## Friday, March 05, 2004

### What is a qubit?

Old Post: I first discussed quantum computation in this blog here.

I'd like to take a moment to expand on the subject of quantum computation, and that means starting with the term "qubit." A qubit is a quantum bit, and it refers to any quantum system that has two states which can serve as zero and one. Examples include spin states of nuclei in a molecule, an electron's orbital states in an atom, photon polarization, or, in a system such as superconductors which exhibit macroscopic quantum coherence, current circulating in a loop. If it's quantum, it's been proposed as a qubit.

Not every quantum system makes a good qubit, however. The criteria necessary for a quantum system which can be used in a quantum computer were formalized by DiVincenzo. The requirements are the following:

First the two states, called the |0> and |1> states, must be measurable. It must be possible to tell the difference between them. This may seem trivial, but quite a few quantum states are difficult to differentiate.

Second, the states must be controllable. This means that one can first place the system in the |0> state accurately. Then, one must be able to rotate the qubit in order to achieve every possible state. The possible states are not just |0> and |1>. If a and b are complex numbers, such that |a|^2+|b|^2=1, a|0>+b|1> describes all the possible states of the qubit. Thus it is possible for the qubit to be in state |0> and |1> at the same time (called a superposition), as long as the proportions add up to 1. Since a and b are complex, it's not simply a matter of achieving the right proportions, but also the correct phase--the correct complex values.

Third, the qubit must be addressable. One needs to be able to decide which qubit to control and measure. If there's a solution filled with millions of identical molecules, and there's a way to rotate the oxygen atom nucleus in all the molecules at the same time, that's still only have one useful qubit (more precisely, it's an ensemble of that qubit). Now if it's possible to address the two carbon atom nuclei and the oxygen atom nucleus on each molecule separately, that's three qubits, and an ensemble of those three qubits. This is what is done in nuclear magnetic resonance quantum computing.

Fourth, one needs to be able to couple qubits together so that they affect one another. Thus one qubit will rotate only if another qubit is in a certain state. This is how one makes quantum gates.

Finally, one needs to be able to isolate the qubits from the environment. The environment, which means everything other than the qubits themselves, causes the qubits to decohere. Information is lost as the qubits dephase, drift from the intended phase, and relax, fall to the lowest energy states. If one waits long enough, qubits in just about any system eventually fall to |0>. Only if they remain in the desired states long enough to perform a useful calculation can you make a quantum computer.

And that's the second episode of quantum computation for the layman. Tune in next time as I tell you how you can build your very own quantum computer (with a \$1 million grant and a Ph.D., of course).