<div dir="ltr"><div dir="ltr"><br></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Sun, Sep 17, 2023 at 4:49 PM efc--- via extropy-chat <<a href="mailto:extropy-chat@lists.extropy.org">extropy-chat@lists.extropy.org</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">Hello Jason,<br></blockquote><div><br></div><div>Hi Daniel,</div><div> </div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">
<br>
On Sat, 16 Sep 2023, Jason Resch via extropy-chat wrote:<br>
<br>
> Comparing<br>
> it with the nr of atoms is like comparing apples and oranges. Of course,<br>
> that begs the question... where is the information? How is it encoded? And<br>
> how does it interface with the physical world if it is not based on atoms?<br>
> <br>
> Exactly.<br>
<br>
So clearly it is stored in a different way, as the AI says, and we end<br>
up in the "shut up and calculate", "suspend judgment until more proof<br>
arrives", or any of the interpretations. I think that summarizes where<br>
we are right?<br></blockquote><div><br></div><div>Someone arguing from CI would say the information is stored in the qubits, and the qubits can each simultaneously be in a superposition of two states, such that N qubits can be in 2^N states, and when we apply an algorithm to these qubits in 2^N states, we obtain 2^N results, and when we measure/read this state, the wave function, which includes all these 2^N different results collapses, and we see just one of the possible results.</div><div><br></div><div>CI (at least realist versions) accepts the reality of this great multiplicity of 2^N results existing in a superposition. It just says that when any observer reads/measures/interacts with this quantum computer in 2^N states, that (2^N - 1) of the possibilities suddenly vanish, leaving just 1 behind. This accounts for what we see, but of course, leaves open a gaping hole of: how is our interaction with the quantum computer, any different from any of the interactions of the parts of the quantum computer itself, when we are all just atoms. What is measurement, physically? And why does it cause the 2^N - 1 other possibilities to simply disappear? Where do they go?</div><div><br></div><div>An anti-realist position (like some versions of CI or QBism) would say this superposition is just an abstraction, the wave function is just a calculating device, which doesn't describe anything real. But then, we have the even greater question of how does something purely abstract, which you say is not real, *do anything*, like produce a valid answer to a problem?</div><div><br></div><div>MW would say when anything (an observer, an electron, an atom, etc.) interacts with something in a superposition, that thing becomes part of the superposition. So when we read/measure/interact with the quantum computer, we obtain 2^N different outcomes of the observer, each one independently remembering having seen one of the distinct possible results of he 2^N states the quantum computer could be in. The other 2^N-1 states do not disappear, all states continue to exist and persist. The idea that the rest disappear, is only an *illusion* because each of the 2^N observers only remember seeing one of the 2^N possibilities (since there is a one-to-one correspondence that results from the superposition spreading to whatever interacts with it). There is no mystery of measurement, or collapse, or where or how the quantum computer does what it does, it is just systems of particles interacting deterministically according to the Shrodinger equation, and this math accounts for everything every observer remembers seeing.</div><div><br></div><div> </div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">
<br>
> 2. Is it possible to even build a quantum computer with 4000 qubits?<br>
> <br>
> According to the current theory, yes. Scott Aaronson has offered a $100,000 prize to anyone who can show him it's not possible.<br>
><br>
> Perhaps, once we approach 260 qubits, a limit will emerge?<br>
> <br>
> That could be, but it would require a different theory than current QM to explain. It would certainly excite the physicists to prove<br>
> QM is wrong.<br>
<br>
Would it have to be completely wrong, or would an adjustment be<br>
