AN INTRODUCTION TO NANOCOMPUTING - Bio-Inspired and Nanoscale Integrated Computing - page 20

actually is a combination of both states simultaneously! This combination of two
states, however, is something that cannot be measured directly. When trying to
observe the state of a qubit, we receive a |0 with some probability. This

probability is the actual information contained by a qubit, and it is almost as if
nature teases us by making this information impossible to measure. One of the key
tasks of quantum computing is to manipulate this hidden information in such a
way that it is meaningful to measure the qubit as only a |0

S or |1 S

S or |1 S .

are actually just one ''frame of reference'' in under-
standing the actual underlying quantum system. One of the interesting powers of
quantum computing is that we can freely decide which frame of reference we want
in which to manipulate the qubit. For example, we could view the same qubit
as a combination of |+

The states |0 S and |1 S

, two other states that give us a different way of
looking at the same qubits. Even more peculiar, two or more qubits may be
completely unrelated in one frame of reference, but in another frame of reference,
the qubits become entangled. This means that a change in one qubit will unavoidably
affect the other qubit, and even though this complicates matters, it allows a powerful
way to manipulate multiple qubits. Often, a useful quantum circuit first manipulates
qubits in one frame of reference, where they are entangled, and then uses another
frame of reference where the state of the qubits can be observed.
Perhaps the best known example of the power of quantum computing is its
use in finding the prime factors of a given number. Traditional algorithms can take
extremely long for large numbers. A quantum algorithm known as Shor's
Algorithm [33] uses quantum computing to factor prime numbers. A physical
implementation of this algorithm has been demonstrated using 7 qubits, trium-
phantly factoring the number 15 into the prime numbers 5 and 3 [34]. While the
number 15 is not large and it seems like a trivial task that could have been done
with any other computer, the real landmark of this result is to demonstrate that
quantum computers can indeed work as theoretically proposed.
With every next qubit, the amount of hidden information in a quantum
system effectively doubles. With 7 qubits, there are 128 hidden ''numbers'' that
represent a combination of 128 different states. With 20 qubits, there are more
than a million such hidden numbers. It might take 30-40 qubits to represent
computations that exceed the potential of traditional computers, and each qubit
could possibly be represented by a single nanoscale particle! While this is currently
a distant dream, the foundations towards realizing this dream are being studied
extensively today.
Despite this awe inspiring amount of power that seems possible with quantum
computation, there are many daunting challenges to be addressed before quantum
computing becomes more practical. First, physically implementing a
quantum computer is a tricky task. While it would be ideal to isolate a single
quantum system in reality as we can do mathematically, in practice a quantum
system also interacts with the rest of the world. Therefore, it is difficult to keep the
coherence of a quantum system, where coherence is a measure of how long the
quantum system can stay intact before it gets disrupted by the surrounding
environment. On the other hand, quantum phenomena such as photons of light

S and | S