key in the digital era. So take some time, step back and build a future roadmap for your business. Then you will undoubtedly find the right answer to the on-premise vs cloud equation.


text:
'''
Created on Jun 24, 2014

@author: Alan Tai
'''
from models.models_geo_info import NewAlbumGeoInfo
__author__ = 'Alan Tai'

import logging
import jinja2
import webapp2

from dictionaries.dict_keys_values import KeysVaulesGeneral
from dictionaries.dict_html_pages_reference import HtmlPagesReference
from handlers.handler_webapp2_extra_auth import BaseHandler

# dictionaries
dict_general = KeysVaulesGeneral()
dict_html_ref = HtmlPagesReference()

# jinja environment
jinja_environment = jinja2.Environment(loader=jinja2.FileSystemLoader('static/templates'))

# dispatchers
class FrontPageDispatcher(BaseHandler):
    def get(self):
        """ front page dispatcher """
        template_values = {}
        template_values.update({'title':u'柯文哲-MA柯P'})
        self.render_template(dict_html_ref.front_page, template_values)

class ArticlesDispatcher(BaseHandler):
    def get(self):
        """ articles dispatcher """
        template_values = {}
        template_values.update({'title':u'柯文哲-柯"文"集'})
        self.render_template(dict_html_ref.articles, template_values)

class AlbumsDispatcher(BaseHandler):
    def get(self):
        """ albums dispatcher collect the albums geo info and send to front-end """
        template_values = {}
        albums_geo_info = NewAlbumGeoInfo.query()

        #check if query is empty
        if albums_geo_info.count() <= 0:
            albums_geo_info = None

        template_values.update({'title':u'柯文哲照片集', 'albums_geo_info': albums_geo_info})
        self.render_template(dict_html_ref.albums, template_values)

class VideosDispatcher(BaseHandler):
    def get(self):
        """ videos dispatcher """
        template_values = {}
        template_values.update({'title':u'柯"影"集'})
        self.render_template(dict_html_ref.videos, template_values)

class FinancialDispatcher(BaseHandler):
    def get(self):
        """ financial dispatcher """
        albums_geo_info = NewAlbumGeoInfo.query()

        #check if query is empty
        if albums_geo_info.count() <= 0:
            albums_geo_info = None

        template_values = {}
        template_values.update({'title':u'柯在陽光下', 'albums_geo_info': albums_geo_info})
        self.render_template(dict_html_ref.financial, template_values)

# configuration
config = dict_general.config_setting

# app
app = webapp2.WSGIApplication([
    webapp2.Route(r'/', FrontPageDispatcher, name='front_page'),
    webapp2.Route(r'/base/articles', ArticlesDispatcher, name='articles'),
    webapp2.Route(r'/base/albums', AlbumsDispatcher, name='albums'),
    webapp2.Route(r'/base/videos', VideosDispatcher, name='videos'),
    webapp2.Route(r'/base/financial_summary', FinancialDispatcher, name='financial')
], debug=True, config=config)

# log
logging.getLogger().setLevel(logging.DEBUG)

redpajama_set_name: RedPajamaGithub


We are approaching the centenary of the 1918 Armistice and the end of the Great War; tonight's game against Hungerford will be the closest home game to this unique occasion.
The British Legion will be present at the game selling poppies and also taking a bucket collection.
Please give as generously as you are able. Thank you.


Us based payment service square is hiring crypto engineers while offering to pay them for their service in digital currency. This is according to a tweet sent out by Square CEO Jack Dorsey March 20.
He went to state that the decision to pay the soon to be recruited engineers in digital currency is based on the intention "to make the broader crypto ecosystem better," which will contribute to bettering the crypto community.
Square has had tremendous success in relation to crypto-currencies having registered $166 million in Bitcoin revenue last year alone. It doesn't end there, Square also hit an impressive $52 million in Bitcoin sales in Q4, which beat Q3's sales by 9 Million and $Q2's by more than $15 million. Clear profits from the Bitcoin operations which involve Square's consumer cash app, remain low, as purchasing costs account for the vast majority of revenue.
Dorsey, a known Bitcoin advocate himself went on to declare that he believes Bitcoin is the internet's native currency.
Dorsey's endorsement of Bitcoin paints a picture of how a vast number of top industry players have evolved in their perception and hardline stances on crypto-currency. If you go as far back as mid last year you will recall the slapping of social media bans on crypto advertisements. This was eventually lifted, with social media giants such as Facebook, making a serious foray into crypto.
Traditional financial institutions such as Fidelity bank, and Santander in Spain have also followed suit. JPMorgan have taken it a step further though, with the release of their crypto token dubbed "JPM Coin". More recently, we saw citi- the third largest bank in the US- drop plans of rolling out their own coin, but promise to continue exploring cryptos.
Square's announcement that it will be bringing in crypto staff further proves what we have been saying here at cryptonewsbytes. Opportunities are abound for crypto experts and will continue to grow for the foreseeable future.


Do you want to see duck puppies? I ask, scooping my niece up in my arms and jogging down the drive with her bouncing and giggling. I take her to the pond below her house. Unfortunately, the "duck puppies" are hiding amidst the cattails, but I spy them later when I return on my own. It is the season for avian births, I guess, because I have stumbled upon two happy families this week. First, when I visited a local pond to show my nephew a good fishing spot and then today at my niece Ellie's.
I have returned three times to watch the Canadian geese and their clan of seven goslings. The parents stand watch over them so diligently, the babies sticking close to the mama. One gets brave and waddles down to the shore and Mama eventually goes in after him, the other six in tow. She gathers them back on shore, but when they become weary of watching me, the parents finally move them, forming a single-file line across the water.
The duck's behavior is similar, but there is no papa around. Mama is a single lady in this scenario, but she keeps her brood just as close. I spy them again as I stand at the water's edge photographing flowers. Suddenly there is a splash beneath me and the bank flutters threatening to toss me in the water. Instead, I catch my balance just in time to raise my camera and capture a picture of the moving huddle of ducks, which had been camped out in the weeds beneath me. Mama transplants them to a safer venue and soon they are a brown blotch against the weeds.
Families can be complicated, relations strained as children grow older and seek independence. These happy tribes have not reached that point yet; nature will take its course in due time. Right now they are true units, working as one. I visit and soak in their happy energy. Whether it be ducks. humans or puppies, I am drawn to the notion of tribes, the allure of babies and the magic inherent in those first steps of discovery. I wish I could bottle it all. I wish I could claim it for my own.


