.. _examples_page:

Examples
========

This page demonstrates how QCircuits can be used to simulate example
quantum algorithms.

Producing Bell States
=====================

Example code producing each of the four entangled Bell states for a two-qubit system.

The circuit diagram is

.. image:: images/bell.png
    :width: 70%


where \|x⟩ and \|y⟩ are each one of the computational basis states, \|0⟩ or \|1⟩.

E.g., :math:`|\beta_{00}⟩ = \frac{1}{\sqrt{2}} (|00⟩ + |11⟩)`.

**Code**:

.. literalinclude:: ../../examples/produce_bell_states.py

Quantum Teleportation
=====================

.. image:: images/teleport.png
    :width: 100%

**Code**:

.. literalinclude:: ../../examples/quantum_teleportation.py

Quantum Parallelism
===================

.. image:: images/parallel.png
    :width: 100%

**Code**:

.. literalinclude:: ../../examples/quantum_parallelism.py

Deutsch's Algorithm
===================

.. image:: images/deutsch.png
    :width: 100%

**Code**:

.. literalinclude:: ../../examples/deutsch_algorithm.py

The Deutsch-Jozsa Algorithm
===========================

.. image:: images/deutsch_jozsa.png
    :width: 100%

**Code**:

.. literalinclude:: ../../examples/deutsch_jozsa_algorithm.py

Superdense Coding
=================

.. image:: images/superdense.png
    :width: 100%

**Code**:

.. literalinclude:: ../../examples/superdense_coding.py


Phase Estimation
================

We are give a black-box d-qubit operator U and one of its eigenstates.
The task is to estimate the phase of the corresponding eigenvalue,
storing the result in a t-qubit register.

**Code**:

.. literalinclude:: ../../examples/phase_estimation.py


Grover's Algorithm
==================

We are given a black-box boolean function f(x) that evaluates to
1 for exactly one value of x.
Grover's algorithm finds the solution with resources proportional
to the square root of the size of the search space.

**Code**:

.. literalinclude:: ../../examples/grover_algorithm.py