Review of:

Programming the Universe.

A quantum computer scientist takes on the cosmos.

by Simon Laub, april 2007.

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Computations are everywhere,

Computations are everywhere. Sure, your modern day laptop computer is doing a lot of computation. But look further and you will find computation everywhere.

In Seth Lloyds book, we are taken on a journey, where we start with the dance of atoms and light. All we need to produce everything we see. Here quantum fluctuations inject information (virtual particles) into empty vacuum for the laws of nature to process (i.e. to compute).

Pretty amazing computation this atomic dance btw. To simulate accurately just a just a tiny fraction of the universe on a classical computer for just a fraction of second - say just a few hundreds atoms for less than a second - would be outside the reach of modern computers. Here we would need something better - a quantum computer.

Actually, according to Seth Lloyd, the universe is indistinguishable from a quantum computer. The universe supports quantum computation and can be efficiently simulated by a quantum computer. Put another way - when two physics systems can simulate each other efficiently - they are logically equivalent. No easy trick though - to simulate the entire universe - in order to it, a quantum computer would need exactly as many qubits as the universe. Talk about Jupitor sized computers.

And, quantum computers can do stuff that normal classical computers cant do. With Shors factoring algorithm a quantum computer can factor large numbers far more efficiently than a classical computer. And with Grovers search algorithm quantum computers can find things much faster then classical computers etc.

All very well described in the book. So ok, the book gives an insight into computation with atoms in a quantum world. And perhaps this is more than enough for most readers to come to grasps with - Surely, it alone will keep humanity occupied for decades to come. Still, for a book that claims to take on computation in all its glory a lot of stones are left unturned.

E.g. we all know that work is being done on quantum gravity theories. What is computation like here? I suspect that Seth Lloyd wanted to keep the reading "light" and compact, and perhaps he thinks quantum gravity will not add anything new to quantum computers - but completely ignoring these "if"s certainly also takes away value from the book.

If there is no efficient algorithm for simulating quantum systems on classical computers. Then - If a quantum computer can't simulate a quantum gravity computer that would highlight yet another huge leap in computing power? And wouldn't the gates of quantum gravity computer work at scales where there is no causality? If a quantum gravity computer can see its result before running its algorithms - it is essential the same as quantum computer strapped to a timemachine. But not a word about such ideas in Seth Lloyds book?

I.e. on quantum gravity computer it goes: Quantum gravity does away with cause and effect. In classical computing one thing follows after another. "if" is usually followed by "then". Even quantum computers has this notion of input followed by output. Quantum gravity computers will not be constrained by such considerations. Noone knows how space and time act on the scale of quantum gravity, but there will certainly be no such thing as a fixed sequence of processing steps.

And what about logic in the world of quantum computers?

I.e. Sets are merely the most familiar example of the more general concept of a topos. A topos is a somewhat technical concept. But all topos share one feature, they give rise to their own variety of logic. Sets obey the laws of standard logic and boolean alegebra. For a general topos one would need new definitions for AND, OR and NOT operations. Boolean algebra would normally allow a statement to be either true or false. However, this turns out to be the exception in the world of topos. Normally one find statements to true, false and all shades of grey in between. E.g. in the world of quantum physics - the associated topos might allow a statement to be both true and false and all in between..

This is all only hinted at his book. One might suspect that he thinks such ideas are above a casual reader. But come on - would a casual reader pick up a book on quantum computations anyway?

And what about the brain - what kind of computations do we have here? If Seth Lloyd thinks that we have nothing but classical computation going on here - he should have said so. But he gives us nothing here.

A comment about physicists Freeman Dysons remark that mind and intelligence are "woven into the fabric of the universe" would have been appropriate imho.

But ok - quantum computers are only getting started and something like IBMs Blue Gene computer with these 280 trillion calculations per second - the current record - would have been hard to imagine back in 1942, when classical computers got started. So we shouldn't be surprised that there are still stones unturned in the world of quantum computers.

April 22, 2007

Simon Laub