text:
2023: OLAWEPO-HASHIM MEETS KWARA COUNCIL CHAIRMEN, ENDORSES GOV ABDULRAZAQ FOR SECOND TERM
According to Segun Awogbade, Chairman, Isin Council, "Mr Olawepo-Hashim is a very kind man, I have been his supporter for 25 years
A week after he hosted Party Chairmen from the States in North Central geo-political zone in Abuja on his 2023 ambition, frontline presidential aspirant in the ruling All Progressive Congress, APC, Mr. Gbenga Olawepo-Hashim moved to Ilorin, Kwara State over the weekend to consult with Chairmen of the party across the sixteen Local Government Council Areas.
At the parley, Olawepo-Hashim restated his desire to seek the ticket of his party, and subsequently lead the country back to the path of growth and development in 2023. While informing the gathering of his intention to formally declare for the race on Tuesday, May 3rd, 2022, he expressed his commitment to unite the country which he said is "presently badly divided along ethnic and religious lines."
He assured the crowd of keeping his promise of running an inclusive government to accommodate various tendencies in order to heal and assuage the pains arising from the various divisions and controversies across the nation.
He maintained that the "solution to National Security, the Unemployment problem, High cost of Petroleum products and basic items requires new and fresh approach to handle, that those who have never paid for anything they consume in the past 23 years cannot understand.
He also used the occasion to applaud the performance of the state governor in the last three years and subsequently endorsed his second term bid to govern the state in 2023.
According to him, worthy of commendation is the governor's policy of giving political space to youths and women, while also commending his efforts to restore the dignity of the state in the areas of education, infrastructures and human capital development.
During his earlier visit to the state late last year, Olawepo-Hashim had maintained that the liberation of Kwara took several decades and inflicted several battle scars on the participants, adding that the state must not be allowed to go back to slavery and socio-political emasculation that had arrested the progress of the state for many years.
The chairmen, many of whom are traditional political associates of the aspirant pledged their loyalty and support to who they say "he is our own and ally of our Governor".
According to Segun Awogbade, Chairman, Isin Council, "Mr Olawepo-Hashim is a very kind man, I have been his supporter for 25 years," while Alhaji Shehu Yahaya, Chairman, Asa added that "we fought for the freedom of Kwara together as our leader".
APC STRATEGISTS LOOKS IN DIRECTION OF OLAWEPO-HASHIM AS 2023 PLOT THICKENS
N266 MILLION FRAUD: COURT REFUSES BAIL APPLICATION FOR "CHIEF OF ARMY STAFF"
N266 MILLION FRAUD: COURT REFUSES BAIL APPLICATION FOR "CHIEF OF ARMY STAFF"


Some prescribed TOK essay titles may require you to find a knowledge issue or a problem of knowledge which relates to the title. Sometimes there are several hidden issues. How can you find them? This edition should motivate you to play with ideas to find a possible hidden knowledge issue.
The identification of a problem of knowledge in the prescribed TOK essay title is probably one of the most important first steps. But it may also be one of the most difficult tasks. What is the problem of knowledge that is implied in the title? How can one identify it? It may not always be necessary to identify an implied problem of knowledge in the prescribed title, but it may be helpful in structuring the essay.
The TOK Essay is marked against 4 criteria (A-D). I will explain these criteria to sensitize you on what to look out for when you write the essay.
In this edition I will give you a brief introduction into the marking criteria for the TOK essay.
Depth and breadth of understanding: Are you considering different ways of knowing and areas of knowledge and do you explore them in sufficient depth? Are you comparing them?
Careful: Is the knowledge issue relevant to the prescribed title?
There are some common, recurring problems with the TOK Essay. The prescribed title question is not answered explicitly, the examples are not explained, the essay is not organized, the….. Here is an overview of the most common problems.
The following audio files should give some basic advice for the TOK essay.
Defining terms using only dictionary definitions without interpretation of the definition.
Use of generalizing statements and words: all, none, few, many….. It has always been known that…..
Introductions that make not explicit reference to the topic, or introductions that do not properly interpret the topic question.


text:
\section*{Key points}

\begin{itemize}

\item
Quantum logic: superposition and entanglement

\item
Quantum algorithms for complex dynamical systems

\item
Quantum simulations on actual quantum hardware

\end{itemize}

\section{Introduction}

Miniaturization provides us with an intuitive way of
understanding why, in the near future, quantum mechanics will become
important for computation. The electronics industry
for computers grows hand-in-hand with the decrease in size of integrated
circuits. This miniaturization is necessary to increase
computational power, that is, the
number of floating-point operations per second (flops) a
computer can perform. In the 1950's, electronic computers based on vacuum-tube
technology were capable of performing approximately $10^3$ floating-point
operations per second, while nowadays (2022) there exist
supercomputers whose power is greater than $100$ petaflops
(a 1 petaflops computer is capable of performing
$10^{15}$ floating-point operations per second).
This enormous growth of computational power
has been made possible owing to progress in
miniaturization, which may be quantified
empirically in Moore's law. This law is the result of a remarkable
observation made by Gordon Moore in 1965: the number of
transistors on a single integrated-circuit chip doubles approximately
every $18-24$ months. This exponential growth has not yet
saturated and Moore's law is still valid. At the present
time the limit is close to $10^{10}$ transistors per
chip and the typical size of circuit components is of the order
of $5-10$ nanometres. Extrapolating Moore's
law, it is estimated that within a few years, one
would reach the atomic size for storing a single bit of
information. At that point, quantum effects will become
unavoidably dominant.

Quantum physics sets fundamental limitations on
the size of the circuit components.
The first question under debate is
whether it would be more convenient to push the silicon-based transistor
to its physical limits or instead to
develop alternative devices, such as quantum dots,
single-electron transistors or molecular switches. A
common feature of all these devices is that they are at the nanometre
length scale, and therefore quantum effects play a crucial role.

So far, the quantum switches that could substitute
silicon-based transistors and possibly be connected together to execute
classical algorithms based on Boolean logic were discussed. In this perspective, quantum
effects are simply unavoidable corrections that must be taken into
account owing to the nanometre size of the switches. A
quantum computer represents a radically different challenge: the aim is to
build a machine based on quantum logic, that is, it
processes the information and performs logic operations in agreement with the
laws of quantum mechanics~\cite{qcbook}.

\section{Quantum logic}

The elementary unit of quantum information is called a qubit (the quantum
counterpart of the classical bit) and a quantum computer may be
viewed as a many-qubit system. Physically, a qubit is a
two-level system, like the two spin states of a spin-$1/2$
particle, the vertical and horizontal polarization states of a single
photon or two levels of an atom.

A classical bit is a system that can exist in two distinct states, which are
used to represent $0$ and $1$, that is, a single binary digit. The only
possible operations (gates) in such a system are the identity
($0\to0$, $1\to1$) and NOT ($0\to1$, $1\to0$).
In contrast, a quantum bit (qubit) is a two-level quantum system,
described by a two-dimensional complex Hilbert space. In this space, one
may choose a pair of normalized and mutually orthogonal quantum
states, called $|0\rangle$ and $|1\rangle$ (say, the eigenstates of the Pauli
operator $\sigma_z$), to represent the values $0$ and $1$ of a
classical bit. These two states form a computational basis.
From the superposition principle, any state of the qubit
may be written as
\begin{equation}
  |\psi\rangle = \alpha |0\rangle + \beta |1\rangle \,,
  \label{alphabetaqubit}
\end{equation}
where the amplitudes $\alpha$ and $\beta$ are complex numbers,
constrained by the normalization condition
$|\alpha|^2 + |\beta|^2 = 1$.

A quantum computer can be seen as a collection of $n$
qubits and therefore its wave function resides in a $2^n$-dimensional
complex Hilbert space.
While the state of an $n$-bit classical computer is described in binary
notation by an integer $k\in [0,2^n-1]$,
\begin{equation}
  k = k_{n-1} \, 2^{n-1} + \cdots + k_1 \, 2 + k_0 \,,
  \label{binary}
\end{equation}
with $k_0,k_1,\dots ,k_{n-1}\in [0,1]$ binary digits, the state of an
$n$-qubit quantum computer is
\begin{align}
  |\psi\rangle & =
  \sum_{k=0}^{2^n - 1} c_k \, |k\rangle
  \nonumber
  \\ &=
  \sum_{k_{n-1},...,k_1,k_0=0}^1
  c_{k_{n-1}, \dots, k_1, k_0 } \,
  |k_{n-1}\cdots k_1 k_0\rangle,
  \label{superposition}
\end{align}
where $|k_{n-1}\cdots k_1 k_0\rangle\equiv |k_{n-1}\rangle \otimes \cdots
\otimes |k_1\rangle \otimes |k_0\rangle$. Notice that the
complex numbers $c_k$ are constrained by the normalization condition
$\sum_{k=0}^{2^n-1} |c_k|^2 = 1$.

