Quantum Computing for Computer Scientists

  वेळा पाहिला 1,002,111

Microsoft Research

2 वर्षांपूर्वी

This talk discards hand-wavy pop-science metaphors and answers a simple question: from a computer science perspective, how can a quantum computer outperform a classical computer? Attendees will learn the following:
- Representing computation with basic linear algebra (matrices and vectors)
- The computational workings of qbits, superposition, and quantum logic gates
- Solving the Deutsch oracle problem: the simplest problem where a quantum computer outperforms classical methods
- Bonus topics: quantum entanglement and teleportation
The talk concludes with a live demonstration of quantum entanglement on a real-world quantum computer, and a demo of the Deutsch oracle problem implemented in Q# with the Microsoft Quantum Development Kit. This talk assumes no prerequisite knowledge, although comfort with basic linear algebra (matrices, vectors, matrix multiplication) will ease understanding.
See more at www.microsoft.com/en-us/research/video/quantum-computing-computer-scientists/

High Plains Drifter
High Plains Drifter दिवसापूर्वी
Krista Jacko Josza, my dear old friend. If youre reading this then let me appologise for my behaviour. You were, and i imagine still are, the best friend anyone could wish for. Please dont hate me, in aldult life ive been diagnosed with many mental problems. As a kid i loved you dearly and im sorry i never said so. Please take care and i send love to your dad, mum and sisters. If you.can find it in your heart, please forgive me. Im a wanty lol. Xx
Akus 3 दिवसांपूर्वी
I'm surprised that wokesters didn't shit themselves over term quantum supremacy..
Andrew Helwer
Andrew Helwer 3 दिवसांपूर्वी
It has been replaced by the term quantum advantage, yes. A welcome change!
Joshua P
Joshua P 4 दिवसांपूर्वी
It's a long story but but the CIA has been harassing me (regarding my discovered intellectual property) and attempting to commit Piracy regarding the Theory of Everything but just so everyone knows who wants to analyze the Fundamental Principal behind the Theory of Everything (TOE) can be expressed by connection to the equation *e^(iπ) + 1 = 0* (where e is approximately 2.7182818284590452356 and i represents √(-1) ) This equation basically reduces to -1 + 1 = 0. The (TOE) does NOT require time to solve for it. *Don't worry when the time variable disappears.* I don't want to provide too much information. This way professors and students can review it without having to worry about piracy (sadly, especially from those you think are meant to protect the law) *Once you find it out please publish it*. I have been hiding it. The CIA has offered me a job and money for it. Please stand up for scientists and GLOBAL learning. You can figure it out.
Michael Salmon
Michael Salmon 4 दिवसांपूर्वी
This guy got paid in Diet Coke. Also, nice talk
Aidan Sgarlato
Aidan Sgarlato 5 दिवसांपूर्वी
Kinda sad that there were like 3 people in the room
Andrew Helwer
Andrew Helwer 5 दिवसांपूर्वी
I was a bit disappointed at the time but lots of people online seem to have enjoyed it so it all worked out in the end!
Diego Esparza
Diego Esparza 6 दिवसांपूर्वी
If the values of the qbit vector can be complex numbers, with the condition that v[0]^2 + v[1]^2 = 1, say you had v = {i, √2} which satisfies the condition. How do you interpret the probabilities that the qbit is 0 or 1? -100% and 200%?
Andrew Helwer
Andrew Helwer 5 दिवसांपूर्वी
You're missing absolute value, it's |v[0]|² + |v[1]|² = 1. So |i|² = 1. See en.wikipedia.org/wiki/Absolute_value#Complex_numbers
Zhan Caitao
Zhan Caitao 6 दिवसांपूर्वी
Very very good tutorial (I am a computer science Ph.D. candidate). One interesting piece of information, the instructor of this video left Microsoft.
Andrew Helwer
Andrew Helwer 6 दिवसांपूर्वी
Correct! Decided to try the independent contractor life.
Andrei Negrea
Andrei Negrea 6 दिवसांपूर्वी
Someone give buddy another nice cold can of whatever he's fake sipping on?
