Quantum computing and the financial system

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I have read up on quantum mechanics and especially quantum computing looks really interesting. Not going to claim I even understand half that stuff, but it seems a breakthrough in this field seems somewhat likely in the next 1-2 decades. And if that happens no encryption will be safe. You could crack the best security from the outside in a matter of days?

Any more knowledgable people here on this subject? Or will this not be a big deal.

In case you are interested, here is some good reading material:

http://abyss.uoregon.edu/~js/21st_century_science/index.html (pretty basic and explains it quite well)

http://feynmanlectures.caltech.edu/III_toc.html (supplementary and also interesting to read)

These video's are also interesting:

This one explains quantum entanglement

Mindblowing stuff , recommended reading. You will see the world quite differently after reading that :) .  allthough you will have to break your brain a bit .

Recent break through:

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People have been working on this for a while now. There have been a number of breakthroughs but my understanding is that we're far away from building one of these things of any practical scale.

The connection to cryptography is interesting.  Two of the most widely used public key crypto schemes are the RSA cryptosystem and the Diffie-Hellman key exchange.  The security of the RSA system is based on the presumed difficulty of factoring very large numbers, particularly large numbers that are the product of two large primes.  The security of the Diffie-Hellman key exchange is based on the presumed difficulty of computing "discrete logarithms". (That is, your job is to find X given  B and N and the remainder when B^X is divided by N).    Neither of these problems has been proven to be computationally hard (in a technical sense of the word), but our best algorithms on classical computers are not efficient for large input.  "Efficient" in this case means "the running time is polynomial in the bit-length of the input".

Quite some time ago now, Peter Shor came up with efficient algorithms that would solve both of these problems efficiently on a quantum computer.  To my knowledge, the largest number yet factored on a quantum computer is 143=11 x 13, quite a ways off from the 300-600 digit monster numbers used in highly secure communications today.  But it's cool that they can make this work at all, and honestly use entanglement in doing so.

Also: Security doesn't die with the advent of quantum computers.  Various quantum cryptosystems have already been proposed and studied.

Cool stuff.

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Used to be a better value but NVEC or IBM would probably be the best way to play this in my opinion. I know there's some super computer companies (CRAY) or other similar companies but it's tough to invest in cutting-edge tech even if your overall thesis is correct. The best way to profit is usually as a consumer of the products.

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People have been working on this for a while now. There have been a number of breakthroughs but my understanding is that we're far away from building one of these things of any practical scale.

The connection to cryptography is interesting.  Two of the most widely used public key crypto schemes are the RSA cryptosystem and the Diffie-Hellman key exchange.  The security of the RSA system is based on the presumed difficulty of factoring very large numbers, particularly large numbers that are the product of two large primes.  The security of the Diffie-Hellman key exchange is based on the presumed difficulty of computing "discrete logarithms". (That is, your job is to find X given  B and N and the remainder when B^X is divided by N).    Neither of these problems has been proven to be computationally hard (in a technical sense of the word), but our best algorithms on classical computers are not efficient for large input.  "Efficient" in this case means "the running time is polynomial in the bit-length of the input".

Quite some time ago now, Peter Shor came up with efficient algorithms that would solve both of these problems efficiently on a quantum computer.  To my knowledge, the largest number yet factored on a quantum computer is 143=11 x 13, quite a ways off from the 300-600 digit monster numbers used in highly secure communications today.  But it's cool that they can make this work at all, and honestly use entanglement in doing so.

Also: Security doesn't die with the advent of quantum computers.  Various quantum cryptosystems have already been proposed and studied.

Cool stuff.

That is my understanding as well, while currently used crypto systems would become easy to break, quantum computing would make crpto systems possible that are unbreakable even in theory.  So cryptography would actually become more secure, not less.  Of course there could be sometime between when the older systems become breakable to the Feds and when the new quantum based systems are widely available.  This will not be a good situation.

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Let's go through the timeline. First quantum computer is built. Scientists kind of realize how bad it would be if the wrong people get their hands on it. So now they have to convince everyone to install new quantum security?

But ofcourse humans being humans, a good part of security will not be upgraded untill some bad stuff actually happened. Most people will not have a clue how all of it works. It could cause serious panic regarding technology? A lot of ignorant people not really knowing what is going on, and just to be safe, companies installing typewriters in their offices. I can see how people can become very suspicious of technology if that happens.

