t b a b a

calculations many times. The advantage of using quantum algorithms for simulations of
quantum physical systems is that they allow us to determine the value of relevant physical
properties with polynomial bounded statistical errors.
How powerful are quantum computers and quantum algorithms? Nobody can give an
exact answer to such a problem yet. It is still doubtful that a quantum computer is more
powerful than a classical computer. Let us take a brief look at what is known about the
power of quantum computer and classical computer.
An algorithm can be characterized by the number of operations and amount of memory it
requires to compute an answer given an input of a certain size . These characterizations of the
algorithm determine what is called the algorithm’s complexity. Specifically, the complexity of
an algorithm is determined by looking at how the number of operations and memory usage
required to complete the program scales with the input size of the program. Generally,
computer scientists group problems into the following complexity classes:
• P: Polynomial time, the running time of the given algorithm is in the worst case some
polynomial function of the input size.
• NP: Nondeterministic polynomial time, a candidate for an answer can be verified as
a correct answer or not in polynomial time.
• NP-complete: the set of problems such that if any member of this set is in P, then
the set P equals the set NP.
30