[ExI] teachers
efc at swisscows.email
efc at swisscows.email
Sat Sep 16 21:08:08 UTC 2023
Thank you Jason, I think this was very enlightening and made it much more
clear what the differences are.
To answer your questions, I can only see some possibilities:
1. As the AI says, the information is not stored based on atoms. Comparing
it with the nr of atoms is like comparing apples and oranges. Of course,
that begs the question... where is the information? How is it encoded? And
how does it interface with the physical world if it is not based on atoms?
2. Is it possible to even build a quantum computer with 4000 qubits?
Perhaps, once we approach 260 qubits, a limit will emerge? Maybe, once we
start to hit more qubits, the model will break down? Who knows? Will
quantum computing be stuck in the "we'll have it in 10 years" loop like
fusion power?
3. It is based on atoms (or more fundamental particles) but we do not yet
understand it.
And when it comes to nr 1, then there are the interpretations, some are
more specific in their attemps at explaining MWI, and some "shut up and
calculate" and some probably (I don't know) have some other explanation.
And finally, some say "we don't currently know".
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.
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.
> ----------------------
>
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