[ExI] teachers
efc at swisscows.email
efc at swisscows.email
Tue Sep 19 20:56:06 UTC 2023
Hello Jason,
On Mon, 18 Sep 2023, Jason Resch via extropy-chat wrote:
> (GRW). These both say that observation/measurement is not what causes collapse, but rather the system will spontaneously collapse
> when the size of the system gets too large. It would imply a fundamental upper bound to how large a quantum computer could be. It
> implies a theory that gives different predictions, which in principle could be tested (such as the largest size particle we could
> observe an interference effect from in a two-slit experiment).
Wouldn't that be something? QM being replaced or tweaked in our
lifetime!
> And as you pointed out, IBM was at 433!
>
> I too was surprised by that. It was 100-something last time I looked.
Well, let's see if they break the 1000 qubit limit by 2024!
> So that shows the dangers of AI!
> Oh, and IBM precicts 1000 within a year or so. Adding to that, has any
> real and useful work been done with these quantum computers such as
> actually cracking an RSA key? How far away are we from crackin a 1024
> bit key? Seems to me that some intelligence services will soon start to
> sweat! ;)
>
> We are probably a few decades away at the current pace. These qubits are not reliable enough yet to run an algorithm like Shor's
> algorithm for that many qubits. Quantum Error Correction will likely be required, and then we would need some multiple factor
> (perhaps dozens or hundreds) of qubits, beyond the size of the key, for it to work.
>
> If the qubits were perfectly reliable, Shor's algorithm only needs 2N qubits, where N is the number of bits in the RSA modulus.
Exciting times! =)
Best regards,
Daniel
>
> Jason
>
>
> > I do wish that a strong proponent of the other interpretations would take
> > the stage on the list. I think it would be incredibly interesting to hear
> > and compare.
> >
> > In the other thread I give my assessment of why we don't find many strong proponents of CI.
>
> Will have a look!
>
> Best regards,
> Daniel
>
>
> >
> > Jason
> >
> >
> > Best regards,
> > Daniel
> >
> >
> > On Sat, 16 Sep 2023, Jason Resch via extropy-chat wrote:
> >
> > > I asked the question using Bing's chat. I don't know how this AI compares to the others, but these are the
> answers it
> > provided for:
> > > Copenhagen Interpretation:
> > > (426 words, 3 links)
> > >
> > > Shor’s algorithm is a quantum algorithm that can factor large numbers exponentially faster than classical
> > algorithms. It
> > > does so by finding the period of a function, which is a problem that is believed to be hard for classical
> > computers. The
> > > algorithm uses a quantum computer to represent every number from 0 to 2^4000 - 1 using qubits, and then
> performs
> > a
> > > distinct mathematical calculation against each one to get a distinct result. Finally, it uses
> interference to
> > cancel out
> > > the wrong answers to produce a correct result 1.
> > >
> > > In quantum mechanics, the Copenhagen interpretation is one of the most widely accepted interpretations.
> According to
> > this
> > > interpretation, the wave function of a quantum system describes all possible states of the system. When a
> measurement
> > is made,
> > > the wave function collapses into one of these states with a probability given by the Born rule 2.
> > >
> > > In Shor’s algorithm, the quantum computer uses qubits to represent all possible states of the system. These
> states are
> > > represented by complex numbers, which are stored in the amplitudes of the qubits. The number of possible states
> that
> > can be
> > > represented by n qubits is 2^n. In other words, each qubit can represent two possible states (0 or 1), and n
> qubits can
> > > represent 2^n possible states 3.
> > >
> > > The number of qubits required to factor a number of size N using Shor’s algorithm is proportional to log(N).
> For
> > example, if N
> > > has 4000 bits, then approximately 8000 qubits are required . While this may seem like an enormous number of
> qubits, it
> > is
> > > important to note that these qubits do not represent physical objects like atoms. Rather, they are abstract
> > mathematical
> > > objects that exist in a superposition of states until they are measured.
> > >
> > > When a measurement is made on a quantum system, the wave function collapses into one of its possible states
> with a
> > probability
> > > given by the Born rule. In Shor’s algorithm, measurements are made on the qubits at various stages in order to
> extract
> > > information about the period of the function being analyzed. The interference between different paths in the
> quantum
> > > computation allows for incorrect answers to cancel out and correct answers to be amplified .
> > >
> > > In summary, Shor’s algorithm uses a quantum computer to represent all possible states of a system using qubits.
> These
> > qubits do
> > > not represent physical objects like atoms, but rather abstract mathematical objects that exist in a
> superposition of
> > states
> > > until they are measured. The interference between different paths in the quantum computation allows for
> incorrect
> > answers to
> > > cancel out and correct answers to be amplified.
> > >
> > >
> > > Many-Worlds:
> > > (234 words, 0 links)
> > >
> > > Shor’s algorithm is a quantum algorithm that can factor large numbers exponentially faster than classical
> > algorithms. It
> > > works by finding the period of a function, which is used to factor the number. The algorithm requires a
> quantum
> > computer
> > > with a sufficient number of qubits to represent the number being factored.