The superposition principle is clearly visible in
Eq.~(\ref{superposition}): while $n$ classical bits can store only a single
integer $k$, the $n$-qubit quantum register can be prepared in the
corresponding state $|k\rangle$ of the computational basis, but also in a
superposition. The number of states of the computational basis
in this superposition can be as large as $2^n$, which grows
exponentially with the number of qubits. The superposition principle opens up
new possibilities for computation. When one performs
a computation on a classical
computer, different inputs require separate runs. In contrast, a
quantum computer can perform a computation for exponentially many inputs on a
single run. This huge parallelism is the basis of the power of quantum
computation.

The superposition principle is not a uniquely quantum feature.
Indeed, classical waves satisfying the superposition
principle do exist. For instance, consider the wave
equation for a vibrating string with fixed endpoints. Its solutions
$|\varphi_k\rangle$ satisfy the superposition principle and one can write
the most general state $|\varphi\rangle$ of a vibrating string as a linear
superposition of these solutions, analogously to Eq.~(\ref{superposition}):
$|\varphi \rangle = \sum_{k=0}^{2^n-1} c_{k} |\varphi_k\rangle$.
It is therefore also important to point out the importance of
entanglement for the power of quantum computation,
as compared to any classical computation.
Entanglement is the most spectacular and counter-intuitive
manifestation of quantum mechanics, observed in composite quantum systems: it
signifies the existence of non-local correlations between
measurements performed on well-separated particles. After
two classical systems have interacted, they are in
well-defined individual states. In contrast, after
two quantum particles have interacted, in general, they can
no longer be described independently of each other. There
will be purely quantum correlations between two
such particles, independently of their spatial separation.
Examples of two-qubit entangled state are the four states of the
so-called Bell basis,
$|\phi^{\pm}\rangle=\frac{1}{2}(|00\rangle\pm|11\rangle)$ and
$|\psi^{\pm}\rangle=\frac{1}{2}(|01\rangle\pm|10\rangle)$.
The measure of the polarization state of one qubit will
instantaneously affect
the state of the other qubit, whatever their distance is.
There is no entanglement in classical physics.
Therefore, in order to represent the superposition of $N=2^n$ levels
by means of classical waves, these levels must belong to the same system.
Indeed, classical states of separate systems can never be superposed.
Thus, any computation based on classical waves
requires a number $N$ of levels that
grows exponentially with $n$. If $\Delta$ is the typical energy separation
between two consecutive levels, the amount of energy required for this
computation is given by $\Delta2^n$. Hence, the amount of physical
resources needed for the computation grows exponentially with $n$.
In contrast, due to entanglement, in quantum
physics a general superposition of $2^n$ levels may be represented by means of
$n$ qubits. Thus, the amount of physical resources (energy) grows only
linearly with $n$.

To implement a quantum computation, one must be able to control the
evolution in time of the many-qubit state describing the quantum
computer. As far as the coupling to the
environment may be neglected, this evolution is unitary and
governed by the Schr{\"o}dinger equation.
It is well known that a small set of elementary logic gates
allows the implementation of any complex computation
on a classical computer. This is very important: it means that, when one
changes
the problem, one does not need to modify one's computer hardware. Fortunately,
the same property remains valid for a quantum computer.
It turns out that,
in the quantum circuit model, any whatever complex
unitary transformation acting on
a many-qubit system can be decomposed into quantum gates acting
on a single qubit and a suitable quantum gate acting on two qubits.
Any unitary operation on a single qubit can be
constructed using only Hadamard and phase-shift gates.
The Hadamard gate is defined as follows: it turns
$|0\rangle$ into $(|0\rangle + |1\rangle)/\sqrt{2}$ and
$|1\rangle$ into $(|0\rangle - |1\rangle)/\sqrt{2}$.
The phase-shift gate (of phase $\delta$) turns
$|0\rangle$ into $|0\rangle$ and $|1\rangle$ into
$e^{i\delta}|1\rangle$.
One can decompose a generic unitary transformation acting on
a many-qubit state
into a sequence of Hadamard, phase-shift and
CNOT gates, where CNOT is a two-qubit gate, defined as follows:
it turns $|00\rangle$ into $|00\rangle$,
$|01\rangle$ into $|01\rangle$,
$|10\rangle$ into $|11\rangle$, and
$|11\rangle$ into $|10\rangle$.
As in the classical XOR gate, the CNOT gate flips the state of the
second (target) qubit if the first (control) qubit is in the state
$|1\rangle$ and does nothing if the first qubit is in the state
$|0\rangle$.
Of course, the CNOT gate, in contrast to the
classical XOR gate, can also be applied to any superposition of the
computational basis states.

The decomposition of a generic unitary transformation of a $n$-qubit
system into elementary quantum gates is in general inefficient,
that is, it requires a number of gates exponentially large
in $n$ (more precisely, $O(n^2 4^n)$ quantum gates).
However, there are special unitary transformations that can
be computed efficiently in the quantum circuit model, namely
by means of a number of elementary gates polynomial in $n$.
A very important example is given by the quantum Fourier transform,
mapping a generic $n$-qubit state $\sum_{k=0}^{2^n-1} a_k |k\rangle$
into $\sum_{l=0}^{2^n-1} b_l |l\rangle$, where the vector
$\{b_0,...,b_{N-1}\}$ is the discrete Fourier transform of the vector
$\{a_0,...,a_{N-1}\}$, that is,
$b_l=\sum_{k=0}^{N-1} e^{2\pi i k l/ 2^n} a_k$. It can be shown that
this transformation can be efficiently implemented in
$O(n^2)$ elementary quantum gates, whereas the best known classical
algorithm to simulate the Fourier transform, the fast Fourier transform,
requires $O(n 2^n)$ elementary operations.
The quantum Fourier transform is an essential subroutine in many quantum
algorithms.

\section{Quantum algorithms}

As shown above, the power of quantum computation is due to the inherent
quantum parallelism associated with the superposition principle.
In simple terms, a quantum computer can process a large number of
classical inputs in a single run.
For instance, starting from the input state
$\sum_{k=0}^{2^n-1}c_k|k\rangle \otimes |0...0\rangle$,
one may obtain the output
state
\begin{equation}
\sum_{k=0}^{2^n-1}c_k|k\rangle \otimes |f(k)\rangle.
\label{fsuperposition}
\end{equation}
Therefore, the function $f(k)$ is computed for all $k$ in a
single run (note that one needs two quantum registers to compute
by means of a reversible unitary transformation $f(k)$; the second
register requires enough qubits to load the output $f(k)$ for all input values
$k=0,1,..,2^n$, with $n$ number of qubits in the first register).
However, it is not an easy task to extract useful information
from the output state. The problem is that this information
is, in a sense, hidden.
Any quantum computation ends up with a projective measurement
in the computational basis: the
qubit polarization is measured along the $z$-axis for all the qubits.
The output of the
measurement process is inherently probabilistic and the probabilities of
the different possible outputs are set by the basic postulates of quantum
mechanics. Given the state (\ref{fsuperposition}), one obtains
$|\bar{k}\rangle|f(\bar{k})\rangle$ with probability $|c_{\bar{k}}|^2$,
hence, the evaluation of the function $f(k)$ for a single
$k=\bar{k}$, exactly as with a classical computer. However, there exist
quantum algorithms that exploit quantum
interference to efficiently extract useful information.

