Seth Lloyd, a professor of mechanical engineering and physics at MIT, published a paper and a book in which he shows that the universe can be regarded as a giant quantum computer. According to him, all observed phenomena are consistent with the model in which the universe is indistinguishable from a quantum computer, e.g., a quantum cellular automaton.

He considers the following two statements to be true:

  1. The universe allows quantum computation.
  2. A quantum computer efficiently simulates the dynamics of the universe.

To conclude with:

Finally, we can quantize question three: (Q3) ‘Is the universe a quantum cellular automaton?’ While we cannot unequivocally answer this question in the affirmative, we note that the proofs that show that a quantum computer can simulate any local quantum system efficiently immediately imply that any homogeneous, local quantum dynamics, such as that given by the standard model and (presumably) by quantum gravity, can be directly reproduced by a quantum cellular automaton. Indeed, lattice gauge theories, in Hamiltonian form, map directly onto quantum cellular automata. Accordingly, all current physical observations are consistent with the theory that the universe is indeed a quantum cellular automaton.

Does this theory hold up?

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    $\begingroup$ Seems like a pretty boring observation. He may as well have said 200 years ago that all observed phenomena are consistent with Newtonian mechanics, or that all observed phenomena are consistent with [insert religion here]. Or whenever there's a new theory of physics in 100 years from now or whatever, that the universe appears to be a whatever-that-theory-is computer. $\endgroup$
    – Nat
    Mar 21 '18 at 2:23
  • $\begingroup$ You are asking whether work by a distinguished academic is correct. It's good to be critical, but I always found it useful to assume that others are correct until you prove the contrary. At least you should explain why you question his results. That said, I also don't see what we gain from his description. $\endgroup$
    – M. Stern
    Mar 24 '18 at 22:05
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    $\begingroup$ I don't think this question is answerable in less than a book. While a quantum computer as we know it is non-relativistic and does not use gravitation, relativity and gravitation are big in the universe and need a thorough discussion. $\endgroup$ Mar 26 '18 at 12:27

I guess that he's right enough for the moment; quantum mechanics is part of our best theory of the universe, which by definition means that we think the universe works like that.

It's pretty circular though. When we have some model of the universe, what that literally means is that we think that the universe is operating according to that model. Currently that's a quantum model. Still, who cares?

The paper attempts to address that question:

The immediate question is ‘So what?’ Does the fact that the universe is observationally indistinguishable from a giant quantum computer tell us anything new or interesting about its behavior? The answer to this question is a resounding ‘Yes!’ In particular, the quantum computational model of the universe answers a question that has plagued human beings ever since they first began to wonder about the origins of the universe, namely, Why is the universe so ordered and yet so complex [1]?

So, I guess that he's saying that quantum mechanics helps us to model more about the universe than prior models.

Seems like a pretty trivial point. It's weird that someone wrote a paper about it.

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    $\begingroup$ I think the paper is more to be seen as a historical review than as presenting novel results $\endgroup$
    – glS
    Mar 21 '18 at 18:13

If by "giant quantum computer" you mean something that can be simulated very efficiently by a tensor product of sufficiently many qubits, then I think the answer is no.

When we work with finite dimensional systems, it's very clear how to account for the joint description of two subsystems: we simply take the tensor product.

If you want an infinite-dimensional space with continuously many degrees of freedom, then we have to do something more subtle. We'll call this the "commuting operator" model. To every open subset of space we attach an algebra observables corresponding to the local measurements on that part of space. Instead of requiring that the Hilbert space of the universe is the tensor product of all the local hilbert spaces, we just ask that if two regions of space don't intersect, then their algebras of observables commute.

It's known that the commuting operator model gives rise to correlations between spacelike separated parties that do not arise in the tensor product model. See this paper by William Slofstra on the arXiv.

We don't know whether there is an experiment that could tell us that our universe is capable of generating correlations in the commuting operator model. See this blog post by Scott Aaronson, which describes Slofstra's result and some of its implications.

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    $\begingroup$ You seem to claim that only local observables can be implemented on a quantum computer? Even if you would restrict yourself to this situation, what about nonlocal gates before the measurements? Given that we allow for nonlocal interactions, are you sure that there are correlations that could not arise from a discrete hilbert space? $\endgroup$
    – M. Stern
    Mar 24 '18 at 21:54
  • $\begingroup$ @M.Stern I guess the question is a bit more subtle than I thought. Of course if you allow nonlocal interactions, then you can get the desired correlations. If you have an n qubit system and a circuit of depth less than log n, then indeed you can only implement local measurements. This means that if one model has a larger set of correlations than another, there are some small-depth measurements in the larger model that require much more depth to simulate in the smaller model. See e.g. arxiv.org/abs/1704.00690 for such a separation between quantum computers and classical computers. $\endgroup$ Mar 24 '18 at 23:07
  • $\begingroup$ @JalexStark You have an interesting perspective on this. I'm not convinced, however, that you can restrict the possible measurements via the circuit depth. Because clearly with a single CNOT gate we can implement a Bell state measurement, and you could even have a general gate act on all qubits. Maybe you have some implicit assumptions... $\endgroup$
    – M. Stern
    Mar 25 '18 at 4:28
  • $\begingroup$ @M.Stern I think the missing assumption is geometric locality. The Bravyi, Gosset, Koenig result that I linked above doesn't require any geometric locality, but they can "force" the geometric locality by their choice of sampling problem. $\endgroup$ Mar 25 '18 at 4:34

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