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QUANTUM GATES ANDCIRCUITS

In a classical computer, at the most fundamental level there are two basic tasks that we can use when manipulating information. We can move it from one place to another, or we can do some type of basic processing on the information using a logic gate. Sets of logic gates can be connected together to construct digital circuits. In this chapter we will be introduced to the equivalent notions of logic gates and circuits in a quantum computer. We begin with a brief overview of classical logic gates.

CLASSICAL LOGIC GATES

The basic purpose of a logic gate is to manipulate or process information at the bit level in some way. A simple example is the NOT gate. The NOT gate is a single input gate. As its name implies, the NOT gate simply flips or inverts the value of the input bit. That is, if the input to the gate is a 0, the output is a 1, and if the input is a 1, the output is a 0. We can write down the action of the NOT gate schematically as

image

In more complicated situations we will need a more systematic way to write down the action of a gate. This is done using a truth table, which is a table that lists the inputs together with the corresponding outputs of the gate. For a NOT gate, this is very easy to do. We write the values of the single input bit on the left side of the table and the corresponding outputs on the right:

Now we will consider more complicated ...

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