Introduction to Quantum Information: Part 3/7

QUANTUM CIRCUITS AND GATES

In the previous episodes we get into acquittance with qubits and how they behaves when they are entangled.
From now on, we will see how to use and manipulate qubits in order to do computations!

In extreme summary, a quantum computation is represented by the evolution of a quantum system: given an input state, through some operation applied on your system, the system evolves giving you as output the result of the computation you wanted to perform.

Thus, you need to find and implement some operations to manipulate your qubits!

In Quantum Mechanics, the evolution of a system is determined by unitary operators.

You may imagine that there exist an uncountable infinite number of such matrices, therefore you may ask how to "easily" implement a computation.

There are a few matrices coming to the rescue. We will focus on matrices operating on single-qubit and on two-qubit states, because you can build any arbitrary large matrix by means of single and two-qubit matrices.

Before talking of those matrices, and why they can be called "gates", we introduce an handy mathematical framework to visualise quantum computations: the circuit model.

Exactly as its classical counterpart, a quantum logical circuit is a scheme in which there are logical gates (like AND, OR, XOR, NOT, etc.) applied to your qubits.
At the end of this flow of logic gates, you measure the qubits and obtain the result of your computation as classical bits.

Then those evolution matrices are indeed quantum logic gates and they can be represented as gates in a quantum circuit.
In the following I will present the most important single and two-qubit quantum gates

In the following, as an example, you will find the quantum circuit to implement quantum teleportation (the topic of the next post)

Framed "H" is the Hadamard gate, then there are two CNOT gates, finally framed "X" and "Z" are quantum NOT and phase-flip gates, controlled by the classical bits outcoming from measuring the first and the second qubit.

That's all for today!
Stay tuned and see you in the next post! Ready for QUANTUM TELEPORTATION?

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