In 1994, Peter Shor proposed a quantum algorithm that efficiently solves
the prime-factorization problem: given a composite odd positive
integer $N$, find its prime factors.
This is a central problem in computer science and it is
conjectured, though not proven, that for a classical computer it
is computationally difficult to find the prime factors.
Indeed, the best classical
algorithm, the number field sieve, requires
$\exp(O(n^{1/3}(\log{n})^{2/3}))$ operations.
Shor's
algorithm instead efficiently solves the integer factorization problem
in $O((n^2\log{n}\log\log{n}))$ elementary quantum gates, where
$n=\log N$ is the number of bits necessary to code the input $N$.
Therefore it provides an exponential improvement in speed with
respect to any known classical algorithm.
The integer factoring problem can be reduced to the problem of
finding the period of the function $f(k)=a^k$ mod $N$, where $N$
is the number to be factorized and $a<N$ is chosen randomly.
The modular exponentiation can be computed efficiently on a
quantum computer and, starting from the state
$\frac{1}{\sqrt{N}} \sum _{k=0}^{2^n-1} |k\rangle | 0... 0 \rangle$
(the equal superposition of all basis states in the first register can be obtained by
applying one Hadamard gate for each qubit),
one arrives at
$\frac{1}{\sqrt{N}} \sum _{k=0}^{2^n-1} |k\rangle | f(k) \rangle$.
Notice that there are two quantum registers, the first one stores
$k$, the second $f(k)$.
By measuring the second register, one obtains the outcome
$f(\bar{k})$. Thus, the quantum computer wave function collapses onto
$\frac{1}{\sqrt{m}} \sum_{j=0}^{m-1} |\bar{k} + j r\rangle
|f(\bar{k})\rangle$,
where $m$ is the number of $k$ values such that $f(k)=f(\bar{k})$,
and $r$ is the period of $f(k)$, that is $f(k)=f(k+r)$.
To determine the period $r$, one has to
perform the quantum Fourier transform
of the first register.
The resulting wave function is peaked around
integer multiples of $N/r$.
From the measurement of this state, one can extract
the period $r$.
It is worth mentioning that
there are cryptographic systems, such as RSA, that are used
extensively today and that are based on the conjecture that
no efficient algorithms exist for solving the prime
factorization problem. Hence Shor's algorithm, if implemented on a large scale
quantum computer, would break the RSA cryptosystem.

Other quantum algorithms have been developed. In particular, Grover has
shown that quantum computers can also be useful for solving the problem
of searching for a marked item in an unstructured database of
$N=2^n$ items. The best one can do with a classical computer is to
go through the database, until one finds the solution. This requires
$O(N)$ operations. In contrast, the same problem can be solved by
a quantum computer in $O(\sqrt{N})$ operations.
In this case, the gain with respect to classical
computation is quadratic.

\section{Quantum simulation of physical systems}

The simulation of quantum many-body problems on a classical computer is
a difficult task as the size of the Hilbert space grows exponentially
with the number of particles. For instance, if one wishes to simulate a chain
of $n$ spin-$1/2$ particles, the size of the Hilbert space is $2^n$.
Namely, the state of this system is determined by $2^n$ complex numbers.
As observed by Feynman in the 1980's, the growth in memory requirement
is only linear on a quantum computer, which is itself a many-body quantum
system. For example, to simulate $n$ spin-$1/2$ particles one
only needs $n$ qubits. Therefore, a quantum computer operating with only
a few tens of qubits can outperform a classical computer. Of course, this is
only true if one can find an efficient quantum algorithm and if one
can efficiently extract useful information from the quantum computer.
Quite interestingly, a quantum computer can outperform a classical computer not only for the
investigation of the properties of many-body quantum systems, but also
for the study of the quantum and classical dynamics of complex single-particle
systems.