> > >
> > > In Shor’s algorithm, the qubits are used to represent every number from 0 to 2^4000 - 1, and a distinct
> mathematical
> > > calculation is performed against each one to get a distinct result. The qubits are then measured, and the
> result is
> > used to
> > > determine the period of the function. Finally, interference is used to cancel out the wrong answers to produce
> a
> > correct
> > > result.
> > >
> > > The question of where these computations are being performed is an interesting one. In the many-worlds
> interpretation
> > of
> > > quantum mechanics, there are an infinite number of parallel universes, each containing a different version of
> reality.
> > In this
> > > interpretation, the computations are being performed in all possible universes simultaneously. The interference
> that
> > occurs in
> > > Shor’s algorithm is due to the fact that some universes will produce correct results while others will not. The
> correct
> > results
> > > are then selected by interference between these universes.
> > >
> > > It’s important to note that this is just one interpretation of quantum mechanics, and there are other
> interpretations
> > that do
> > > not involve parallel universes. However, the many-worlds interpretation is one of the most popular and widely
> studied
> > > interpretations.
> > >
> > >
> > > Quantum Bayesianism:
> > > (376 words, 4 links)
> > >
> > > Quantum computers are designed to harness the principles of quantum mechanics to perform complex
> calculations.
> > Unlike
> > > classical computers that use bits to represent information as either 0 or 1, quantum computers use
> qubits, which
> > can
> > > represent multiple states simultaneously through a phenomenon called superposition1. This allows quantum
> > computers to
> > > perform computations on a vast number of possibilities in parallel.
> > >
> > > In the case of Shor’s algorithm, the quantum computer uses its qubits to represent every number from 0 to
> 2^4000 - 1
> > > simultaneously2. This is made possible by exploiting the superposition property of qubits. By performing a
> distinct
> > > mathematical calculation against each possible number, the quantum computer obtains a set of results that
> contain both
> > correct
> > > and incorrect answers.
> > >
> > > Here’s where interference comes into play. Interference is another fundamental principle of quantum mechanics.
> It
> > allows the
> > > quantum computer to manipulate the probability amplitudes associated with each possible result3. Through
> carefully
> > designed
> > > operations, the quantum computer can enhance the probability amplitudes of correct answers while suppressing
> those of
> > incorrect
> > > answers. This process is analogous to constructive and destructive interference in wave phenomena.
> > >
> > > The final step involves measurement, which collapses the superposition of qubits into a single state. The
> measurement
> > process
> > > reveals one of the possible results, and with high probability, it will be a correct factorization of the input
> > number4. The
> > > computations are not performed in a physical sense on atoms or particles but rather through the manipulation of
> qubits
> > and
> > > their associated probability amplitudes.
> > >
> > > It’s important to note that while Shor’s algorithm demonstrates the potential power of quantum computers for
> certain
> > tasks,
> > > building practical large-scale quantum computers is still an ongoing scientific and engineering challenge.
> Researchers
> > are
> > > actively working on improving qubit stability, reducing errors, and developing error-correcting codes to make
> quantum
> > computers
> > > more reliable and scalable.
> > >
> > > Regarding Quantum Bayesianism, it is an interpretation of quantum mechanics that emphasizes subjective
> probabilities
> > and
> > > Bayesian reasoning. It provides an alternative perspective on how to interpret and understand quantum phenomena
> but
> > does not
> > > directly address the technical aspects of how quantum computers work.
> > >
> > > I hope this explanation helps shed some light on how quantum computers can represent and process an enormous
> number of
> > > possibilities simultaneously while leveraging principles from quantum mechanics. Let me know if you have any
> further
> > questions!
> > >
> > >
> > >
> > >
> > >
> > >
> > > I leave it to the reader to consider which answer explained the most and was the least obfuscatory.
> > >
> > > I note that only one answer even addresses my question of "where are the computations performed?"
> > >
> > > Jason
> > >
> > >
> > >
> > > On Sat, Sep 16, 2023 at 11:34 AM BillK via extropy-chat <extropy-chat at lists.extropy.org> wrote:
> > > On Sat, 16 Sept 2023 at 15:44, Jason Resch via extropy-chat
> > > <extropy-chat at lists.extropy.org> wrote:
> > > >
> > > > Interesting results Bill.
> > > > If you are interested, you might try Deutsch's question on it. For example, prompting it with something
> like:
> > > >
> > > > ------
> > > > "A quantum computer of 8000 qubits can, using Shor's algorithm, factor a 4000-bit number. This
> algorithm does
> > so by
> > > using the qubits to represent every number from 0 to 2^4000 - 1, and performing a distinct mathematical
> > calculation
> > > against each one to get a distinct result. Finally, it uses interference to cancel out the wrong answers
> to
> > produce a
> > > correct result.