김영선 9 दिवसांपूर्वी
The obedient crocodile intriguinly unlock because square bodily offer times a mean letter. bouncy, murky grass
Sprints William
Sprints William 12 दिवसांपूर्वी
Elon Musk is not Isaac Newton eating an Apple
Pixel Bots
Pixel Bots 14 दिवसांपूर्वी
I feel asleep watching what if we nuked tge moon and woke up a 6:00 am watching this
Sacrament of Wilderness
Sacrament of Wilderness 16 दिवसांपूर्वी
A very nice, easy to follow and exhaustive introduction. Really love the speaker!
Mani Kanth
Mani Kanth 17 दिवसांपूर्वी
He's constantly saying what he said at 13:57 , flip bottom two rows of identity matrix. But immediately next he does a matrix transformation which is (4x4 c-not transformation applied on unit vector in 4-dim) . Though the output is same, the most accurate way of saying is the last 2 columns flipped (kind of basis vectors).
Andrew Helwer
Andrew Helwer 17 दिवसांपूर्वी
Yes that's the explanation that 3blue1brown is fond of. However, there's more than one way to look at matrix transformation; change-of-basis is only one of them.
Martin Tunnicliffe
Martin Tunnicliffe 17 दिवसांपूर्वी
One of the clearest explanations I've ever seen
Tienke Bosher Pelzmann
Tienke Bosher Pelzmann 18 दिवसांपूर्वी
watch the Hebrew, the DNA of creation will help you understand what stuff is made off. Rabbi Kraft
AetherDivision 21 दिवसापूर्वी
🎵Dunna nunna nunna dun.... shut and calculate 🤓🎶
Huntracony 22 दिवसांपूर्वी
Great presenter! Please teach me anything and everything.
Jane Allsep
Jane Allsep 25 दिवसांपूर्वी
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Drino Zhao
Drino Zhao 25 दिवसांपूर्वी
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Ashwin K Raghu
Ashwin K Raghu 27 दिवसांपूर्वी
There's too much nifty in this lecture :P Loved it!
Clement Gervaise
Clement Gervaise 28 दिवसांपूर्वी
Chris Costello
Chris Costello 28 दिवसांपूर्वी
Jesus christ take a sip every 4 sentences.
H.İ. Iskender
H.İ. Iskender 29 दिवसांपूर्वी
tideview 29 दिवसांपूर्वी
Another math element that may help some in accepting the weirdness of quantum physics is the introduction of negative probability, itself a concept hard to grasp, but a valid approach to mathematically describing intermediate states that a quantum system may realize on its way to the final state as detected by a measurement.
Anita Reason To Believe
Anita Reason To Believe महिन्यापूर्वी
It makes no sense to me that you can complicate with it which is .measuring it...why does does it no it collapse in then?
Jakob Zupanec
Jakob Zupanec महिन्यापूर्वी
I had a stroke trying to read this.
Andrew Helwer
Andrew Helwer महिन्यापूर्वी
i-uki-d i-imut
i-uki-d i-imut महिन्यापूर्वी
two years later, it remains the best video on quantum cumputing, Bravo and thank you
Andrew Helwer
Andrew Helwer महिन्यापूर्वी
Glad you enjoyed!
kelly thomas
kelly thomas महिन्यापूर्वी
The materialistic venezuelan logically consist because news immediately ban about a ugliest stream. striped, elite pastry
MCPE grejer
MCPE grejer महिन्यापूर्वी
he is not so good at answearing the questions so that they understand i see them ask like the same question in different ways five times and still not understanding because he does not explain it to 100 percent.
Andrew Helwer
Andrew Helwer महिन्यापूर्वी
You can only lead a horse to water.
MCPE grejer
MCPE grejer महिन्यापूर्वी
44:57 i dont get how that is reversible it just sets the bit to zero how is that revirsible?
Andrew Helwer
Andrew Helwer महिन्यापूर्वी
Because you store the input, that makes it reversible.
sk8punk318 महिन्यापूर्वी
I just woke up and somehow I was brought here
sk8punk318 महिन्यापूर्वी
Packed house lol
Mel Yu
Mel Yu महिन्यापूर्वी
The various parent excitingly squash because owner socioeconomically stuff including a spotted answer. adorable, numerous responsibility
Tooth महिन्यापूर्वी
So at the end he said we'd know within a year or two whether that exponential limit exists -- it's been two years, does it?
Andrew Helwer
Andrew Helwer महिन्यापूर्वी
Still not determined. Google claims they established quantum supremacy but it isn't quite as clear-cut as we want.
