21
$\begingroup$

I have heard a few times that one way of describing quantum computers is that they essentially use the computing power of their counterparts in alternate realities that they access through superposition. My first question is, of course,

  1. is this actually an accurate description of how quantum computers work, or just a misrepresentation?

Also, if it were to be assumed true and taken literally, then presumably all the possible outcomes of any given computation done would be experienced by each of these alternate realities. I have a few questions regarding the implications of this:

  1. Would it be correct to say that our universe essentially "spawns" these alternate realities to use for each computation, or that they all exist simultaneously in a higher dimension and only come into contact via the initiation of superposition by each computer at the same time?
  2. Would it be possible to create contact between universes via this connection? I'd expect that, if it was, it would be entirely random, and so not only would not cause any information transfer, it also would be completely undetectable, because the deviations would be within the expected probabilities of error rates - but is there any way to circumvent this?
$\endgroup$
  • 2
    $\begingroup$ Just a thought on: "2.Would it be correct to say that our universe essentially "spawns" these alternate realities to use for each computation". In the multiverse theories a new universe would split off every time a quantum event happens--which is constantly. For instance--every time a neuron fires in your brain, that involves a quantum event. Most likely an uncountable number of billions per second just for a flower sitting in the sun. $\endgroup$ – Bill K Nov 4 at 21:09
  • $\begingroup$ @BillK I guess that slipped my mind and I didn't factor it into my question. Thank's for pointing that out - I guess #2 is somewhat moot, then. $\endgroup$ – Snowshard Nov 4 at 23:23
  • $\begingroup$ Also, instead of thinking of it as "Using" different universes I've come to think of the result as "Probably observing the result from one of the specific universes with the correct solution" (Remember, quantum solutions are probabilistic, an infinite number of "you" (Yet a small fraction of infinite) will still end up universes with incorrect results). It all hurts my head. $\endgroup$ – Bill K Nov 5 at 21:41
  • $\begingroup$ @BillK If quantum computers simply observed the correct solution found by another quantum computer in a parallel universe, then that solution itself would have to have come about the same way, so shouldn't that imply an infinite recursion of observation, since every "correct solution found" would have to come from a new observation? $\endgroup$ – Snowshard Nov 5 at 23:34
  • $\begingroup$ The quantum computer didn't observe--you did. If the multi-universe theories are accurate, you aren't in one universe, you're in an infinite number and they are dividing all the time. The "You" who looks at the answer from a quantum operation is likely looking at the "Correct" one since nearly all outcomes fall into that category, but some of "You" will see different outcomes since all possible outcomes actually happen. At least that's one way to look at it that seems to work and resolve some of the weird problems with observations of quantum systems. $\endgroup$ – Bill K Nov 6 at 0:00
10
$\begingroup$

Question 1

This description lies somewhere between the two extremes of a theory and mysticism, depending on how amiable one is to the concept. David Deutsch is vocal proponent of the former, Lee Smolin of the latter (he categorizes it as "Mystical Realism").

The general idea was initiated by one of John Wheeler's PhD students, Hugh Everett III, in his 1957 doctoral thesis, which introduced relative state functions and provided the mathematical foundation for what is commonly known as the many-worlds interpretation (MWI).

In The Beginning of Infinity David Deutsch defines quantum computation as "Computation in which the flow of information is not confined to a single history." This definition is consistent with his expressed belief that MWI is a testable theory and the only theory with any power to explain the operation of quantum computers (here - note that Deutsch takes issue with the label MWI).

Deutsch is highly regarded and was the first to explicitly describe a universal quantum computer (ibid.). However, MWI is a minority view, and many other thought leaders disagree with his stance in this regard (see, e.g., Peter Shor's comment to Mark S's answer below). Another notable thinker, Richard Feynman, commented with regard to MWI, "It's possible, but I'm not very happy with it" (here).

To answer your question explicitly, it's not clear whether or not this is an accurate description.

Question 2

At a fundamental level, Everett describes the situation in his thesis:

...from the standpoint of our theory, it is not so much the system which is affected by an observation as the observer, who becomes correlated to the system.

