Quantum Tutorial
Los Alamos National Laboratory
Quantum information is an exciting field on the cutting edge of
physics, both theory and technology. Some very significant work is
being done here at Los Alamos in
quantum cryptography and quantum computing. The quantum information
team welcomes you and hopes you will find these pages both
interesting and useful!
Why is Quantum Computation Powerful?
The quantum mechanical superposition principle enables a quantum
computer to perform certain computations very much more efficiently
than any classical computer. For example, suppose a quantum computer
holds two registers: a left register that contains the argument of
function; and a right register that will hold the value of the
function at the argument of the left register, after computation of
the function.
Now suppose that the left register is composed of L qubits and we
create a quantum circuit (collection of quantum logic operations)
that evaluates the function at any one of the argument values,
copying its value into the right register. We can equally well
replace the functionÌs argument with a superposition of all
2^L values and in one operation evaluate all values of the function
(in superposition in the right register).
Thus it appears that a quantum computer could perform exponential
computational work in one operation, which gives us a hint of the
underlying power of the method. However, we should note that this
power is not universally useful, because if we were interested in the
functionÌs values we would only be able to recover one of the
2^L values per measurement on the right register. So, we would have
to repeat the function evaluation and measurement 2^L times to obtain
all of the values.
But, if we are instead interested in some joint property held by
all the function values, such as the functionÌs period, this
quantity can be extracted by an additional efficient quantum
procedure known as the quantum Fourier transform. Therefore, any
problem that can be reduced to finding the period of some function is
a candidate for efficient solution by quantum computer. Integer
factorization is such a problem.
This is a series of explanations of basic concepts useful in
understanding quantum information. They are also available as links
from the quantum information, cryptography, and computing sections.
If you reach them in this fashion, you will need to use the back
feature on your browser Return to what you were reading.