勇樹 महिन्यापूर्वी
Happy Valentine's day
Andrew Gould
Andrew Gould महिन्यापूर्वी
The even excellent excited orchestra grossly grin because fowl expectably bury following a steadfast knickers. open, succinct digital
Jhonny Deann
Jhonny Deann महिन्यापूर्वी
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RandomMm Fan
RandomMm Fan महिन्यापूर्वी
2A.M and a video for computer scientists... yeah time to go to bed
trav gran
trav gran महिन्यापूर्वी
The right professor literally suck because sidecar physiologically stop along a dependent knowledge. accurate, lamentable tanker
Andrew महिन्यापूर्वी
This video proves that I am an imbecile 🤦‍♂️🤣
Andrew Helwer
Andrew Helwer महिन्यापूर्वी
Oh no! What did you get stuck on? I am sure you can get it.
Guff महिन्यापूर्वी
Bill Gates is an evil vaxine murderer.
GSZero महिन्यापूर्वी
1:05:26 - I'm still confused about that myself. Maybe you can't transfer data through the entangled particles but if you can collapse it by measuring it at will, if there is a way to tell when that other particle collapses then the collapse itself can be the communication. I'm guessing what he's saying is that there is no way to tell when the state collapses so you can't use it to signal?
Andrew Helwer
Andrew Helwer महिन्यापूर्वी
Yes correct, you cannot tell whether the state is collapsed.
Ben Wing
Ben Wing महिन्यापूर्वी
The delicate propane consecutively scatter because dry psychologically talk through a noiseless boundary. fluttering, soft clipper
ALWIN SEBASTIAN महिन्यापूर्वी
Can you show an algorithm in Quantum computing?
Andres Gomez
Andres Gomez महिन्यापूर्वी
I'm just going to pretend to understand this I have like a million question
Andrew Helwer
Andrew Helwer महिन्यापूर्वी
@Andres Gomez learning the math is really the only way. Don't be intimidated - this is linear algebra that most people learn on their first or second day in class in a first-year undergrad course! 3blue1brown has a set of linear algebra videos that people really like.
Andres Gomez
Andres Gomez महिन्यापूर्वी
@Andrew Helwer well the math is beyond me I came here trying to understand how a superposition could be created? Also I still dont understand how this allows Qbit to be able to process information faster then a traditional computer? I'm not a computer scientist but I still want grasp how this can be possible
Andrew Helwer
Andrew Helwer महिन्यापूर्वी
Go ahead and ask!
Mario Ristovski
Mario Ristovski महिन्यापूर्वी
he is cute
Tuyen Mai
Tuyen Mai महिन्यापूर्वी
Love you.
ALEX GIBSON महिन्यापूर्वी
It's because they are connected via hyperdimensional geometry and are essentially at the same location in this hyperdimensional space. It's all derived by the 8d packing of fields in the e8 lattice, the subsection of it projected down to the next lower dimension, and that dimensional projection is then itself projected to the next lower dimension, etc. Till you get to a 3d "quantum foam" of 20 groups of Planck scale tetrahedra which twist around a central point, who's twist states correlate to quantum mechanics, quantum gravity perturbations, and wave particle duality. Visually similar to the vibrating oil drop experiments. It is at that point we get into physical results at Cern, which Research scientist Garrett Lisi pointed out are coincident with the e8 lie (pronounced "Lee") groups that make up the e8 lattice. At least that's what the math and experiments suggest at any rate.
ALEX GIBSON महिन्यापूर्वी
So to expand on that relationship, essentially the entangled particles occupy 20 group geometry that is connected in the x dimension up from the third dimension. Meaning though they can be in "separate places" in the 3rd, they are actually just the same hyperdimensional geometry viewed from two hyperdimensional angles that render visually as 2 points in space.
Hiro San
Hiro San महिन्यापूर्वी
I'm more confused about the superposition of the soda in his can
cwif rbm
cwif rbm महिन्यापूर्वी
Props to Andrew for being so active in the comments and helping out people who have questions
Jonah Deegan
Jonah Deegan महिन्यापूर्वी
2:08 “We could undermine our global financial system, which is pretty cool.”
Annie Griffin
Annie Griffin महिन्यापूर्वी
The halting community multivariably count because authority taxonomically coil at a spurious mini-skirt. many, red month
WHK Yan महिन्यापूर्वी
No se entiende nada.