Aren't the russians doing that? They thought, screw all that computer security, we will just go back to typewriters. Might be good to buy companies that sell cabinets and typewriters  :) .

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Let's go through the timeline. First quantum computer is built. Scientists kind of realize how bad it would be if the wrong people get their hands on it. So now they have to convince everyone to install new quantum security?

But ofcourse humans being humans, a good part of security will not be upgraded untill some bad stuff actually happened. Most people will not have a clue how all of it works. It could cause serious panic regarding technology? A lot of ignorant people not really knowing what is going on, and just to be safe, companies installing typewriters in their offices. I can see how people can become very suspicious of technology if that happens.

Aren't the russians doing that? They thought, screw all that computer security, we will just go back to typewriters. Might be good to buy companies that sell cabinets and typewriters  :) .

I don't think it is a matter if simply convincing everyone. It will be a matter of cost. The first quantum computers will cost \$Millions.  You can bet the NSA will be one of the first to acquire one, as will Google and other large organizations.  It will be a long time however before you have one in your home to do quantum encryption on your hard disk.  Right now you and I can easily and at no extra cost with the hardware we already have encrypt our files so that even a large well funded organization or government can not gain access to them.  (Of course they could kidnap/arrest you, put a gun to your head (or simply threaten to throw you in a cage for a long time), and demand that you decrypt them, but that will always be possible).  Once the first quantum computers become available their will be no way to electronically keep secrets from some organizations.  And the problem with typewriters and filing cabinets is where/how to store them securely.

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Quantum entanglement basicly means that information is transmitted faster then light right?

If 2 entangled particles exist like a lightyear away from eachother in a superposition, and one is observed, you can predict in what state the other particle collapsed as well right?

The outcome for both is truly random, but when just one is observed, the superposition of the other one that is very far away instantly collapses too?

I still struggle to understand how they can make computers out of this.

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I still struggle to understand how they can make computers out of this.

Don't worry, so do the folks trying to build quantum computers.

You'll notice that whenever people announce they have built a quantum computer and performed a computation, there is some debate as to what they actually accomplished.  (i.e  Was it really a computation that breaks the classical computing paradigm?  Was there entanglement?)  This is a very hot research area, and has been for some time.  As is usual in those areas, the headlines are always more punchy than the details.

As for security of today's codes:  They've already built quantum computers, or at least toy models of them.  It's a question of scale and stability/duration.  A large-scale quantum computer will not magically appear in the labs of IBM, Google, or even the NSA.  Classical computers have increased in power at an amazing rate (exponentially), yet we've managed to stay ahead of the game.  Quantum computation would be an absolutely giant leap, but it doesn't instantly render all computations trivial.

Also note that there's a difference between breaking public key schemes like RSA and private-key schemes like AES. As it stands, cracking a 256-bit AES key would still take an awful long time on a quantum computer.  (Basically a quantum computer lets you search an unsorted database of size N in sqrt(N) time, whereas the best you could do on a classical computer is time N. So a 256-bit keyspace can be searched in time 2^128 versus time 2^256.  One number is colossally larger than the other, but the smaller one is still huge.)

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Quantum entanglement basicly means that information is transmitted faster then light right?

If 2 entangled particles exist like a lightyear away from eachother in a superposition, and one is observed, you can predict in what state the other particle collapsed as well right?

The outcome for both is truly random, but when just one is observed, the superposition of the other one that is very far away instantly collapses too?

I still struggle to understand how they can make computers out of this.

You can't transmit information faster than light with entanglement. Entanglement is essentially a way of saying that two particles are correlated, you will still need measurement of the whole system to transmit information which can only be done with classical slower than light communication.

For example, by conservation of angular momentum you can fix the total spin of a two-particle system to be zero. This tells us that if we measure one particle as spin "up", we must measure the other as spin "down". But, importantly, the measurement of "up" (or "down") is inherently probabilistic; one can interpret this by saying that it only takes on a definite value when you measure it. The main point being that quantum systems are fuzzy and probabilistic and can't be said to be "in" any definite state until you measure it.

