Tuesday, April 24, 2007

Living and Computing in Lloyd's Universe

I recently read Seth Lloyd’s Programming the Universe. This is a thought-provoking (if a bit meandering) book which explains why we should envision the universe as a quantum computer and how doing so may illuminate our understanding of some difficult questions (it is out in paperback – page references below are to this edition). In addition it offers a useful summary of quantum computing for the general reader, along with discussions of cosmology, thermodynamics and introductory quantum mechanics (all with a computing “gloss”). In this post and one or two to follow, I’ll discuss a couple of Lloyds’ ideas. (For a general review, the NYT’s is here).

As a layperson who had read explanatory books and articles about quantum physics for many years before I ever heard about quantum computers, the first theme the book hammered home for me was that quantum computing in an important sense just is quantum physics. A classical computer can be instantiated in a variety of physical set-ups; a quantum computer is itself a quantum system. While you can try to model a quantum system on a classical computer, you will quickly overwhelm its computational resources. So, quantum computing, in addition to its potential for practical acceleration of computing power generally, gives us a useful and appropriate logical framework to analyze the physics of our world.

The next step is to explore the implications of the ability to perform this kind of “quantum simulation”. Here’s a thumbnail sketch of how the simulation is done (p.149): “Every part of the quantum system to be simulated is mapped onto a collection of qubits in the quantum computer, and interactions between these parts become a sequence of quantum logic operations.” In fact: “…quantum computers could function as universal quantum simulators, whose dynamics could be the analog of any desired physical dynamics. (p.151)” At this point, Lloyd makes the conceptual case that, logically, there is no reason to distinguish between what’s happening in the simulation and the original system.

Now, the step which motivates the book title: while we can’t do it yet, in principle the universe (the accessible part, anyway) is finite in extent, and hypothetically could be simulated in a quantum computer. But, following the point above, since the computer has the same number of qubits as the universe, and since the operations on the qubits simulate the universe’s dynamics, we can say: “Such a quantum computation would constitute a complete description of nature, and so would be indistinguishable from nature. Thus, at bottom, the universe can be thought of as performing a quantum computation. (p.154, emphasis original).”

So what does it mean? What can this view do for us? I think there are two possible answers, one concrete and one more intangible. First, ideas from quantum computing may help in the quest for a theory of quantum gravity. Second, it may offer an improved paradigm for interpreting and understanding the physical world. I’ll follow up on these in future posts.

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