AmericanFreedom911 महिन्यापूर्वी
Gotta give this kid credit for his effort at explaining the unexplainable. Good job!
Sandeep Iyer
Sandeep Iyer महिन्यापूर्वी
For the identity black box , why not just pass through the input x to both the outputs ? Why do we need a cnot? Or is it that we have no identity operator?
Andrew Helwer
Andrew Helwer महिन्यापूर्वी
Quantum computers don't have the ability to copy a qbit value, so we have to make do with CNOT.
Crunchy Duck
Crunchy Duck महिन्यापूर्वी
The lecturer is cute. He seems to genuinely enjoy teaching and it makes me enjoy learning.
Drug Dealer
Drug Dealer महिन्यापूर्वी
32:22 - "Imagine I show up on your doorstep and I give you a package, its just a black box that has a function on one bit, what a horrible present" 😂
Kenichi Mori
Kenichi Mori महिन्यापूर्वी
Statistics computing is quantum approach command size and ten.Quantum point.=QP Yellow Hand.
Sandeep Iyer
Sandeep Iyer महिन्यापूर्वी
Why no example of inputs outputs bb at 36:55. I was with you till then Just saying this is the most difficult part without further explaining didn’t help Hoping someone reading the comment would explain
Andrew Helwer
Andrew Helwer महिन्यापूर्वी
@Sandeep Iyer Happy to hear! It certainly took a long amount of staring for me.
Sandeep Iyer
Sandeep Iyer महिन्यापूर्वी
@Andrew Helwer thanks . I got it eventually by more staring :)
Andrew Helwer
Andrew Helwer महिन्यापूर्वी
It's conceptually difficult, hence explaining it is also difficult. The sort of thing you just have to stare at for a while.
Nax Eni
Nax Eni महिन्यापूर्वी
Maaf ya allah hamba liat ini.
Joseph C
Joseph C महिन्यापूर्वी
I am not a programmer at any rate but at 9mins, this video explains to me that quantum computing built a language(mathematical) to utilize superposition as a means to "computate" possible outcomes in exponents of 2 states possible at the same time that when combined with algorithms with another cubit will speed up computations by being able to perform more instead of on at a time like a classical computer. So this tells me, to treat it akin to getting a solution like a classical computer, a compute scientist will need to learn this way of modeling his "question" to the the right answer.
Andrew Helwer
Andrew Helwer महिन्यापूर्वी
It is sort of like that but there is an important bottleneck: although we compute with an exponential number of amplitudes while the qbits are entangled or in superposition, in order to actually get information out of the system we have to measure it - and we can only get out as many bits of information as there are qbits. This huge bottleneck means we have to be very tricky about how we design our algorithms, and can only get a speedup in certain cases rather than in general.
Tony Faulknor
Tony Faulknor महिन्यापूर्वी
Have you guys have you found God yet? scuse me 'iggy boson. When's the last time you spoke to Higgs Boson? I think Quantum Physics is a real waste of time and life, eh? it's just up the garden path physics. It's really smart people trying to find ways to hide more and more shit, you become Gods when you multiply the deceived amounts you. Thank God the real Gd coming back, it's known as the light, by which, no other light could have been made, including this AI, 2nd light, light that you're all currently having a lovefest with.
Felipe Constantino
Felipe Constantino महिन्यापूर्वी
This is pretty cool. I'm amazed
Ean Erickson
Ean Erickson महिन्यापूर्वी
These machines are going to have a giant market: this guy and his friends.
Sachin Thakkar
Sachin Thakkar महिन्यापूर्वी
7:44 Dinesh spotted from silicon valley 😂😂
WheelsakaSpeedy महिन्यापूर्वी
32:22 - "Imagine I show up on your doorstep and I give you a package, its just a black box that has a function on one bit, what a horrible present" 😂
azeddine benabbou
azeddine benabbou महिन्यापूर्वी
Very nice presentation. Thank you
Bacon Invader
Bacon Invader महिन्यापूर्वी
finally. I've watched and read so many things that just talk about the fact that superposition is a thing without actually going in to what it means for computation
Ghryst VanGhod
Ghryst VanGhod महिन्यापूर्वी
stfu n show me the quantum gaming
Welcome Guest
Welcome Guest महिन्यापूर्वी
And he’s confident enough to even sip out of a soda can sideways after explaining complex quantum dimensions.. “Are you all getting this?” Haha.. Great video
The Great Dream
The Great Dream महिन्यापूर्वी
Pretty nifty indeed! What I'm suspecting is that qubits can be thought of as unit quaternions, which for me at least, makes it a lot more intuitive to think about them. But maybe for most people it wouldn't be! But if they're points on a 3-sphere, that sort of makes it make sense to me that you might have opposite "poles" of a sphere - the two different half and half superpositions - which project to the same ultimate value but are different - it's just phase again, like polarization.
