Moore’s Law-
Moore's Law is the difficulty in increasing the overall size of a system (like an organism) because surface area increases slower than volume, thus the total available input needs to account for a lot more volume and needs to have a more complex transport system.
are at best poor quality
Wires are really bad for transferring quantum data (which is why it requires an optic wire in the best case)
immediate threat to all RSA encryption
impact
The horizontal axis is the length of the number to be factored. The steep curve is nFS, with the marked point at L = 768 requiring 3,300 CPu-years. The vertical line at L = 2048 is nIST’s 2007 recommendation for RSA key length for data intended to remain secure until 2030. The other lines are various combinations of quantum computer logical clock speed for a three-qubit operation known as a Toffoli gate (1Hz and 1MHz), method of implementing the arithmetic portion of Shor’s algorithm (bCDP, D, and F), and quantum computer architecture (nTC and AC, with the primary difference being whether or not long-distance operations are supported). The assumed capacity of a machine in this graph is 2L2 logical qubits. This figure illustrates the difficulty of making pronouncements about the speed of quantum computers.
The kind of architecture utilized by the quantum computer makes a HUGE difference in how fast the execution of the algorithm will be.
guarding against loss of fragile quantum data
If there is a way to protect against this, it would greatly appease the very skeptical author from before.
General-purpose quantum computers capable of efficiently solving difficult problems will be physically large, comprising millions or possibly billions of quantum bits in distributed systems.
I'm guessing this may be compressed, like how supercomputers used to be giant and now can fit on a phone.
Structurally, when built, a “quantum computer” will in fact be a hybrid device, with quantum computing units serving as coprocessors to classical systems.
So it basically uses quantum computing for very specialized tasks, while it's essentially a regular computer? (Sort of like how a GPU works). This might be what actually "replaces" classical computer, just including a separate chip that is good at calculating certain, specialized things
factoring of large numbers
Shor's algorithm again
accurate enough
This is a key problem with quantum computers as per other article
commercially viable systems
This was in dispute in some of the articles I've read (although those may have been out of date).
in reducing the quantum bits at a practical level,
Reducing the quantum bits enough would potentially make it possible to break the algorithm with the quantum computers that are currently avaialble today.
Because of the parallelism achievable with quantum computers, many existing public key cryptographic sys-tems (ELGamal, RSA, ECC, etc.) are no longer secure.
This is an interesting statement to say right after improving the algorithm responsible for this
propose a new polynomial-time quantum algorithm for directly recovering the RSA plaintext M from the ci-phertext C without explicitly factoring the modulus n, and hence break the RSA public-key cryptosystem.
A small but seemingly signiiicantly detail to skip in the original algorithm
The new algorithm has the following properties: 1) recovering the RSA plaintext M from the ciphertext C without factoring n; 2) avoiding the even order of the element; 3) having higher success probability than Shor’s; 4) having the same complexity as Shor’s.
An improvement on the well-known algorithm
hor proposed a quantum polynomial-time integer factorization algorithm to break the RSA public-key cryptosystem
I know well about Shor's algorithm now
2017
One last really recently written article to show the advances that quantum computing has made recently. I most likely won't be able to fully understand most of this though.
None of this entire article really means anything to me except that it is a way to decrease the error in quantum computing. This seems like it might be pretty poorly written too....
Lack of exploration in core topology, this paper claims.
This method uses a naturally fractal structure for quantum state calculation to better remove chance of error.
Another extremely detail-oriented, yet very very recent, article on the topics
The slower the particles are moving (which is based on temperature) the less prone to error the quantum calculations are essentially.
Uses cryogenic technology to improve the error rate of the quantum computers and make the qubits go into a more stable superposition.
"opportunites include, prime factorization, quantum simulations for synthesis of drugs, and complex optimizations".
This is an INCREDIBLY detail-oriented and dense paper about the exact way to improve quantum computing, but this is a really good recent and peer-reviewed paper.
3.Canwe build one?
Unimportant for me from here on out
efresh the ancilla bits that are used to compute the syndromein order to achieve a reasonable transmission rat
It is also bounded by resources and the error of not having enough repeaters or stations in the network
it has a serious limitation: the signal becomes attenuated in thecommunication channel (such as an optical bre), andit cannot be ampli ed
The security of perfect quantum algorithm is speed and bandwidth bounded, meaning it can't ever be really improved to be faster.
If we could build such a devicereasonably soon, would it be useful? Would it have commercial potential?
Do quantum computers today have commerical potential? IBM does have a quantum cloud server
I feel that a deep understanding ofwhyquantum algorithms work is still lacking.