possible?<br></blockquote><div><br></div><div>It would be wrong, and refuted as a theory in the same sense that Newtonian Gravity is refuted by General Relativity.</div><div>General Relativity shows that Newtonian gravity is wrong, even though in most cases they yield similar results, to the extent that we can still use Newtonian gravity for most situations.</div><div><br></div><div>It could be that we only need to make a minor tweak to the Shrodinger equation to make it right, but there would be no escaping that this is different math (and a different theory).</div><div><br></div><div>Two examples of theories like this are objective collapse theories, such as: the <a href="https://en.wikipedia.org/wiki/Di%C3%B3si%E2%80%93Penrose_model">Diósi–Penrose model</a> and <a href="https://en.wikipedia.org/wiki/Ghirardi%E2%80%93Rimini%E2%80%93Weber_theory">Ghirardi–Rimini–Weber theory</a> (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).</div><div><br></div><div> </div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">
<br>
> Will<br>
> quantum computing be stuck in the "we'll have it in 10 years" loop like<br>
> fusion power?<br>
> <br>
> Lately the number of qubits in quantum computers has been growing as fast or faster than Moore's law. Unlike with transistor<br>
> miniaturization, I don't see any fundamental physical limits on the horizon coming up that would limit the number of qubits.<br>
<br>
And as you pointed out, IBM was at 433!</blockquote><div><br></div><div>I too was surprised by that. It was 100-something last time I looked.</div><div> </div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"> So that shows the dangers of AI!<br>
Oh, and IBM precicts 1000 within a year or so. Adding to that, has any<br>
real and useful work been done with these quantum computers such as<br>
actually cracking an RSA key? How far away are we from crackin a 1024<br>
bit key? Seems to me that some intelligence services will soon start to<br>
sweat! ;)<br></blockquote><div><br></div><div>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.</div><div><br></div><div>If the qubits were perfectly reliable, Shor's algorithm only needs 2N qubits, where N is the number of bits in the RSA modulus.</div><div><br></div><div>Jason</div><div> </div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">
<br>
> I do wish that a strong proponent of the other interpretations would take<br>
> the stage on the list. I think it would be incredibly interesting to hear<br>
> and compare.<br>
> <br>
> In the other thread I give my assessment of why we don't find many strong proponents of CI.<br>
<br>
Will have a look!<br>
<br>
Best regards, <br>
Daniel<br>
<br>
<br>
> <br>
> Jason <br>
> <br>
><br>
> Best regards,<br>
> Daniel<br>
> <br>
><br>
> On Sat, 16 Sep 2023, Jason Resch via extropy-chat wrote:<br>
><br>
> > 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<br>
> provided for:<br>
> > Copenhagen Interpretation: <br>
> > (426 words, 3 links)<br>
> ><br>
> > Shor’s algorithm is a quantum algorithm that can factor large numbers exponentially faster than classical<br>
> algorithms. It<br>
> > does so by finding the period of a function, which is a problem that is believed to be hard for classical<br>
> computers. The<br>
> > algorithm uses a quantum computer to represent every number from 0 to 2^4000 - 1 using qubits, and then performs<br>
> a<br>
> > distinct mathematical calculation against each one to get a distinct result. Finally, it uses interference to<br>
> cancel out<br>
> > the wrong answers to produce a correct result 1.<br>
> ><br>
> > In quantum mechanics, the Copenhagen interpretation is one of the most widely accepted interpretations. According to<br>
> this<br>
> > interpretation, the wave function of a quantum system describes all possible states of the system. When a measurement<br>
> is made,<br>
> > the wave function collapses into one of these states with a probability given by the Born rule 2.<br>
> ><br>
> > In Shor’s algorithm, the quantum computer uses qubits to represent all possible states of the system. These states are<br>
> > represented by complex numbers, which are stored in the amplitudes of the qubits. The number of possible states that<br>
> can be<br>
> > represented by n qubits is 2^n. In other words, each qubit can represent two possible states (0 or 1), and n qubits can<br>
> > represent 2^n possible states 3.<br>
> ><br>
> > The number of qubits required to factor a number of size N using Shor’s algorithm is proportional to log(N). For<br>
> example, if N<br>
> > has 4000 bits, then approximately 8000 qubits are required . While this may seem like an enormous number of qubits, it<br>
> is<br>