> > > >
> > > > My question is: how is it that the quantum computer can represent 2^4000 distinct numbers, and perform
> 2^4000
> > distinct
> > > computations as it performs Shor's algorithm? Our universe only has some 2^260 atoms in it, there's not
> enough
> > atoms in
> > > the universe to represent all these values. So then, where are all these numbers being represented? Where
> in
> > reality are
> > > all these computations being performed? They must be done somewhere given we get the correct result,
> where are
> > they all
> > > happening?
> > > >
> > > > Please explain as best you can, answers to these questions assuming that XXXXX is the correct
> description of
> > quantum
> > > mechanics."
> > > > ------
> > > >
> > > > You could experiment having the AI answer this question in different sessions but change XXXXX to
> different
> > > interpretations, such as:
> > > >
> > > > "The Copenhagen Interpretation"
> > > > "Many-Worlds"
> > > > "Pilot-wave Theory"
> > > > "Quantum Bayesianism"
> > > >
> > > > The great thing about AI is we can have it answer these questions, where someone who believes in CI,
> for
> > example, might
> > > refuse to answer or ignore the question.
> > > >
> > > > Jason
> > > > _______________________________________________
> > >
> > >
> > >
> > > Well, the AI has already said that the different interpretations are
> > > not relevant, as the quantum computer just calculates regardless. It
> > > doesn't care what nearby humans might think is happening during the
> > > calculation.
> > > A bit like we use GPS without bothering about the continual
> > > Einsteinian relativistic adjustments that need to be applied.
> > >
> > > I fear that I am getting to the stage where I don't understand either
> > > the question asked or the answer received! :)
> > > Daniel has my sympathies. :)
> > >
> > > BillK
> > >
> > > Anyway, I asked the AI -
> > > How can a quantum computer represent 2^4000 distinct numbers, and
> > > perform 2^4000 distinct computations as it performs Shor's algorithm?
> > >
> > > The AI immediately replied (no thinking time required!) —
> > > A quantum computer can represent 2^4000 distinct numbers and perform
> > > 2^4000 distinct computations due to its unique property of leveraging
> > > quantum bits, or qubits, which can exist in multiple states
> > > simultaneously. Unlike classical bits that can only be in a state of 0
> > > or 1, qubits can be in a superposition of both states at the same
> > > time. This allows quantum computers to perform parallel computations
> > > on a massive scale.
> > >
> > > To understand how a quantum computer can represent such a large number
> > > of distinct numbers, we need to delve into the concept of qubit
> > > superposition. In classical computing, an n-bit register can represent
> > > 2^n distinct numbers by assigning each bit a value of either 0 or 1.
> > > In contrast, a quantum computer with n qubits can represent 2^n
> > > complex numbers simultaneously. This is because each qubit can be in a
> > > superposition of both 0 and 1 states, resulting in an exponential
> > > increase in the number of possible combinations.
> > >
> > > In the case of representing 2^4000 distinct numbers, a quantum
> > > computer would require a register consisting of 4000 qubits. Each
> > > qubit can independently exist in a superposition of both 0 and 1
> > > states, allowing for an astronomical number of possible combinations.
> > > The total number of distinct numbers that can be represented is given
> > > by 2^4000.
> > >
> > > Similarly, when performing Shor's algorithm on a quantum computer, the
> > > ability to represent and manipulate such a large number of distinct
> > > numbers becomes crucial. Shor's algorithm is a quantum algorithm that
> > > efficiently factors large integers, which has significant implications
> > > for cryptography.
> > >
> > > The key component of Shor's algorithm is the quantum Fourier transform
> > > (QFT), which enables the efficient computation of periodicity. By
> > > representing the input number as a superposition of different values,
> > > the QFT allows for simultaneous evaluation of multiple potential
> > > factors. This parallelism is what gives quantum computers their
> > > exponential speedup over classical computers for certain problems.
> > >
> > > During the execution of Shor's algorithm, the quantum computer
> > > performs a series of operations on the qubits, including modular
> > > exponentiation and QFT. These operations exploit the unique properties
> > > of qubits to efficiently find the factors of the input number. The
> > > final result is obtained through a measurement process that collapses
> > > the superposition into a single outcome.
> > >
> > > It is important to note that while a quantum computer can represent
> > > and perform computations on an exponentially large number of states,
> > > extracting useful information from these superpositions requires
> > > careful design and implementation. Quantum error correction techniques
> > > are necessary to mitigate the effects of noise and decoherence, which
> > > can disrupt the delicate quantum states.
> > >
> > > In summary, a quantum computer can represent 2^4000 distinct numbers
> > > and perform 2^4000 distinct computations by utilizing qubit
> > > superposition. The ability of qubits to exist in multiple states
> > > simultaneously allows for an exponential increase in the number of
> > > possible combinations, enabling quantum computers to tackle complex
> > > problems like factoring large integers using algorithms such as Shor's
> > > algorithm.
> > > ----------------------
> > >
> > > _______________________________________________
> > > extropy-chat mailing list
> > > extropy-chat at lists.extropy.org
> > > http://lists.extropy.org/mailman/listinfo.cgi/extropy-chat
> > >
> > >
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> >
> >
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