[ExI] teachers

[BillK]

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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