Re: Quantum computation



Hi,

For example, given "a>0" and "b>0" such that a^2 + b^2 = 1, is it
always possible to make
a|0> + b|1> ? If so, how could one be sure about that claim ?

If you have a Hamiltonian H such that a|0> + b|1> is an eigenvector
of H, then of course, and by measuring H, you can sort out wave-
functions that are up to a phase the requested vector. For example,
if we put |psi> := a|0> + b|1>, then the projection P = |psi><psi|
is a hermitian operator, thus a Hamiltonian, with eigenvalues 0 and
1, and if you use this as measuring tool and insert an arbitrary
state |chi> and measure a 1, you know that the state of the system
afterwards is a multiple of |psi>. Thus, P can be used to prepare
the system.

Whether one can realize P physically I can't tell without knowing
what |0> and |1> is, of course.

So long,
Thomas
.