Feynman expanded on this point of view (here),

...that many-world picture says that the wave function $\psi$ is what's real, and damn the torpedos if there are so many variables, $N^R$. All these different worlds and every arrangement of configurations are all there just like our arrangement of configurations, we just happen to be sitting in this one.

Deutsch has further refined the concept considerably over the years in both scientific papers (e.g., early: 1, 2; recent: 3) and popular science books (4, 5). He generally speaks of an infinite variety of universes within the multiverse, some proportion of which align with each other in particular instances.

In that sense, your second statement is closer to MWI. From what I understand, I think it would be more accurate to say the universes "doing the computation" were identical at the point of state preparation and branch on measurement.

Question 3

Contact in the form of "message sending" between universes is prohibited by special relativity. As stated by Everett (page 98-99 of his thesis)

Only the totality of these observer states, with their diverse knowledge, contains complete information about the original object-system state - but there is no possible communication between the observers described by these separate states.

If I understand Deutsch correctly, there is a possibility of some form of directed interference that would allow "an observer to 'feel' himself split into two branches" (experiment proposed here), but message sending between the two branches is still prohibited. Apparently, classification of MWI as interpretation or theory (under conventional scientific methodology) depends largely on the viability of this experiment, or one very similar.

Edit: Revised after reading Everett and Deutsch more carefully.

$\endgroup$
17
$\begingroup$

Regarding your first question, you are essentially asking about the validity of a position taken by David Deutsch - a founder of quantum computing! For example, in his book 'The Fabric of Reality', Deutsch states:

When Shor’s algorithm has factorized a number, using $10^{500}$ or so times the computational resources that can be seen to be present, where was the number factorized? There are only about $10^{80}$ atoms in the entire visible universe, an utterly minuscule number compared with $10^{500}$. So if the visible universe were the extent of physical reality, physical reality would not even remotely contain the resources required to factorize such a large number. Who did factorize it, then? How, and where, was the computation performed?

The implication is that the number was factored in the multiverse.

However, there are some issues with Deutsch's position that others have pointed out.

For example, quantum computers can’t seem to access all of the multiverse to efficiently solve any problem - they still seem to have limitations! Aaronson, I believe in his book 'Quantum Computing Since Democritus', notes that Deutsch's arguments about multiple universes working together would apply equally well to problems in the so-called $\mathrm{NP\:Complete}$ complexity class. However, quantum computers likely cannot efficiently solve such problems.

So if we "use the computing power of their counterparts in alternate realities that they access through superposition," as espoused by Deutsch, then the computing power so-granted is still very limited - and then the question becomes why can the interacting universes within the multiverse allow us to factor large integers efficiently but not allow all other problems in $\mathrm{NP}$ to be solved efficiently?

Because the above question is not clearly answerable, the idea that the multiverse works together to factor a large number is maybe incomplete...

$\endgroup$
  • $\begingroup$ Doesn't Deutsch's quote also assume that the visible universe is the only part of this universe with which we can interact (via quantum computing)? Why does the limited number of atoms in the visible universe ground his conclusion that there must be multiple universes instead of just concluding that our universe is bigger than what is visible? $\endgroup$ – jschmitter Nov 5 at 3:21
  • $\begingroup$ I'm not sure I understand Aaronson's objection (at least the way you paraphrased it). Sure, the multiverse might not allow us to solve all NP-complete problems efficiently, but I don't see how that serves as evidence against the MWI. It's like saying that the physical restrictions imposed on the universe by the laws of thermodynamics is evidence against the laws of thermodynamics. $\endgroup$ – Sanchayan Dutta Nov 5 at 3:49
  • 1
    $\begingroup$ @Sanchayan I don’t think it was meant as an objection to MWI per se; however I interpreted it as an objection to Deutsch’s position that Shor’s algorithm proves MWI.. I’ll try to dig up the exact Aaronson quote. I don’t event think Aaronson objects to MWI - I sense he’s agnostic and favors the “shut up and calculate” philosophical principal. $\endgroup$ – Mark S Nov 5 at 3:55
  • $\begingroup$ @MarkS Did Deutsch really say Shor's algorithm proves MWI? If so, I'd like to see the source. Shor's algorithm can certainly be described in MWI-ian and Bohmian terms, but I'd be surprised if Deutsch actually said that the algorithm is a proof of some interpretation. $\endgroup$ – Sanchayan Dutta Nov 5 at 4:03
  • 5
    $\begingroup$ Deutsch's reasoning is very suspect. My favorite analogy is with transportation. Think of a quantum computer as a boat and a classical computer as a car. Suppose you want to go from New London, CT to Orient, NY. The ferry will take 80 minutes. Google Maps says the distance is 210 miles. So clearly, the ferry is averaging 157.5 miles per hour, right? No, it's taking a different path that is shorter (but that only boats can take). Similarly, Shor's algorithm is taking a different path that is shorter (but that only quantum computers can take). $\endgroup$ – Peter Shor Nov 7 at 11:27
6
$\begingroup$

