Anders and Briegel in Python
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 .. 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 _ 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 $pip install --user abp==0.6.3 Alternatively, clone from the github repo _ and run setup.py: .. code-block:: bash$ 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 pytest::$ pytest ... 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