Andrew900460 महिन्यापूर्वी
So..... The probabilities, are the states.....
Andrew Helwer
Andrew Helwer महिन्यापूर्वी
Basically, except amplitudes aren't quite probabilities - they can be complex or negative, and the sum of their squares has to equal 1 rather than just their sum (as is the case with regular probabilities).
James Shelnutt
James Shelnutt 2 महिन्यांपूर्वी
I'm not an idiot I think but this stuff is over my head
Andrew Helwer
Andrew Helwer 2 महिन्यांपूर्वी
You can do it! Anything specific you're having trouble with?
atul kumthekar
atul kumthekar 2 महिन्यांपूर्वी
nice video! good collection of topics and good presentation... I tried to access quantumexperience.ng.bluemix.net/ but no luck.
atul kumthekar
atul kumthekar 2 महिन्यांपूर्वी
@Andrew Helwer Thank you, this one seems to be working.
Andrew Helwer
Andrew Helwer 2 महिन्यांपूर्वी
Looks like they moved it: quantum-computing.ibm.com/
Eric Funderburg
Eric Funderburg 2 महिन्यांपूर्वी
Hey buddy, you look really handsome and have great hair! Do you know anything about computers?? No!? Well that's okay, we'll figure that stuff out later. #Microsoft
Yixuan Lee
Yixuan Lee 2 महिन्यांपूर्वी
This is not for any scientist, why is the guy explaining matrix
Andrew Helwer
Andrew Helwer 2 महिन्यांपूर्वी
Some people forget their linear algebra!
Sunzalea 2 महिन्यांपूर्वी
How did i fall asleep to this?
kurt Mora
kurt Mora 2 महिन्यांपूर्वी
"So you can send entangled Qbits by laser?" "Yes" "Okay that's even cooler" love that guy 😂
Andrew Kim
Andrew Kim 2 महिन्यांपूर्वी
I tried to read so many articles to get an intuition about how QC works, but it seems it just never rings the bell. I honestly think the best part in this vid for me is when he said "shut up and do the math". Really over the years I've been reminded again and again how "trying to understand it intuitively" is nothing if not backed up by concrete and hard working math/calculations.
Indian Girl
Indian Girl 2 महिन्यांपूर्वी
Yang pilih allah like.
Amiko Malania
Amiko Malania 2 महिन्यांपूर्वी
In case you're looking for slides www.microsoft.com/en-us/research/uploads/prod/2018/05/40655.compressed.pdf
Andrew Helwer
Andrew Helwer 2 महिन्यांपूर्वी
Saul Covarrubias
Saul Covarrubias 2 महिन्यांपूर्वी
Pretty neat, quantum computing is just an application of vector and tensor algebra or potentially just an application of probability theory?
Andrew Helwer
Andrew Helwer 2 महिन्यांपूर्वी
It's kind of an extension of probability theory, in that instead of all the probabilities summing to 1, the absolute value squared of probabilities (amplitudes) sum to 1. 2-norm vs. 1-norm.
pizzaplanet 22
pizzaplanet 22 2 महिन्यांपूर्वी
Why am i here don't even know quantum computing
Matt D
Matt D 2 महिन्यांपूर्वी
I finally found the smart people
QMG The Quantum Mechanics Guy
QMG The Quantum Mechanics Guy 2 महिन्यांपूर्वी
This video was my introduction to quantum computing....now, I was able to recreate the "delayed choice quantum eraser experiment" using the IBM computer....A million thanks to this video. Here is my paper: www.academia.edu/resource/work/44494928
Love Night
Love Night 2 महिन्यांपूर्वी
1:40 dog: help my please
ronald jorgensen
ronald jorgensen 2 महिन्यांपूर्वी
i can build what circuit or draw it up for intel chip production now ?
ronald jorgensen
ronald jorgensen 2 महिन्यांपूर्वी
can you show this in octal and hexidecimal ?
ronald jorgensen
ronald jorgensen 2 महिन्यांपूर्वी
pulse them to rms integers in magnetic beam control in CRT to see the majick happen in real time subset infinity in all calculus
Utkarsh Dubey
Utkarsh Dubey 2 महिन्यांपूर्वी
The doubt at 1:09:45, the language of probability isn't accurate. Well with the small domain of my understanding, I can vouch for the fact that Accuracy can't be an artifact of probability.