For a concrete example, consider the quantum-mechanical motion of a
particle in one dimension (the extension to higher dimensions is straightforward).
It is governed by the Schr{\"o}dinger equation
\begin{equation}
  i \hbar \, \frac{d}{dt} \, \psi(x,t) =
  H \, \psi(x,t) \,,
  \label{1Dsch}
\end{equation}
where the Hamiltonian $H$ is given by
\begin{equation}
  H =
  H_0 + V(x,t) =
  -\frac{\hbar^2}{2m} \, \frac{d^2}{dx^2} + V(x,t) \,.
\end{equation}
The Hamiltonian $H_0=-(\hbar^2\!/2m)\,d^2\!/dx^2$ governs the free motion of
the particle, while $V(x,t)$ is a (possibly time-dependent) one-dimensional potential. To solve
Eq.~(\ref{1Dsch}) on a quantum computer with finite resources (a finite number
of qubits and a finite sequence of quantum gates), one must first of all
discretize the continuous variables $x$ and $t$. If the motion essentially
takes place inside a finite region, say $-d\le{x}\le{d}$, decompose this
region into $2^n$ intervals of length $\Delta=2d/2^n$ and
represent these intervals by means of the Hilbert space of an $n$-qubit
quantum register (this means that the discretization step drops exponentially
with the number of qubits). Hence, the wave function $|\psi(t)\rangle$ is
approximated as follows:
\begin{equation}
  |\tilde{\psi}(t)\rangle =
  \frac1{\mathcal{N}} \sum_{i=0}^{2^{n}-1} \psi(x_i,t) \, |i\rangle \,,
\end{equation}
where
$x_i \equiv -d + \left(i + \tfrac12\right) \Delta$,
$|i\rangle=|i_{n-1}\rangle\otimes\dots\otimes|i_0\rangle$
is a state of the computational basis of the $n$-qubit quantum register and
${\mathcal{N}} \equiv \sqrt{\sum_{i=0}^{2^n-1} |\psi(x_i,t)|^2}$
is a factor that ensures correct normalization of the wave
function. It is intuitive that $|\tilde{\psi}\rangle$ provides a good
approximation to $|\psi\rangle$ when the discretization step $\Delta$
is much smaller than the shortest length scale relevant for the motion of the
system.
The Schr{\"o}dinger equation (\ref{1Dsch}) may be integrated
by propagating the initial wave function $\psi(x,0)$
for each time-step $\epsilon$ as follows:
\begin{equation}
  \psi (x,t + \epsilon) =
  e^{-\frac{i}\hbar [H_0 + V(x,t)] \epsilon} \, \psi(x,t) \,.
\end{equation}
If the time-step $\epsilon$ is small enough,
it is possible to write the Trotter decomposition
\begin{equation}
  e^{-\frac{i}\hbar [H_0+ V(x,t)] \, \epsilon} \approx
  e^{-\frac{i}\hbar H_0 \, \epsilon}
  e^{-\frac{i}\hbar V(x,t) \, \epsilon} \,,
  \label{Trotter}
\end{equation}
which is exact up to terms of order $\epsilon^2$.
The operator on the right-hand side of
Eq.~(\ref{Trotter}) is still unitary, simpler than that on the
left-hand side, and, in many interesting physical problems,
can be efficiently implemented on a quantum computer.
Advantage is taken of the fact that the Fourier transform can be
efficiently preformed by a quantum computer.
One can then write
the first operator in the
right-hand side of (\ref{Trotter}) as
\begin{equation}
  e^{-\frac{i}\hbar H_0 \, \epsilon} =
  F^{-1} \,
  e^{+\frac{i}\hbar \left(\frac{\hbar^2k^2}{2m}\right) \epsilon} \,
  F \,,
\end{equation}
where $k$ is the variable conjugated to $x$ and $F$ the discrete
Fourier transform.
This represents a transformation
from the $x$-representation to the $k$-representation, in which this operator
is diagonal. Then, using the inverse Fourier transform $F^{-1}$, one returns to
the $x$-representation, in which the operator $\exp(-iV(x,t)\epsilon/\hbar)$ is
diagonal. The wave function $\psi(x,t)$ at time $t=l\epsilon$ is obtained from
the initial wave function $\psi(x,0)$ by applying $l$ times the unitary
operator
\begin{equation}
  F^{-1} \,
  e^{+\frac{i}\hbar \left(\frac{\hbar^2k^2}{2m}\right) \epsilon} \,
  F \,
  e^{-\frac{i}\hbar V(x,t) \, \epsilon}.
\end{equation}
Therefore, simulation of the Schr{\"o}dinger equation is now
reduced to the implementation of the Fourier transform plus diagonal operators
of the form
\begin{equation}
  |x\rangle \to e^{icf(x)} \, |x\rangle \,,
  \label{eifx}
\end{equation}
where $c$ is some real constant. Note that an operator of the form (\ref{eifx})
appears both in the computation of $\exp(-iV(x,t)\epsilon/\hbar)$ and of
$\exp(-iH_0\epsilon/\hbar)$, when this latter operator is written in the
$k$-representation.
The quantum computation of (\ref{eifx}) is
possible, using an ancillary quantum register $|y\rangle_a$, by means of
the following steps:
\begin{align}
  |0\rangle_a    \otimes |x\rangle
  &\to
  |f(x)\rangle_a \otimes |x\rangle
  \to
  e^{icf(x)} \,
  |f(x)\rangle_a \otimes |x\rangle
  \nonumber
\\
  &\to
  e^{icf(x)} \,
  |0\rangle_a    \otimes |x\rangle
  =
  |0\rangle_a    \otimes  e^{icf(x)} \, |x\rangle \,.
  \label{eifxsteps}
\end{align}
The first step is a standard function evaluation and
may be implemented by means of $O(n2^n)$ elementary
quantum gates. Of course, more efficient implementations
(polynomial in $n$) are possible when the function $f(x)$ has some structure,
as it is the case for the potentials $V(x,t)$ usually considered in
quantum-mechanical problems.
The second step in (\ref{eifxsteps}) is the
transformation $|y\rangle_a\to{}e^{icy}|y\rangle_a$ and can be performed in $m$
single-qubit phase-shift gates, $m$ being the number of
qubits in the ancillary register. Indeed, one may write the
binary decomposition of an integer $y\in[0,2^m-1]$ as
$y=\sum_{j=0}^{m-1}y_j2^j$, with $y_j\in\{0,1\}$. Therefore,
\begin{equation}
  \exp(i y) =
  \exp\bigg( \, \sum_{j=0}^{m-1} i c y_j 2^j \bigg) =
  \prod_{j=0}^{m-1} \exp(i c y_j 2^j) \,,
\end{equation}
which is the product of $m$ single-qubit gates, each
acting non-trivially (differently from identity) only on a
single qubit. The $j$-th gate operates the transformation
$|y_j\rangle_a\to\exp(icy_j2^j)|y_j\rangle_a$, with
$|y_j\rangle_a\in\{|0\rangle,|1\rangle\}$ vectors of the computational basis
for the $j$-th ancillary qubit.
The third step in (\ref{eifxsteps}) is just the reverse of the first
and may be implemented by the same array of gates as the first
but applied in the reverse order. After this step the ancillary
qubits are returned to their standard configuration $|0\rangle_a$ and
it is therefore possible to use the same ancillary qubits for
every time-step.
Note that the number of ancillary qubits $m$ determines the
resolution in the computation of the diagonal operator (\ref{eifx}).
Indeed, the function $f(x)$ appearing in (\ref{eifx}) is
discretized and can take $2^m$ different values.

An example of an interesting dynamical model that can be
simulated efficiently (and without ancillary qubits)
on a quantum computer is
the so-called quantum sawtooth map.
This map represents the dynamics of a periodically driven
system and is derived from the Hamiltonian
\begin{equation}
  H(\theta,I;\tau) =
  \frac{I^2}{2} + V(\theta)
  \sum_{j=-\infty}^{+\infty} \delta(\tau-jT) \,,
  \label{sawham}
\end{equation}
where $(I,\theta)$ are conjugate action-angle variables
($0\leq\theta<2\pi$), with
the usual quantization rules, $\theta\to\theta$ and
$I\to{}I=-i\partial/\partial\theta$ (set $\hbar=1$)
and $V(\theta)=-k(\theta - \pi)^2/2$.
This Hamiltonian is the sum of two terms,
$H(\theta,I;\tau)=H_0(I)+U(\theta;\tau)$, where $H_0(I)=I^2\!/2$ is
just the kinetic energy of a free rotator (a particle moving on a circle
parametrized by the coordinate $\theta$), while
$U(\theta;\tau) = V(\theta) \sum_j \delta(\tau-jT) $
represents a force acting on the particle
that is switched on and off instantaneously at time intervals
$T$. Therefore, its is said that the dynamics described by Hamiltonian
(\ref{sawham}) is kicked.
The (quantum) evolution from
time $tT^-$ (prior to the $t$-th kick) to time $(t+1)T^-$
(prior to the $(t+1)$-th kick) is described by a
unitary operator $U$ acting on the wave function $\psi$:
\begin{align}
  &\psi_{t+1} = U \, \psi_t = U_T U_k \,\psi_t\,;\nonumber\\
  \nonumber \\
  &U_T= e^{-i T I^2\!/2} \,,\;\;
  U_k= e^{ik(\theta -\pi)^2\!/2}\,.
  \label{sawquantum}
\end{align}
This map is called the quantum sawtooth map, since the force
$F(\theta)=-dV(\theta)/d\theta=k(\theta-\pi)$ has a sawtooth shape, with a
discontinuity at $\theta=0$.

In the following, an exponentially efficient quantum algorithm for
simulation of the map (\ref{sawquantum}) is described.
It is based on the forward/backward quantum Fourier transform between action
and angle bases. Such an approach is convenient since the operator $U$
is the product of the two operators
$U_k$ and $U_T$, which are diagonal in the $\theta$ and $I$
representations, respectively. This quantum algorithm requires the following
steps for one map iteration:
\begin{enumerate}
\item
Apply $U_k$ to the wave function $\psi(\theta)$. In order to decompose
the operator $U_k$ into one- and two-qubit gates, we first of all
write $\theta$ in binary notation:
\begin{equation}
  \theta=2\pi\sum_{j=1}^n \alpha_j 2^{-j} \,,
\label{thetaexpand}
\end{equation}
with $\alpha_i\in \{ 0,1 \}$. Here $n$ is the number of qubits, so that the
total number of levels in the quantum sawtooth map is $N=2^n$.
One can insert (\ref{thetaexpand}) into the unitary operator $U_k$,
obtaining the decomposition
\begin{equation}
e^{\imath k(\theta -\pi)^2/2} = \prod_{i,j=1}^n
e^{\imath 2 \pi^2 k( \alpha_i 2^{-i} -
\frac{1}{2n})
(\alpha_j 2^{-j} -
\frac{1}{2n})},
\label{dec}
\end{equation}
which is the product of $n^2$ two-qubit gates, each
acting non-trivially only on the $4$-dimensional
subspace spanned by the qubits $i$ and $j$.
\item
The change from the $\theta$ to the $I$ representation is obtained by means
of the quantum Fourier transform, which requires
and $\frac12 n(n+1)$ elementary quantum gates.
\item
In the $I$ representation, the operator $U_T$ has essentially the same
form as the operator $U_k$ in the $\theta$ representation, and therefore
it can be decomposed into $n^2$ two-qubit
gates, similarly to Eq.~(\ref{dec}).
\item
Return to the initial $\theta$ representation by application
of the inverse quantum Fourier transform.
\end{enumerate}
Thus, overall, this quantum algorithm requires $3n^2+n$
gates per map iteration. This number is to be compared with the
$O(n2^n)$ operations required by a classical computer to simulate
one map iteration by means of a fast Fourier transform. Thus,
the quantum simulation of the quantum sawtooth map dynamics is exponentially
faster than any known classical algorithm.
Note that the resources required to the quantum computer to simulate
the evolution of the sawtooth map are only logarithmic in the
Hilbert space dimension $N$.

