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Dear Richard Feynman,

How does a quantum computer work?

Warmly,

Andrew Mayne

Determination

Dear Andrew:

Any quantity, like the magnetic moment of the electron, may be measured by an ordinary magnetometer. The observed values of the quantity are quantized. The same is true of the values obtained by measuring the charge on the electron. We say that the measurements are made with an accuracy of 1 part in 1,000,000,000. The observed values are in good agreement with the values obtained by ordinary magnetometer. By an ordinary magnetometer is meant a device that gives the quantity by using Faraday’s law of electromagnetic induction.

It is perfectly possible to build a machine that measures the quantity by using quantum theory instead of Faraday’s law of electromagnetic induction. The measurements are accurate to 1 part in a billion. The machine is, of course, a quantum magnetometer. The measurements may be done with an accuracy of 1 part in a billion because the machine is quantum, and quantum theory is our very accurate description of a billion electrons.

Quantum theory is about any number of objects, not just the ordinary measuring instruments that we are accustomed to. Thus, one would like to talk about “the mass of the electron,” and mean it in an ordinary way. But when one tries to explain just what one means by “the mass of the electron,” it turns out to be very much the same problem as explaining what the “charge of the electron” is. (When a physicist says “mass,” he means the same thing as “charge.”) The way that the mass is measured is also exactly like the way that the charge is measured, namely by a quantum magnetometer. It’s hard to be exactly sure how to define the mass. On the other hand, the mass that is measured with a quantum magnetometer is in very good agreement with the mass of the electron as defined in chemistry. That’s why it’s so easy to overlook the fact that the mass of the electron is a difficult thing to measure. One makes a measurement in chemistry, and the results agree very well with the results of a quantum magnetometer. The chemist can forget about the problem of measuring the mass of the electron. This is just like how it is with the charge of the electron, which is one of the difficult things to measure.

Let me emphasize this point. The chemist talks about a thing called the mass of the electron, and believes it to be a quantity with a meaning. He is sure that the mass he talks about is not really a million-millionth of a gram. He is also sure that the mass has a value that is determined by experiments made with chemical apparatus, and that is determined to be 1 part in a billion of the mass determined by ordinary magnets.

How does the quantum magnetometer work? It’s a very complicated machine. It has many problems. The more the machine deviates from the ordinary magnetometer, the harder the problems become. On the other hand, a very crude device can measure the charge and the mass in the manner of a quantum magnetometer. That is a useful trick for the purpose of testing the laws of quantum theory.

You ask what quantum theory is about. Quantum theory is about all quantities that can be measured by the use of quantum magnetometers. These quantities are, in general, much more difficult to measure than ordinary quantities like the position of a piece of iron. It’s hard to be sure just how much of a deviation from the ordinary behavior of a magnetometer you are going to get. This makes the problem of finding a suitable machine for making the measurement difficult. The resulting measurements are not necessarily related to what one would like to measure.

Richard Feynman