> > important to note that these qubits do not represent physical objects like atoms. Rather, they are abstract<br>
> mathematical<br>
> > objects that exist in a superposition of states until they are measured.<br>
> ><br>
> > When a measurement is made on a quantum system, the wave function collapses into one of its possible states with a<br>
> probability<br>
> > given by the Born rule. In Shor’s algorithm, measurements are made on the qubits at various stages in order to extract<br>
> > information about the period of the function being analyzed. The interference between different paths in the quantum<br>
> > computation allows for incorrect answers to cancel out and correct answers to be amplified .<br>
> ><br>
> > In summary, Shor’s algorithm uses a quantum computer to represent all possible states of a system using qubits. These<br>
> qubits do<br>
> > not represent physical objects like atoms, but rather abstract mathematical objects that exist in a superposition of<br>
> states<br>
> > until they are measured. The interference between different paths in the quantum computation allows for incorrect<br>
> answers to<br>
> > cancel out and correct answers to be amplified.<br>
> ><br>
> ><br>
> > Many-Worlds:<br>
> > (234 words, 0 links)<br>
> ><br>
> > Shor’s algorithm is a quantum algorithm that can factor large numbers exponentially faster than classical<br>
> algorithms. It<br>
> > works by finding the period of a function, which is used to factor the number. The algorithm requires a quantum<br>
> computer<br>
> > with a sufficient number of qubits to represent the number being factored.<br>
> ><br>
> > In Shor’s algorithm, the qubits are used to represent every number from 0 to 2^4000 - 1, and a distinct mathematical<br>
> > calculation is performed against each one to get a distinct result. The qubits are then measured, and the result is<br>
> used to<br>
> > determine the period of the function. Finally, interference is used to cancel out the wrong answers to produce a<br>
> correct<br>
> > result.<br>
> ><br>
> > The question of where these computations are being performed is an interesting one. In the many-worlds interpretation<br>
> of<br>
> > quantum mechanics, there are an infinite number of parallel universes, each containing a different version of reality.<br>
> In this<br>
> > interpretation, the computations are being performed in all possible universes simultaneously. The interference that<br>
> occurs in<br>
> > Shor’s algorithm is due to the fact that some universes will produce correct results while others will not. The correct<br>
> results<br>
> > are then selected by interference between these universes.<br>
> ><br>
> > It’s important to note that this is just one interpretation of quantum mechanics, and there are other interpretations<br>
> that do<br>
> > not involve parallel universes. However, the many-worlds interpretation is one of the most popular and widely studied<br>
> > interpretations.<br>
> ><br>
> ><br>
> > Quantum Bayesianism:<br>
> > (376 words, 4 links)<br>
> ><br>
> > Quantum computers are designed to harness the principles of quantum mechanics to perform complex calculations.<br>
> Unlike<br>
> > classical computers that use bits to represent information as either 0 or 1, quantum computers use qubits, which<br>
> can<br>
> > represent multiple states simultaneously through a phenomenon called superposition1. This allows quantum<br>
> computers to<br>
> > perform computations on a vast number of possibilities in parallel.<br>
> ><br>
> > In the case of Shor’s algorithm, the quantum computer uses its qubits to represent every number from 0 to 2^4000 - 1<br>
> > simultaneously2. This is made possible by exploiting the superposition property of qubits. By performing a distinct<br>
> > mathematical calculation against each possible number, the quantum computer obtains a set of results that contain both<br>
> correct<br>
> > and incorrect answers.<br>
> ><br>
> > Here’s where interference comes into play. Interference is another fundamental principle of quantum mechanics. It<br>
> allows the<br>
> > quantum computer to manipulate the probability amplitudes associated with each possible result3. Through carefully<br>
> designed<br>
> > operations, the quantum computer can enhance the probability amplitudes of correct answers while suppressing those of<br>
> incorrect<br>
> > answers. This process is analogous to constructive and destructive interference in wave phenomena.<br>
