t b a b a

2.3 Quantum Circuits
In the classical world, a logic circuit is composed of wires and gates. Wires carry information
to and from gates. Gates perform simple computational operations. For example, the NOT
gate will flip the input bit, taking 0 to 1 and vice versa.
A logic gate computes a Boolean function f : {0, 1} k → {0, 1} l from a fixed number
of input bits to some fixed number of output bits. For example, the NOT gate is a gate
with one input bit and one output bit, which takes the function f(a) = 1 ⊕ a, where ⊕
denotes addition modulo 2. There are many other elementary logic gates such as the OR
gate, the AND gate, the XOR gate and the NAND gate. These gates can be interconnected
to realize an enormous variety of functions f : {0, 1} k → {0, 1} l . A circuit specifies the input
bits and the output bits and how the gates are connected among each other. Any Boolean
function can be implemented by such elemental gates. A classical circuit has been proven to
be equivalent to the Turing model.
In quantum mechanics, a quantum circuit is a specific model for a quantum computational
device. In this model, a quantum computer is built from a quantum circuit containing wires
and elementary quantum gates to carry around and manipulate the quantum information.
Experiments have already been carried out which can be regarded as implementing a seven-
qubit quantum computer that implements Shor’s factorization algorithm. Quantum circuits
are also theoretically interesting as a tool for understanding the power and limitations of
quantum computation.
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