Imagine that Alice and Bob take two particles entangled in this way and move 10 light-minutes away from each other. Alice the measures her particle and finds "up", so Alice immediately knows that Bob's particle is "down" without directly measuring it. If Bob measures his particle any time after Alice measures hers (so including times less than the 10 minutes it would take the light to reach him) he will definitely get "down". What brings it back down to Earth is that in order for Bob to know his particle will be measured as "down", he has to wait 10 minutes for a normal "classical" signal from Alice to get there.

There's no way to influence what spin you measure, so there's no way to "send" any information through the system to your colleague who is measuring the other particle. Only after you and your colleague come together and compare results do you find the correlation.

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I understand that it cannot be used for communication. But technically information is being transmitted instantly over extremly large distances right? Because even though we cannot use it to communicate, if one thing causes another thing to change, that is an information transfer in the world of physics right?

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I understand that it cannot be used for communication. But technically information is being transmitted instantly over extremly large distances right? Because even though we cannot use it to communicate, if one thing causes another thing to change, that is an information transfer in the world of physics right?

Information still isn't being transferred between the two photons because one photon isn't causing the other to change, the properties of the photons are already in place. It just so happens that when you as an observer measure one photon you discover what properties it has and are able to infer the properties of the other entangled photon.

Lets try a different metaphor; say that we have two different coins (same size but different colour) in a dark box. I take one coin without looking at it and you take another coin without looking at it. You travel to New York and I head to London, when we arrive at our destinations and look at our coins I will know what coin you have based on the one I have and you will know what I have based on what you have. However no information would have been transmitted between the coins, there is no cause and effect which is an important thing when defining information in physics. Information transfer is always bound by the speed of light.

And further more, if an observer tries to change one of the properties of an entangled photon like the spin it won't have any effect on the other photon and the entanglement between the two photons will be broken.

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I thought the properties are not in place before they are observed? Isn't that true randomness? What they will be before you observe them is truly random, and not determined right? And determined for both, the moment you interact with one?

I thought true randomness is one of the things that is so strange about quantum mechanics as this is not observable in the macroscopic world.

And why can i actually do this at home? I just tried it, and I got the wave pattern? Isnt there suposed to be loads of interference?

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I thought the properties are not in place before they are observed? Isn't that true randomness? What they will be before you observe them is truly random, and not determined right? And determined for both, the moment you interact with one?

I thought true randomness is one of the things that is so strange about quantum mechanics as this is not observable in the macroscopic world.

That was a simplified analogy to try and break it down but the coins we have will actually be in both states so nothing will be predetermined. So yes it is a random process and the act of looking at one coin will collapse the wavefunction but you still can't transmit information with it, you're simply measuring what you observe. You do collapse the wavefunction by measuring the state of your coin but its essentially a random distribution and you have no effect on what state the coin ends up in.

Changing the properties of any photon will break the entanglement between them. It becomes even trickier when consider frames of reference with people apart because its hard to determine who acted first, whether my coin has the properties it has because you looked at yours first or because I looked at mine before you. Maybe there will be a time when we can transmit information at speeds of faster than light with it but based on what we currently know and how we define information we don't consider entanglement to be a transfer of information at FTL speeds.

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Maybe you can explain this too.

If I shoot an electron through a vaccuum of 10 metres wide start to end. If It does not interact with light or other particles it behaves like a wave right? It is no where and everywhere at once at the same time. Basicly all that quantum magic.

Let's say you observe that vaccuum 8 metres after the starting point with a lightbeam of short wave length. There is a certain probability you will see it after x amount of time right? But in the quantum world, a particle can go from point a to b faster then the speed of light right? It has a certain chance of showing up at different times 8 metres after the starting point? By far the largest chance is exactly the time of light speed it takes to get there. But there is also a small chance you will see it before light could possibly get there right?

Basicly the probability distribution states that right after shooting into the vacuum it can show up anywhere in that vacuum if observed at that point. The probability is low, but it can happen?

Is this correct? I was under the impression that classical physics rules of relativity and newton can be broken in the quantum world like this. Or is this wrong?

Same thing for quantum tunneling. If there is an obstacle in the middle of that 10 metre vaccuum, it still has a probability of showing up after the obstacle, basicly teleporting itself through that obstacle?

UNLESS ofcourse it is observed before the obstacle. In that case it behaves like a particle and has a zero chance of going through the obstacle.

Hope I phrased the question clear enough

TIA :)

Edit: added a picture. The wave thing might not be drawn correctly or the correct shape, but whatever. Is the statement right in that picture?

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