> ><br>
> > The final step involves measurement, which collapses the superposition of qubits into a single state. The measurement<br>
> process<br>
> > reveals one of the possible results, and with high probability, it will be a correct factorization of the input<br>
> number4. The<br>
> > computations are not performed in a physical sense on atoms or particles but rather through the manipulation of qubits<br>
> and<br>
> > their associated probability amplitudes.<br>
> ><br>
> > It’s important to note that while Shor’s algorithm demonstrates the potential power of quantum computers for certain<br>
> tasks,<br>
> > building practical large-scale quantum computers is still an ongoing scientific and engineering challenge. Researchers<br>
> are<br>
> > actively working on improving qubit stability, reducing errors, and developing error-correcting codes to make quantum<br>
> computers<br>
> > more reliable and scalable.<br>
> ><br>
> > Regarding Quantum Bayesianism, it is an interpretation of quantum mechanics that emphasizes subjective probabilities<br>
> and<br>
> > Bayesian reasoning. It provides an alternative perspective on how to interpret and understand quantum phenomena but<br>
> does not<br>
> > directly address the technical aspects of how quantum computers work.<br>
> ><br>
> > I hope this explanation helps shed some light on how quantum computers can represent and process an enormous number of<br>
> > possibilities simultaneously while leveraging principles from quantum mechanics. Let me know if you have any further<br>
> questions!<br>
> ><br>
> ><br>
> ><br>
> ><br>
> ><br>
> ><br>
> > I leave it to the reader to consider which answer explained the most and was the least obfuscatory.<br>
> ><br>
> > I note that only one answer even addresses my question of "where are the computations performed?"<br>
> ><br>
> > Jason<br>
> ><br>
> ><br>
> ><br>
> > On Sat, Sep 16, 2023 at 11:34 AM BillK via extropy-chat <<a href="mailto:extropy-chat@lists.extropy.org" target="_blank">extropy-chat@lists.extropy.org</a>> wrote:<br>
> > On Sat, 16 Sept 2023 at 15:44, Jason Resch via extropy-chat<br>
> > <<a href="mailto:extropy-chat@lists.extropy.org" target="_blank">extropy-chat@lists.extropy.org</a>> wrote:<br>
> > ><br>
> > > Interesting results Bill.<br>
> > > If you are interested, you might try Deutsch's question on it. For example, prompting it with something like:<br>
> > ><br>
> > > ------<br>
> > > "A quantum computer of 8000 qubits can, using Shor's algorithm, factor a 4000-bit number. This algorithm does<br>
> so by<br>
> > using the qubits to represent every number from 0 to 2^4000 - 1, and performing a distinct mathematical<br>
> calculation<br>
> > against each one to get a distinct result. Finally, it uses interference to cancel out the wrong answers to<br>
> produce a<br>
> > correct result.<br>
> > ><br>
> > > My question is: how is it that the quantum computer can represent 2^4000 distinct numbers, and perform 2^4000<br>
> distinct<br>
> > computations as it performs Shor's algorithm? Our universe only has some 2^260 atoms in it, there's not enough<br>
> atoms in<br>
> > the universe to represent all these values. So then, where are all these numbers being represented? Where in<br>
> reality are<br>
> > all these computations being performed? They must be done somewhere given we get the correct result, where are<br>
> they all<br>
> > happening?<br>
> > ><br>
> > > Please explain as best you can, answers to these questions assuming that XXXXX is the correct description of<br>
> quantum<br>
> > mechanics."<br>
> > > ------<br>
> > ><br>
> > > You could experiment having the AI answer this question in different sessions but change XXXXX to different<br>
> > interpretations, such as:<br>
> > ><br>
> > > "The Copenhagen Interpretation"<br>
> > > "Many-Worlds"<br>
> > > "Pilot-wave Theory"<br>
> > > "Quantum Bayesianism"<br>
> > ><br>
> > > The great thing about AI is we can have it answer these questions, where someone who believes in CI, for<br>
> example, might<br>
> > refuse to answer or ignore the question.<br>
> > ><br>
> > > Jason<br>
> > > _______________________________________________<br>
> ><br>
> ><br>
> ><br>
> > Well, the AI has already said that the different interpretations are<br>
> > not relevant, as the quantum computer just calculates regardless. It<br>
> > doesn't care what nearby humans might think is happening during the<br>
