Adds parametrized template support

[josh146]

This PR adds support for:

• Parametrized Blackbird templates

• Pattern matching of template parameters (blackbird.utils.match_template())

• a utility function for converting a Blackbird program to a NetworkX directed acyclic graph (blackbird.utils.to_DiGraph())

Templates

This PR adds support for creating Blackbird 'templates', that can be loaded and used as parametrized functions. Template parameters use the syntax {parameter_name}, and can be placed within any arithmetic expression. This syntax is inspired by the Python templating library Jinja.

For example, consider the following template file ('teleport.xbt'), with two template parameters {alpha} and {sq}.

name StateTeleportation
version 1.0

# state to be teleported:
Coherent({alpha}) | 0

# teleportation algorithm
Squeezed(-{sq}) | 1
Squeezed({sq}) | 2
BSgate(pi/4, 0) | (1, 2)
BSgate(pi/4, 0) | (0, 1)
MeasureX | 0
MeasureP | 1
Xgate(sqrt(2)*q0) | 2
Zgate(sqrt(2)*q1) | 2

Deserializing the template:

>>> prog = blackbird.load("teleportation.xbt")
>>> prog.is_template()
True
>>> prog.parameters
{'alpha', 'sq'}

We can also use the template to generate static blackbird programs:

>>> prog_new = prog(alpha=0.54, sq=4)

Benefits

Support for templated Blackbird scripts will be advantageous for:

• Variational quantum circuits, where the circuit need only be compiled once, but certain parameters can be updated independently

• Serializing/deserializing parametrized quantum programs in Strawberry Fields

• Communicating template parameters (for example, large or sparse graphs) separately from the blackbird template.

Future work

• Support for including templates in Blackbird scripts will be added. Example:

  name coherent_teleport
  version 1.0
  # include the template file
  include "state_teleportation.xbt"
  target gaussian (shots=1000)
  
  # state to be teleported:
  Coherent(0.543) | 0
  # call the template, using its 'name', and passing
  # required values of template parameters
  StateTeleportation(sq=4) | [0, 1, 2]
  MeasureHeterodyne() | 2

• Load a template into Strawberry Fields, to create a 'program factory':

  template = sf.load('state_teleportation.xbt')
  eng.run(template(sq=2), backend='fock')

• Save a parametrized program from Strawberry Fields, to create a template. This will necessitate adding some sort of 'placeholder' variable class to Strawberry Fields.

  import strawberryfields as sf
  from strawberryfields import tparam
  
  prog = sf.Program(2)
  
  with prog.context as q:
  Dgate(0.54) | q[0]
  Sgate(tparam('r'), 0.543) | q[0]
  
  # can run the program
  eng.run(prog(r=0.1), backend='gaussian')
  # or save it as a template
  sf.save('new_template.xbt', prog)

[codecov[bot]]

Codecov Report

Merging #13 into master will increase coverage by 0.94%. The diff coverage is 100%.

@@            Coverage Diff             @@
##           master      #13      +/-   ##
==========================================
+ Coverage    95.6%   96.54%   +0.94%     
==========================================
  Files          10       12       +2     
  Lines        1182     1475     +293     
==========================================
+ Hits         1130     1424     +294     
+ Misses         52       51       -1

Impacted Files	Coverage Δ
blackbird_python/blackbird/listener.py	100% <100%> (ø)	:arrow_up:
blackbird_python/blackbird/auxiliary.py	100% <100%> (ø)	:arrow_up:
blackbird_python/blackbird/tests/test_utils.py	100% <100%> (ø)
blackbird_python/blackbird/utils.py	100% <100%> (ø)
blackbird_python/blackbird/tests/test_program.py	100% <100%> (ø)	:arrow_up:
blackbird_python/blackbird/program.py	100% <100%> (ø)	:arrow_up:
blackbird_python/blackbird/tests/test_listener.py	100% <100%> (+0.52%)	:arrow_up:

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[co9olguy]

maybe we could overload the select argument as a way to pass placeholders?

[co9olguy]

Please add the "Future work" items to backlog

[josh146]

All suggested changes applied.