Joe Kalani
Joe Kalani 2 महिन्यांपूर्वी
I dont know how to even use excel and can barely use MS word, I have no idea how I got here but I cant leave
Enlightened Penguin
Enlightened Penguin 2 महिन्यांपूर्वी
40:00 The confusion here is that there are two qbits, one named 'input' and one named 'output', but these two are both passed into the quantum black box to be operated on. The 'input' qbit is left unscathed after the black box, but it is the 'output' qbit which is rewritten with the value of [the possibly nonreversible function f : applied to whatever the value of our 'input' bit is]
Baby Dragon
Baby Dragon 2 महिन्यांपूर्वी
UMMMM THIS WAS ON MY BIRTHDAY WTF I'm intrigued and curious and tripped out
compuholic82 2 महिन्यांपूर्वी
Great talk. But at first I had trouble understanding why his "reversible set to zero" function is built the way it is. So to anyone who is asking himself the same question, here is my explanation: The non-reversible way of writing "set to zero" is the matrix [[1,1], [0, 0]] which is of course is rank-deficient so it is not invertible. So you need to avoid a row of zeros in the matrix while keeping all rows linearly independent from one another. The way to do that is to write the matrix in the following way [[0,0,1,1], [0,1,0,0], [0,0,1,0], [0,0,0,1]]. The last two rows perform what he labelled Input->Input' in his diagram. The first two rows perform the actual "set to zero" operation (labelled Input->Output' in his diagram), assuming that the first two values of the input vector are [1, 0, ...] which of course corresponds to the |0> input that is confusingly labelled "Output" in his diagram. I really wish he had written the operation as a matrix. Then it would have been clear to me immediately. That is also the reason why the "actual input" is the second parameter but the "actual output" is the first parameter: To get the [[1,1], [0,0]] submatrix away from the main diagonal.
Lance Coleman
Lance Coleman 2 महिन्यांपूर्वी
this new bible is as bad as the the bible bible ... yawn
Mehmet Sarıgül
Mehmet Sarıgül 2 महिन्यांपूर्वी
Thanks for sharing this video. It was the thing I am looking for. But I have two questions; How do we know if they are not pre-coordinated? and how other qbit collapse when I measure the other one?. Do "Collapse" means it take that value already or in the same time?
Mehmet Sarıgül
Mehmet Sarıgül 2 महिन्यांपूर्वी
@Blue Traveller let's say i measure one of them. Then the other one is still in superposition. Is that mean whenever l measure it i will find the same value?
Andrew Helwer
Andrew Helwer 2 महिन्यांपूर्वी
We know they're not pre-coordinated because we've devised an experiment to test for this - look up Bell Test experiments or check out this blog post I wrote: ahelwer.ca/post/2018-12-07-chsh/
Mike 2 महिन्यांपूर्वी
Why can’t I stop watching this?
Brad Dark
Brad Dark 2 महिन्यांपूर्वी
ahhh yes build a big black box that is absolutely going to become self aware and hmmmm wonder what happens then
alan 2 महिन्यांपूर्वी
Guys, never trust "the math" You can make an equation to express anything. If none of the analogies make sense, it's because they're being used to describe something not real.
Andrew Helwer
Andrew Helwer 2 महिन्यांपूर्वी
Yes, equations can express anything. The specific equations presented here accurately model all observed quantum-mechanical phenomena. Thus if you stay within the model and follow its rules, you can trust the math.
BOMO 2 महिन्यांपूर्वी
I wish I could be smart, but I'm deformed💩
Fred Phillips
Fred Phillips 2 महिन्यांपूर्वी
On the Deutche Oracle confusion. Would it be fair to say that we are defining a variable called Output that is initally zero?
Andrew Helwer
Andrew Helwer 2 महिन्यांपूर्वी
Yes that would be accurate.
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