abp/doc/index.rst

.. abp documentation master file, created by
   sphinx-quickstart on Sun Jul 24 18:12:02 2016.
   You can adapt this file completely to your liking, but it should at least
   contain the root `toctree` directive.


``abp``
===============================

This is the documentation for ``abp``. It's a work in progress.

.. toctree::
   :hidden:
   :maxdepth: 2

   modules


``abp`` is a Python port of Anders and Briegel' s `method <https://arxiv.org/abs/quant-ph/0504117>`_ for fast simulation of Clifford circuits. 
That means that you can make quantum states of thousands of qubits, perform any sequence of Clifford operations, and measure in any of :math:`\{\sigma_x, \sigma_y, \sigma_z\}`.

Installing
----------------------------

You can install from ``pip``:

.. code-block:: bash

   $ pip install --user abp==0.5.0

Alternatively, clone from the `github repo <https://github.com/peteshadbolt/abp>`_ and run ``setup.py``:

.. code-block:: bash

   $ git clone https://github.com/peteshadbolt/abp
   $ cd abp
   $ python setup.py install --user

If you want to modify and test ``abp`` without having to re-install, switch into ``develop`` mode:

.. code-block:: bash

   $ python setup.py develop --user  

Quickstart
----------------------------

Let's make a new ``GraphState`` object with a register of three qubits:

    >>> from abp import GraphState
    >>> g = GraphState(3)

All the qubits are initialized by default in the :math:`|+\rangle` state::

    >>> print g.to_state_vector()
    |000❭: 	 √1/8	+ i √0
    |100❭: 	 √1/8	+ i √0
    |010❭: 	 √1/8	+ i √0
    |110❭: 	 √1/8	+ i √0
    |001❭: 	 √1/8	+ i √0
    |101❭: 	 √1/8	+ i √0
    |011❭: 	 √1/8	+ i √0
    |111❭: 	 √1/8	+ i √0

We can also check the stabilizer tableau::

    >>> print g.to_stabilizer()
     0  1  2
    ---------
     X      
        X   
           X

Or look directly at the vertex operators and neighbour lists::

    >>> print g
    0:  IA	-
    1:  IA	-
    2:  IA	-

This representation might be unfamiliar. Each row shows the index of the qubit, then the **vertex operator**, then a list of neighbouring qubits. To understand vertex operators, read the original paper by Anders and Briegel.

Let's act a Hadamard gate on the zeroth qubit -- this will evolve qubit ``0`` to the :math:`H|+\rangle = |1\rangle` state::

    >>> g.act_hadamard(0)
    >>> print g.to_state_vector()
    |000❭: 	 √1/4	+ i √0
    |010❭: 	 √1/4	+ i √0
    |001❭: 	 √1/4	+ i √0
    |011❭: 	 √1/4	+ i √0
    >>> print g
    0:  YC	-
    1:  IA	-
    2:  IA	-

And now run some CZ gates::

    >>> g.act_cz(0,1)
    >>> g.act_cz(1,2)
    >>> print g
    0:  YC	-
    1:  IA	(2,)
    2:  IA	(1,)
    >>> print g.to_state_vector()
    |000❭: 	 √1/4	+ i √0
    |010❭: 	 √1/4	+ i √0
    |001❭: 	 √1/4	+ i √0
    |011❭: 	-√1/4	+ i √0

Tidy up a bit::

    >>> g.del_node(0)
    >>> g.act_hadamard(0)
    >>> print g.to_state_vector()
    |00❭: 	 √1/2	+ i √0
    |11❭: 	 √1/2	+ i √0

Cool, we made a Bell state. Incidentally, those those state vectors and stabilizers are genuine Python objects, not just stringy representations of the state::

    >>> g = abp.GraphState(2)
    >>> g.act_cz(0, 1)
    >>> g.act_hadamard(0)
    >>> psi = g.to_state_vector()
    >>> print psi
    |00❭: 	 √1/2	+ i √0
    |11❭: 	 √1/2	+ i √0

``psi`` is a state vector -- i.e. it is an exponentially large vector of complex numbers. We can still run gates on it::

    >>> psi.act_cnot(0, 1)  
    >>> psi.act_hadamard(0)
    >>> print psi
    |00❭: 	 √1	+ i √0

But these operations will be very slow. Let's have a look at the stabilizer tableau::

    >>> tab = g.to_stabilizer()
    >>> print tab
     0  1
     ------
     Z  Z
     X  X
    >>> print tab.tableau
    {0: {0: 3, 1: 3}, 1: {0: 1, 1: 1}}
    >>> print tab[0, 0]
    3

Quantum mechanics is nondeterminstic. However, it's often useful to get determinstic behaviour for testing purposes. You can force ``abp`` to behave determinstically by setting::

    >>> abp.DETERMINSTIC = True


Visualization
----------------------

You can visualize states in 3D using the tool at `https://abv.peteshadbolt.co.uk/`. At some point I will merge the code for that server into this repo.

In order to visualize states you must give each node a position attribute::
    
    >>> g.add_qubit(0, position={"x": 0, "y":0, "z":0}, vop="identity")
    >>> g.add_qubit(0, position={"x": 1, "y":0, "z":0}, vop="identity")

There's a utility function in ``abp.util`` to construct those dictionaries::

    >>> from abp.util import xyz
    >>> g.add_qubit(0, position=xyz(0, 0, 0), vop="identity")
    >>> g.add_qubit(1, position=xyz(1, 0, 0), vop="identity")

Then it's really easy to get a 3D picture of the state::

    >>> g.push()
    Shared state to https://abv.peteshadbolt.co.uk/lamp-moon-india-leopard

That's a secret URL that you can use to collaboratively edit and view graph states in the browser. There are only a few billion such URLs so it should not be considered extremely secure. If you want, you can also load an existing state::

    >>> g = GraphState()
    >>> g.pull("https://abv.peteshadbolt.co.uk/lamp-moon-india-leopard")
    >>> g.show()

GraphState API
-------------------------

The ``abp.GraphState`` class is the main interface to ``abp``.  

.. autoclass:: abp.GraphState
    :special-members: __init__
    :members:

.. _clifford:

The Clifford group
----------------------

.. automodule:: abp.clifford

|

The ``clifford`` module provides a few useful functions:

.. autofunction:: abp.clifford.use_old_cz
    :noindex:

Testing
----------------------

``abp`` has a bunch of tests. It tests against all sorts of things, including the circuit model, Anders & Briegels' original code, Scott Aaronson's  ``chp``, and common sense. You can run all the tests using ``nose``::

    $ nosetests
    ...
    53 tests run in 39.5 seconds (53 tests passed)

Currently I use some reference implementations of ``chp`` and ``graphsim`` which you won't have installed, so some tests will be skipped. That's expected.

Reference
----------------------------

More detailed docs are available here:

* :ref:`genindex`
* :ref:`modindex`
* :ref:`search`