As an example of the efficiency of this quantum algorithm,
Fig.~\ref{fig1} shows the Husimi functions, taken after $1000$
map iterations.
It is noted that $n=9$ qubits are sufficient to observe
the appearance of integrable
islands, while at $n=16$ these islands exhibit a
complex hierarchical structure in the phase space.

\begin{figure}
\centering
\includegraphics[scale=0.48]{fig1a.pdf}
\includegraphics[scale=0.48]{fig1b.pdf}
\caption{Husimi function for the sawtooth map
for $n=9$ (left) and $n=16$ (right) qubits,
in action angle variables $(I,\theta)$, with
$-N/2 \leq I < N/2$ (vertical axis, $N=2^n$) and
$0\leq \theta < 2\pi$ (horizontal axis),
averaged in the interval $950\le t \le 1000$,
for $T=2\pi/N$ and $kT=-0.1$.
An action eigenstate,
$|\psi_0\rangle=|m_0\rangle$, with $m_0=[0.38 N]$ is considered as
initial state at time $t=0$.
The color is proportional to the density: blue for zero and
red for maximal density.
}
\label{fig1}
\end{figure}
However, there is an additional aspect to be taken into account.
Any quantum algorithm has to address the problem of efficiently
extracting useful information from the quantum computer wave function.
Indeed, the result of the simulation of a quantum system is the wave
function of this system, encoded in the $n$ qubits of the quantum
computer. The problem is that, in order to measure all $N=2^n$
wave function coefficients by means of standard polarization
measurements of the $n$ qubits, one has to repeat the quantum
simulation a number of times exponential in the number of qubits.
This procedure would spoil any quantum algorithm, even in the
case, like the present one,
in which such algorithm could compute the wave function
with an exponential gain with respect to any classical computation.
Nevertheless, there are some important physical questions that can be
answered in an efficient way.

The quantum computation can provide an exponential gain
(with respect to any known classical computation) in problems
that require the simulation of dynamics up to a time $t$ which is
independent of the number of qubits. In this case, provided that
one can extract the relevant information in a number of measurements
polynomial in the number of qubits, one should compare, in
the example of the quantum sawtooth map,
$O(t(\log{N})^2)$ elementary gates (quantum computation)
with $O(tN\log{N})$ elementary gates (classical computation).
This is, for instance, the case of
dynamical correlation functions of the form
\begin{equation}
  C_t \equiv
  \langle\psi_0| \, A_t^\dagger \, B_0 \, |\psi_0\rangle =
  \langle\psi_0| \, (U^\dagger)^t \, A_0^\dagger \, U^t \, B_0 \, |\psi_0\rangle
  \,,
  \label{corrfun}
\end{equation}
where $U$ is the time-evolution operator (\ref{sawquantum}) for the
quantum sawtooth
map. Similarly, one can efficiently compute the fidelity of quantum
motion,
which is a quantity of central interest in the study of the stability
of quantum motion under perturbations.
The fidelity $f(t)$ (also called
the Loschmidt echo), measures the accuracy with which a quantum
state can be recovered by inverting, at time $t$, the dynamics with a
perturbed Hamiltonian. It is defined as
\begin{equation}
  f(t) = \langle\psi| \, (U^\dagger_\epsilon)^t \, U^t \, |\psi\rangle
  = \langle\psi| \, e^{iH_\epsilon t} \, e^{-iHt} \, |\psi\rangle
\,.
\end{equation}
Here the wave vector $|\psi\rangle$ evolves forward in time with
Hamiltonian $H$ up to time $t$ and then evolves
backward in time with a perturbed Hamiltonian $H_\epsilon$.
If the evolution operators $U$ and $U_\epsilon$
can be simulated efficiently on a quantum computer, as is
the case in many physically interesting situations, then the fidelity of
quantum motion can be evaluated with exponential speed up with respect
to known classical computations.
As shown in Fig.~\ref{fig2}, it is possible to measure the fidelity
by means of a Ramsey-type quantum interferometer method.
A single ancillary qubit is needed, initially prepared in the state
$|0\rangle$, while the input state for the other $n$ qubits is
a given initial state $|\psi_0\rangle$ for the quantum sawtooth map.
Two Hadamard gates are applied to the ancillary qubit, and in between
these operations a controlled-$W$ operation is applied ($W$ is a
unitary operator), namely $W$ is applied to the other $n$ qubits
only if the ancillary qubit is in its $|1\rangle$ state.
As a result, one obtains the following
final overall state for the $n+1$ qubits:
\begin{equation}
\frac{1}{2}\,
[(|0\rangle +|1\rangle) |\psi_0\rangle
+ (|0\rangle -|1\rangle) W|\psi_0\rangle].
\end{equation}
If $W=(U_\epsilon^\dagger)^t U^t$, then one can derive the fidelity
from polarization measurements of the ancillary qubit. One obtains
\begin{equation}
f(t)= \langle \sigma_z \rangle^2+
\langle \sigma_y \rangle^2,
\end{equation}
where
$\langle \sigma_z\rangle$ and $\langle \sigma_y\rangle$ are the
expectation values of the Pauli operators
$\sigma_z$ and
$\sigma_y$.
Provided that the quantum algorithm implementing $U$ is efficient,
as it is the case for the quantum sawtooth map, the fidelity
can then be computed efficiently.

\begin{figure}[h]
\centering
\vspace{0.5cm}
\includegraphics[scale=0.45]{fig2.pdf}
\caption{Schematic drawing of a quantum circuit implementing a
Ramsey-type quantum interferometer.
The top line denotes a single ancillary qubit, the bottom
line a set of $n$ qubits, $H$ the Hadamard gate and $W$ a
unitary transformation.}
\label{fig2}
\end{figure}

\section{Simulating complex dynamics on actual quantum hardware}

Present-day quantum computers, whether they are based on superconducting qubits or on trapped ions,
suffer from significant decoherence and the effects of various noise sources.
Therefore, achieving the quantum advantage in practically relevant problems
such as chemical reactions, new materials design, or biological processes, is an imposing task.
Note that quantum advantage is achieved when a quantum computer can solve a problem that no classical
computer can solve in a feasible amount of time. The progress of currently available quantum processors
can nevertheless be benchmarked by simulating complex dynamics.

