PDF (double-sided) - Physics Department, UCSB - University of ...

states, effectively giving it 2 n+1 − 2 analog numbers for calculations in the form of
the complex probability amplitudes of each of the 2 n states. Therefore, the number
of “registers” that a quantum computer has available for calculations scales
exponentially with its number of quantum bits, while for a classical computer this
scaling is linear.
If a quantum computer then performs an operation on one of the bits, this
one operation will affect the probability amplitudes of all 2 n states. For example,
if a three bit quantum computer performs a “NOT” operation on its first bit, it
effectively performs four swap operations that exchange the probability amplitudes
of the 000 and 100, the 001 and 101, the 010 and 110, as well as the 011 and
111 states. This makes it possible to design algorithms that allow a quantum
computer to process data in a massively parallel fashion, with the number of
possible simultaneous operations scaling exponentially with the number of its
quantum bits.
This makes a 65-bit quantum computer twice as powerful as a 64-bit quantum
computer, while a 65-bit classical computer is only about 1.5% more powerful
than a 64-bit classical computer.
8