Potentially they are still not completely understood to this day
no quantumalgorithm can solve the problem faster than time of orderpN
There must be a separate class of problems specifically for Quantum computers for P and NP.
a problem whose solution, though perhaps hard to nd, is easyto verify)
Turing reducability from the earlier article
Grover's very clever method for search-ing an unsorted database (Grover 1996). In a database containingNitems, the oneitem that meets a speci ed criterion can be found with a quantum computer in a timeof orderpN. On a classical computer, the database search would take a time of orderN,
Grover's algorithm is one that can find an item in an unsorted database in sqrt(N)??? Crazy
et sometimes we save much e ortby invoking the brute force method rather than the one that requires exceptionalcleverness
The idea of over-engineering
to simulatethe behaviour of quantum systems
The "can computers simulate physics" question from the earlier article!
I do not expect factoring to be one of the most important applications ofquantum computing
So far it seems like it still may be one of the most important applications today, especially with the increased focus on cryptography
N3
The complexity of N^3 is ridiculously good for this kind of an algorithm
Howwill we build on
This question is also less important now that we already have built one
Canwe build one?
We know now that it is possible
we should thus try to imagine how they will be used in the future.
"Do the pros outweigh the cons?"
199
Pretty relatively old article on this topic
The author's argument is that the error inherent in the quantum computers of today are so egregious that there is no way that it will be feasible and profitable in the near future
Many interesting graphics and not-so informative graphs...
Talks about the history of quantum computing like most of the other articles
"Arms race" both with cryptography and with other fields apparently
Written in 2019, a very recent article
2000
Most recent article is from 2000
Any practical implementation of Shor’salgorithm is years away.
We're a lot closer today than when this was written
This will cause both Person Aand Person B to have different values fortheir secret keys. As a check for eaves-dropping, Persons A and B can compare
like tamper-evident packaging
just trying to determine the polariza-tion destroys it[6].
if you tried to read someone's data it would immediately change
quantum parallelism
like regular parallelism in computing, but quantum computing forces you to do operations on entire superpositions instead of single values
represents both zero and one simultane-ously, and therefore exists in multiplesstates at the same time.
this is why quantum computers can't really be used like regular computers
that the two parti-cles had opposite spins
kind of like two gears spinning together, you know that they always spin opposite even if you don't know the spin of one of them
on a verysmall scale
Quantum literally means "very small" in latin
he article begins with anoverview of three quantum theory con-cepts: superposition, entanglement, andthe measurement problem.
Already read articles about most of these quantum phenomena
Talks a lot about the different actions and algorithms that can combat these new developments
Quantum Entanglement between qubits is "spooky action". it can't exchange information, but it can reduce environmental noise
The quantum bit is the same except that its state can exist in between and will be inconsistent when measured
Currently quantum computers can only be built for their specific purpose
Things that can be done very easily on classical computers are much more difficult using quantum computers... They can't replace them then?
US National Security Agency even stressed how important it was to move to quantum-resistant algorithms.. big deal.
Table shows how much of current cryptography is rendered useless by quantum algorithms
T)=n0)+.311
the rest of the article goes into the math of it, which I'm not as interested in right now
it is as if somehow or other it appears as if theprobabilities would have to go negative" .
that makes no sense to me
ll potential com-putation paths are taken simultaneously in a single piece of hardware, in accord with thesuperposzti.on principleof quantum mechanics
superpositions contain all possible positions and states of a particle
In a classical probabilistic calculation
Classical "randomness"
a mere ten years ago
And is now reaching prominence
1 October 1994
Quantum computing originated a lot earlier than I expected
That no quantum computer has yet been built should not be considered more fundamen-tal an issue than was the fact that no classical computers existed when Turing set forth hismodel of computation
outdated. many quantum computers have now been built
actable problems should be broadened to include thosethat can be solved in expected polynomial time by probabilistic machines
Quantum computing superpositions and randomness give way to more possibly polynomial algorithms for problems
quantum cryptography [3, 4, 8], which exploits Heisenberg's uncertaintyprinciple to establish a communications channel on which undetected eavesdropping is im-possible even if the eavesdropper has unlimited computing power, indeed even if she hasaquantum computer at. her disposal
So quantum computing CAN be used to be resistant to other quantum computing. (everyone needs QC to be safe eventually?)
ut they becomevulnerable if their keys are exchanged with public-key techniques
Things can be indirectly affected because RSA is used by so much of the current system
will crumble
Very definitive statement here...
any efficient simulation of physics on a classical computer—
So how do all video games simulate physics so well? Using tricks?
Richard Fevnman
One of the greatest "explainers" of his time. I once watched a video of him explaining how a train stayed on the tracks when making turns. It was really cool