An illustrative example is again provided by the quantum sawtooth map. The classical limit of such map is chaotic
when $kT<-4$ or $kT>0$.
Although the sawtooth map is a deterministic system, in the chaotic regime the motion along the
action direction is in practice indistinguishable from a random walk, with diffusion in the
action variable.
If one considers a classical ensemble of trajectories with fixed initial
action $m_0$ and random initial angle $\theta$, the second moment of the action distribution
grows linearly with the number $t$ of map iterations, $\langle (\Delta I)^2 \rangle \approx D(k) t$,
with a diffusion coefficient $D$ dependent on $k$.
The quantum sawtooth map, in agreement with the correspondence principle, initially
exhibits diffusive behavior, with the classical diffusion coefficient $D$. However, after a break time
$t^\star$, quantum interference leads to suppression of diffusion.
For $t>t^\star$, the quantum distribution reaches a steady state which decays exponentially over the action eigenbasis:
\begin{equation}
  W_m \equiv \big| \langle m | \psi \rangle \big|^2 \approx
  \frac1{\ell} \, \exp\!\left[ -\frac{2|m-m_0|}{\ell} \right] ,
  \label{expdecay}
\end{equation}
where the index $m$ singles out the action eigenstates ($I|m\rangle=m|m\rangle$),
the system is initially prepared in the eigenstate $|m_0\rangle$, and
$\ell$ is known as the localization length of the system.
Therefore, for
$t>t^\star$ only
\begin{equation}
\sqrt{\langle(\Delta I)^2\rangle}\approx \sqrt{D t^\star}\approx \ell
\label{siberia1}
\end{equation}
levels are populated.
This phenomenon, known as dynamical localization, is due to quantum interference effects, suppressing the
underlying classical diffusion process after a time $t^\star\approx \ell\approx D$.

Fig.~\ref{fig:distribution}  shows the results of a dynamical localization experiment with $n=3$ qubits
on a real and freely available IBM quantum processor, with superconducting qubits,
remotely accessed through cloud quantum programming~\cite{localization}.
The initial condition is peaked in action,
$\psi_0(m)=\langle m |\psi_0\rangle=\delta_{m,m_0}$, with $m_0=0$. The quantum algorithm for the
sawtooth map allows one to compute the wave vector $\psi_t(m)$ as a function
of the number of map steps, and then the probability distribution
$W_t(m)=|\psi_t(m)|^2$. In the figure $k\approx 0.273 < 1$, so that the
distribution is already localized after a single map step. On the other hand,
here $k T=1.5$, corresponding to diffusive, chaotic behavior for the underlying classical
dynamics.
In Fig.~\ref{fig:distribution}  the
ideal, noiseless distribution after $t=1$ map step is compared  with the
results of the real quantum hardware and with a simulator
(Qiskit, provided by IBM), which takes into account a few relevant noise sources,
modeling in particular dephasing, relaxation, and readout errors.
The results show that the quantum hardware exhibits a localization peak,
which emerges from quantum interference. Note that
the quantum algorithm performs forward-backward Fourier transform, thus exploring the entire Hilbert space of the quantum register
in a complex multiple-path interferometer that leads to wave-function localization. As such, dynamical localization is a very fragile quantum phenomenon, extremely sensitive to noise.
The height of the peak,
is significantly smaller than
the noiseless value
and the prediction of the Qiskit simulator.
These results show that the Qiskit
simulator underestimate some of the relevant noise channels,
such as fluctuations of the qubit quality parameters between calibrations
of the quantum computer, memory effects, and cross-talks between qubits.

\begin{figure}[t]
    \centering
    \includegraphics[width=8cm]{fig3.pdf}
    \caption{Dynamical localization in the quantum sawtooth map with $n=3$ qubits,
    $kT=1.5$, $k\approx 0.273$.
    Data from the IBM quantum processors {\it lima} (red) are obtained after averaging over 10 repetitions of 8192 experimental runs,
    and compared with the Qiskit simulator (blue) and the noiseless simulation (green).}
    \label{fig:distribution}
\end{figure}

The presence of these noise channels also shows the imposing difficulties
in scaling quantum algorithms to a large number of qubits and of quantum gates.
On the other hand, striking progress has been reported in recent years,
quantified for instance by the quantum volume $V_Q$, a single number meant to encapsulate the quantum computer performance,
including number of available qubits and number of quantum gates that can be reliably implemented, before errors dominate~\cite{qvolume}.
The quantum volume is defined as
\begin{equation}
\log_2 V_Q = {\arg\max}_{\kappa\le n}\{\min[\kappa,d(\kappa)]\},
\end{equation}
where $n$ is the number of qubits in the quantum computer, and $d(\kappa)=1/(\kappa\epsilon_{\rm eff}(\kappa))$,
known as circuit depth, is determined by an effective error rate $\epsilon_{\rm eff}(\kappa)$ for a subset
of $\kappa\le n$ qubits, on which sequences of random two-qubit unitaries are implemented.
From January, 2020 to December, 2021, the reported values of $V_Q$ have increased from $V_Q=32$
to $V_Q=2048$ (for a comparison, data from Fig.~\ref{fig:distribution} have been obtained with a machine
with quantum volume $V_Q=8$).

\section{Outlook}

A few significant examples have been discussed showing the
capabilities of a quantum computer in the simulation of
complex physical systems. A quantum computer with a few
tens of qubits and a long enough decoherence time to allow the implementation of
a large number of quantum gates, would outperform a
classical computer in this kind of problems.

Any practical implementation of a quantum computer has
to face errors, due to the inevitable coupling of the computer
to the surrounding environment or to
imperfections in the quantum computer hardware.
The first kind of error is known as decoherence and
is a threat to the actual implementation of any quantum computation.
More generally,
decoherence theory has a fundamental interest beyond quantum information
science, since it provides explanations for the emergence of classicality
in a world governed by the laws of quantum mechanics~\cite{zurek}. The core of the
problem is the superposition  principle, according to which any
superposition of quantum states is an acceptable quantum state.
This entails consequences that are absurd according
to classical intuition, like the superposition of ``cat alive'' and
``cat dead'' that is considered in the Schr\"odinger's cat paradox.
The interaction with the environment can destroy the coherence
between the states appearing in a superposition (for instance,
the ``cat alive'' and ``cat dead'' states).
Therefore, decoherence invalidates the
quantum superposition principle, which is at the heart of the
power of quantum algorithms.
The presence of device imperfections, although not leading to any
decoherence, also hinders the implementation of any quantum computational
task, introducing errors.
Therefore, decoherence and imperfection effects
appear to be the ultimate obstacle to the realization of a
large-scale quantum computer.

Note that a quantum computer is not necessarily required
for implementing quantum simulation. Simpler quantum devices, called
(analog) quantum simulators can mimic the evolution of other quantum systems
in an analog manner. Such simulators are problem-specific quantum machines,
namely controllable quantum systems used to simulate other quantum systems~\cite{nori}.

At present (2022) it is not clear if and when a useful quantum computer,
capable of outperforming existing classical computers in important computational tasks, will be built.
In order to perform coherent controlled evolution of a many-qubit system, one needs to take into account the problem of decoherence,
and therefore large-scale quantum computers appear unrealistic with present technology.
On the other hand, progress in the field has been huge
in recent years. Moreover, we should bear in mind that technological breakthroughs (such as the transistor was for the classical computer) are always possible and that no fundamental objections have been found against the possibility of building a quantum computer.

