Shor's algorithm could be used to break public-key cryptography schemes, such as the widely used RSA scheme. RSA is based on the assumption that factoring large integers is computationally intractable.
Shor uses something called the quantum Fourier transform, or QFT. My challenge is, how can I explain the QFT to you without using any actual math? Hmmmm…
the quantum analogue of the inverse discrete Fourier transform.
https://www.scottaaronson.com/blog/?p=208
So that blog post is an excellent overview of how quantum Fourier transform works...
But last week JR Minkel, an editor at Scientific American, asked me to write a brief essay about how quantum algorithms do work, [The Shor algorithm [1,2] for efficiently factoring numbers on a quantum computer...Given an integer , find its prime factors]
Another way to think about this is in terms of interference. I mean, the key point about quantum mechanics — the thing that makes it different from classical probability theory — is that, whereas probabilities are always nonnegative, amplitudes in quantum mechanics can be positive, negative, or even complex. And because of this, the amplitudes corresponding to different ways of getting a particular answer can “interfere destructively” and cancel each other out.
the non-zero amplitudes are now associated with those values of the first register that are (very close to) multiples of Q/R [time period as phase].
Shor's period-finding algorithm relies heavily on the ability of a quantum computer to be in many states simultaneously. Physicists call this behavior a "superposition" of states. To compute the period of a function , we evaluate the function at all points simultaneously.
Quantum physics does not allow us to access all this information directly, though. A measurement will yield only one of all possible values, destroying all others.
Therefore, we have to carefully transform the superposition to another state that will return the correct answer with high probability. This is achieved by the quantum Fourier transform.
Non-commutative Fourier transform...
So now we get to Eddie Oshins:
http://www.quantumpsychology.com/pdf/Models-and-Muddles-Part-I.pdf
So back to non-commutative quantum Fourier Transform:
and so the momentum as "supermomentum" is inherently curved via general relativity (just as Penrose advocates and Gerard 't Hooft - both are Nobel physicists.
And this is what Professor Basil J. Hiley does as well. So at "zero" time there is already a future and past time overlapping as supermomentum curved spacetime.
In terms of music theory we think of this as subharmonics and overtone harmonics at the same time.
So just as Lenny Susskind argues for EPR=ER then at first the time is "entangled" as noncommutative phase of frequency and time but this is then translated or transduced into momentum spacetime as general relativity. Susskind says this enables then each side to go into the wormhole and meet in the "center." And so even though no signal can be sent through entanglement once the wormhole is created then indeed a signal can be inferred based on the convergence of the curvatures of spacetime. This inference is based simply on the two dimensional parameters as reading the entropy, via the Bekenstein Bound property.
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