Deutsch - computers may use matter that outdoes the brain
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I shall now try to describe Deutsch's scheme for building a quantum
computer. He does not actually try to use some wierd new form of matter
like my hypothetical halting crystal. Instead, he exploits quantum
phenomena that exist everywhere, but which are usually invisible at a
macroscopic scale.
Before I can do so, I must delve into quantum physics. Most of Deutsch's
papers on this are very technical, and you're only likely to be able to
read them if you start working on such things professionally (but if you
do, it will provide - albeit not for ten or fifty years, perhaps - a
major advance in computation.) There's a comparatively non-technical
account in Mind, Brain and the Quantum by Lockwood (PSY AA:L 081),
chapter 14.
Summary of what you must know in order to build a quantum computer.
- Consider an electron or a nucleus in a magnetic field. You can
imagine it as a ball spinning about its axis of rotation. Electrons and
nuclei have an electric charge. Because they're spinning, this causes a
magnetic field which points along the axis.
The axis of rotation can point in various directions. But - first
wierdness - unlike in everyday experience, the directions are quantised. Only a finite number of directions is allowed. This number
depends on the particle's electric charge.
The simplest possibility is that the particle could be pointing ``up'',
or ``down'', but nowhere in between. In this case, we say that the
particle is either ``spin up'' or ``spin down''. I will ignore particles
with more than two possible spin directions in the rest of these notes.
- As I said in the 6th week lecture, today's computers represent
numbers in binary. Each number is represented as a series of
binary digits or bits. For example, the number 3 would be
represented as binary 11, and the number 8 as binary 1000. We can encode
instructions in binary too. Each bit is stored in a separate memory
cell.
- In conventional computers, these cells are built from
cross-coupled transistors. But if we can find some way to make electrons
or nuclei hold still, we could use a single particle to represent a bit.
Use an electron with spin up to represent a 0; an electron with spin
down to represent a 1. It would be possible to read out the state of a
bit, or to change it, using a method related to nuclear magnetic
resonance. We could then build an entire computer memory out of cells,
each of which holds a spin-up or spin-down particle.
- In everyday physics, any object can exist in only one state at a
time. You can't have a door that's both open and closed, or a ball
that's spinning both clockwise and anticlockwise. But in quantum physics
- second wierdness - you can. Particles can exist in a superposition of states, also called a mixed state. So you can
have an electron that's both spin-up and spin-down at the same time.
- Actually, each component state has a probability associated with
it. So our mixed electron is not just spin-up+spin-down, but is (say)
40% spin-up + 60% spin-down, or perhaps 27% spin-up + 73% spin-down.
You can also have pure states: it's possible, even in quantum
physics, for our electron to be 100% spin-up + 0% spin-down.
- This means that we could prepare our computer memory so that some
or all of the cells are in mixed states. Think of such a memory as a
collection of film strips lying on top of one another. Each strip is a
memory in some particular collection of pure states. Each frame in the
strip is one cell, one particle. The entire set of superimposed strips
is a memory in a collection of mixed states.
- It's possible to build a CPU which, given a mixed state,
processes it as though it were processing each of the component states
independently. This gives us a kind of parallel processing. We put in a
collection of memory cells in mixed states, and we get out a collection
of cells in different mixed states. Our CPU is processing all the
film strips at the same time.
- This gives us a form of parallel processing for free. If we'd
built a conventional (non-quantum) parallel computer, we'd need one
CPU for each strip. But here, we have one CPU which is, in effect,
processing all the strips simultaneously.
- So far, what I've described is something which carries out a lot
of computations in parallel. Since each of these can be done on a serial
computer, the quantum machine can't do anything a Turing-equivalent
computer can't do. But it can do so faster. So it is more powerful
in a weak sense; it pushes back the limitations of complexity theory I
described last week.
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Jocelyn Ireson-Paine
Wed Feb 14 23:51:11 GMT 1996