\acknowledgments{We acknowledge use of the IBM
Quantum Experience for Fig. 3 of this work.
The views expressed are those of the authors and do not reflect the official policy or position of IBM company or the IBM-Q team.}

\bibliographystyle{prsty}

redpajama_set_name: RedPajamaArXiv


text:
package etcd

import (
	"strings"
	"time"

	cli "github.com/coreos/etcd/client"
	"golang.org/x/net/context"
)

//gloabal variable for etcd
var ETCD_BASEDIR, ETCD_INSTDIR, ETCD_CONFDIR string

type etcdDB struct {
	C       cli.Client      //The client context
	Kapi    cli.KeysAPI     //The api context for Get/Set/Delete/Update/Watcher etc.,
	Ctx     context.Context //Context for the connection mostly set to context.Background
	Cfg     cli.Config      //Configuration details of the connection should be loaded from a configuration file
	isSetup bool            //Has this been setup
	BaseDir string          //base dir
	InstDir string          //instance dir
	ConfDir string          //config dir
}

//New Function to create an etcDB object
func New() *etcdDB {
	return &etcdDB{isSetup: false}
}

//Login This implements connecting to the ETCD instance
func (db *etcdDB) Login() error {

	var err error
	db.C, err = cli.New(db.Cfg)
	if err != nil {

		return err
	}
	db.Kapi = cli.NewKeysAPI(db.C)
	db.Ctx = context.Background()

	return nil
}

// Setup will create/establish connection with the etcd store and also setup
// the nessary environment if etcd is running for the first time
// framework will look for the following location in the central store
// /framework/instances...... -> Will have the entries of all the instances
// /framework/Config/....		-> Will have the entries of all the config information
func (db *etcdDB) Setup(config string) error {
	var err error
	db.Cfg = cli.Config{
		Endpoints: []string{config},
		Transport: cli.DefaultTransport,
		// set timeout per request to fail fast when the target endpoint is unavailable
		HeaderTimeoutPerRequest: time.Second * 10,
	}

	err = db.Login()
	if err != nil {
		return err
	}

	db.BaseDir = "/Workload"

	ETCD_BASEDIR = db.BaseDir
	err = db.CreateSection(db.BaseDir)
	if err != nil && strings.Contains(err.Error(), "Key already exists") != true {
		return err
	}

	ETCD_INSTDIR = ETCD_BASEDIR + "/Instances"
	db.InstDir = ETCD_INSTDIR
	err = db.CreateSection(db.InstDir)
	if err != nil && strings.Contains(err.Error(), "Key already exists") != true {
		return err
	}

	ETCD_CONFDIR = ETCD_BASEDIR + "/Config"
	db.ConfDir = ETCD_CONFDIR
	err = db.CreateSection(db.ConfDir)
	if err != nil && strings.Contains(err.Error(), "Key already exists") != true {
		return err
	}

	db.isSetup = true
	return nil
}

func (db *etcdDB) IsSetup() bool {
	return db.isSetup
}

func (db *etcdDB) Set(Key string, Value string) error {

	_, err := db.Kapi.Set(db.Ctx, Key, string(Value), nil)
	return err

}

func (db *etcdDB) Get(Key string) (string, error) {

	resp, err := db.Kapi.Get(db.Ctx, Key, nil)
	if err != nil {
		return "", err
	}
	return resp.Node.Value, nil
}

func (db *etcdDB) IsDir(Key string) (error, bool) {
	resp, err := db.Kapi.Get(db.Ctx, Key, nil)

	if err != nil {
		return err, false
	}
	return nil, resp.Node.Dir
}

func (db *etcdDB) IsKey(Key string) (bool, error) {
	_, err := db.Kapi.Get(db.Ctx, Key, nil)

	if err != nil {
		if strings.Contains(err.Error(), "Key not found") != true {
			return false, err
		}
		return false, err
	}
	return true, nil
}

func (db *etcdDB) Update(Key string, Value string, Lock bool) error {

	return nil
}

func (db *etcdDB) Del(Key string) error {

	_, err := db.Kapi.Delete(db.Ctx, Key, nil)

	if err != nil {
		return err
	}
	return nil

}

//CreateSection will create a directory in etcd store
func (db *etcdDB) CreateSection(Key string) error {

	_, err := db.Kapi.Set(db.Ctx, Key, "", &cli.SetOptions{Dir: true, PrevExist: cli.PrevNoExist})

	if err != nil {
		return err
	}

	return nil
}

//DeleteSection section will delete a directory optionally delete
func (db *etcdDB) DeleteSection(Key string) error {

	_, err := db.Kapi.Delete(db.Ctx, Key, &cli.DeleteOptions{Dir: true})
	return err
}

//ListSection will list a directory
func (db *etcdDB) ListSection(Key string, Recursive bool) ([]string, error) {

	resp, err := db.Kapi.Get(db.Ctx, Key, &cli.GetOptions{Sort: true})

	if err != nil {
		return nil, err
	}

	retStr := make([]string, len(resp.Node.Nodes))

	for i, n := range resp.Node.Nodes {
		retStr[i] = n.Key
	}

	return retStr, nil
}

func (db *etcdDB) CleanSlate() error {

	_, err := db.Kapi.Delete(db.Ctx, db.BaseDir, &cli.DeleteOptions{Dir: true, Recursive: true})

	return err
}


text:
GOP suspicious of Obamacare enrollment figures
By Jake Miller
January 11, 2014 / 11:18 AM / CBS News
Another week, another demand from Republicans to repeal the Affordable Care Act.
Carrying the torch this week: Sen. Thad Cochran, R-Miss., who called Saturday for the law to be defunded or repealed and disputed figures from the administration touting a robust expansion of health insurance coverage under Obamacare.
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"The Affordable Care Act was supposed to be fully operational by January 1 of this year, but here we are two weeks into 2014, and the administration continues to struggle to implement the law's burdensome mandates," Cochran said in the weekly Republican address. "The law is not living up to the promises made by its supporters, and it is questionable whether the law will meet its fundamental purpose - to significantly expand health insurance coverage."
The administration and congressional Democrats have recently been touting the law's expansion of coverage to roughly nine million Americans - three million young adults who have been able to stay on their parents' plan, two million consumers who have enrolled in the private insurance exchanges and four million low-income consumers who have been inducted into an expanded Medicaid program.
Cochran, however, argued there may be less to those figures than meets the eye.
"The administration's enrollment numbers don't paint a pretty picture," he said. "They don't tell us how many of the enrollees have actually lost existing coverage and were forced into the exchanges; and the numbers don't tell us whether applicants have actually paid their premiums and received coverage. There is ample reason to be skeptical that those numbers will improve substantially."
Cochran's other complaints about the law had a familiar ring: that it's booting people off of health plans they liked despite the president's promise that people could keep their current insurance; that it's forcing people to change doctors; that many consumers are finding their prices going up under Obamacare.
"If the law can't keep its most basic promise, it should be repealed," he concluded. "We should go back to the drawing board and draft commonsense, bipartisan legislation that will work better for all Americans, without spending billions of taxpayer dollars to support these failing policies."
Obama: Make 2014 a "year of action" on economy
In his own weekly address on Saturday, President Obama reprised his call for 2014 to be a "year of action," urging lawmakers to help accelerate the economic recovery.
He again called on Congress to extend recently lapsed federal unemployment insurance - a "vital economic lifeline" that "helps people support their families while they look for a new job."
Democrats and a handful of Republicans have called for a three-month extension while the specifics of a longer deal are worked out, but most in the GOP have been reluctant to extend benefits without offsetting the cost elsewhere in the budget.
The president also previewed a series of upcoming events aimed at highlighting high-tech manufacturing jobs, job training programs, and work opportunities for the long-term unemployed.
And he offered a glimpse at the central theme of his upcoming State of the Union address: a populist message focused on upward mobility and equality of opportunity.
"I will mobilize the country around the national mission of making sure our economy offers everyone who works hard a fair shot at opportunity and success," he said. "As Americans, that's what we should expect. And after everything you've done to recover and rebuild from crisis these past five years – after all your hard work and sacrifice – that's what you deserve."
First published on January 11, 2014 / 11:18 AM