> > calculation.<br>
> > A bit like we use GPS without bothering about the continual<br>
> > Einsteinian relativistic adjustments that need to be applied.<br>
> ><br>
> > I fear that I am getting to the stage where I don't understand either<br>
> > the question asked or the answer received! :)<br>
> > Daniel has my sympathies. :)<br>
> ><br>
> > BillK<br>
> ><br>
> > Anyway, I asked the AI -<br>
> > How can a quantum computer represent 2^4000 distinct numbers, and<br>
> > perform 2^4000 distinct computations as it performs Shor's algorithm?<br>
> ><br>
> > The AI immediately replied (no thinking time required!) —<br>
> > A quantum computer can represent 2^4000 distinct numbers and perform<br>
> > 2^4000 distinct computations due to its unique property of leveraging<br>
> > quantum bits, or qubits, which can exist in multiple states<br>
> > simultaneously. Unlike classical bits that can only be in a state of 0<br>
> > or 1, qubits can be in a superposition of both states at the same<br>
> > time. This allows quantum computers to perform parallel computations<br>
> > on a massive scale.<br>
> ><br>
> > To understand how a quantum computer can represent such a large number<br>
> > of distinct numbers, we need to delve into the concept of qubit<br>
> > superposition. In classical computing, an n-bit register can represent<br>
> > 2^n distinct numbers by assigning each bit a value of either 0 or 1.<br>
> > In contrast, a quantum computer with n qubits can represent 2^n<br>
> > complex numbers simultaneously. This is because each qubit can be in a<br>
> > superposition of both 0 and 1 states, resulting in an exponential<br>
> > increase in the number of possible combinations.<br>
> ><br>
> > In the case of representing 2^4000 distinct numbers, a quantum<br>
> > computer would require a register consisting of 4000 qubits. Each<br>
> > qubit can independently exist in a superposition of both 0 and 1<br>
> > states, allowing for an astronomical number of possible combinations.<br>
> > The total number of distinct numbers that can be represented is given<br>
> > by 2^4000.<br>
> ><br>
> > Similarly, when performing Shor's algorithm on a quantum computer, the<br>
> > ability to represent and manipulate such a large number of distinct<br>
> > numbers becomes crucial. Shor's algorithm is a quantum algorithm that<br>
> > efficiently factors large integers, which has significant implications<br>
> > for cryptography.<br>
> ><br>
> > The key component of Shor's algorithm is the quantum Fourier transform<br>
> > (QFT), which enables the efficient computation of periodicity. By<br>
> > representing the input number as a superposition of different values,<br>
> > the QFT allows for simultaneous evaluation of multiple potential<br>
> > factors. This parallelism is what gives quantum computers their<br>
> > exponential speedup over classical computers for certain problems.<br>
> ><br>
> > During the execution of Shor's algorithm, the quantum computer<br>
> > performs a series of operations on the qubits, including modular<br>
> > exponentiation and QFT. These operations exploit the unique properties<br>
> > of qubits to efficiently find the factors of the input number. The<br>
> > final result is obtained through a measurement process that collapses<br>
> > the superposition into a single outcome.<br>
> ><br>
> > It is important to note that while a quantum computer can represent<br>
> > and perform computations on an exponentially large number of states,<br>
> > extracting useful information from these superpositions requires<br>
> > careful design and implementation. Quantum error correction techniques<br>
> > are necessary to mitigate the effects of noise and decoherence, which<br>
> > can disrupt the delicate quantum states.<br>
> ><br>
> > In summary, a quantum computer can represent 2^4000 distinct numbers<br>
> > and perform 2^4000 distinct computations by utilizing qubit<br>
> > superposition. The ability of qubits to exist in multiple states<br>
> > simultaneously allows for an exponential increase in the number of<br>
> > possible combinations, enabling quantum computers to tackle complex<br>
> > problems like factoring large integers using algorithms such as Shor's<br>
> > algorithm.<br>
> > ----------------------<br>
> ><br>
> > _______________________________________________<br>
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> ><br>
> ><br>
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