In the many worlds interpretation (MWI) reality consists of a structure called the multiverse that looks like a collection of slightly interacting parallel universes in some circumstances:

Deutsch, David. "The structure of the multiverse." Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences 458.2028 (2002): 2911-2923. [arXiv:quant-ph/0104033]

In the MWI each system exists in multiple instances. Some of those instances are identical to one another in the sense that any measurement you could perform on them can't tell them apart. These correspond to elements of a superposition that are in the same state $|\psi\rangle$. You can write this state as $1/2|\psi\rangle+1/2|\psi\rangle$, or $1/3|\psi\rangle+2/3|\psi\rangle$ or any other combination of numbers that add up to 1. A collection of instances in the same state can evolve to be in multiple different states, like so:

$$|\psi\rangle \to \tfrac{1}{\sqrt{2}}|\psi\rangle + \tfrac{1}{\sqrt{2}}|\alpha\rangle$$

There is no fact of the matter about which instances in the initial state $|\psi\rangle$ have ended up in the state $|\alpha\rangle$ because the instances in the same state can't be distinguished from one another by any measurement. So changing a superposition involves changing the state of some of the instances so that there are multiple different versions of the system. This process doesn't spawn the existence of new instances.

The interference that takes place in a quantum computation combines the information in the different instances to produce a single state with the correct outcome with some probability large enough to make the computation worth doing. Since the intermediate states are all combined to produce a single answer it's not the case that there is one version that receives messages from the other versions. Rather there is a process that uses all those versions to produce a correct answer. You can't copy information between different versions of a system because the process of copying information out of a system in a superposition produces decoherence that prevents interference:

Zurek, Wojciech H. "Wave-packet collapse and the core quantum postulates: Discreteness of quantum jumps from unitarity, repeatability, and actionable information." Physical Review A 87.5 (2013): 052111. [arXiv:1212.3245]

Interference is the process that puts information about all of the different versions into a single version so trying to copy information between different versions of the same system is forbidden by the laws of physics.

$\endgroup$
1
$\begingroup$

The multiverse is not commonly accepted as the right description of reality and is just one of many interpretations of what exactly happens at the moment of the "wave function collapse". The multiverse is in its core just an idea to preserve determinism in nature by the argument: If you know in which exact universe you are, you can trace back every particle back to its original position at the big bang. This is not true in reality as quantum mechanics is inherently unpredictable (Copenhagen interpretation) or in the multiverse (we don't know in which universe we are).

So, if there are no multiverses then your entire question becomes pointless.

For the use in quantum mechanics (and therefore in quantum computers), it is probably more useful to understand how interference of wavefunctions works and interpret the computation in a quantum computer as constructive or destructive interference.

$\endgroup$
  • $\begingroup$ I understand and somewhat agree with your objection, but my question is based on the implicit assumption that the MWI is the correct interpretation of the wave function. Obviously if that assumption were incorrect, the question would be invalidated - but that's so close to being common sense that I didn't feel the need to point it out. $\endgroup$ – Snowshard Nov 5 at 14:11

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.