feature: added controlled-sqrt-not gate

[unprovable]

This makes certain circuits, like CHSH, more straightforward. This commit works in line with the following branches (also committed, separately):
https://github.com/unprovable/amazon-braket-schemas-python.git@ctrl-v-gate
https://github.com/unprovable/amazon-braket-default-simulator-python.git@ctrl-v-gate

Issue #, if available:

Description of changes:

Added the controlled version of the sqrt(NOT) gate, in Braket's parlance this is the V-gate, and so it is named the 'CV-gate' in this PR. I have also made the relevant changes on similarly named branches in the schemas and default-simulator repos. These are located:

• https://github.com/unprovable/amazon-braket-schemas-python.git@ctrl-v-gate
• https://github.com/unprovable/amazon-braket-default-simulator-python.git@ctrl-v-gate

(I'll include this PR number in the PRs for those repositories).

The main motivation for this change is to make circuits a little easier to construct in the simulator, and hopefully later on devices. For example, the CHSH form of the Bell inequality test has a very straightforward form using this gate. (See the 'testing' section for the code that demonstrates this).

Testing done:

I wrote some unit tests and included them in the PR. Also, to check this point the following code was used, based on section 16.2 in https://arxiv.org/abs/1907.09415 -

from braket.circuits import circuit, Circuit, Gate, Moments
from braket.circuits.instruction import Instruction
from braket.devices import LocalSimulator
import numpy as np

def chsh_circuit():
    """
    function to perform CHSH form of Bell Inequality Test.
    Based on material in 1907.09415, Section 16.2 (arXiv)
    """

    # instantiate circuit object
    circuit = Circuit()
    
    # put referees in superposition
    circuit.h(2)
    circuit.h(3)
    
    #entangle Alice and Bob
    circuit.h(0)
    circuit.cnot(0, 1)
    
    # spin Alice
    circuit.rx(0, -(3*np.pi)/16)
    
    # apply sqrt(NOT) based on referees flip
    circuit.cv(2,0)
    circuit.cv(3,1)

    return circuit

device = LocalSimulator()
cq = chsh_circuit()
my_task = device.run(cq, shots=1000)
my_task.result()

# check win percentage - should be around 85%, and certainly over 75%.
wins = 0
for i in my_task.result().measurements:
    if i[0] ^ i[1] == i[2] & i[3]:
        wins += 1

print((wins/len(my_task.result().measurements))*100)

This circuit produces the correct results using a modified version of the amazon-braket-sdk library. The code has been copied into this (and related) PR's to enable these simulations in the main AWS braket repo.

Merge Checklist

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General

• I have read the CONTRIBUTING doc
• I used the commit message format described in CONTRIBUTING
• I have updated any necessary documentation, including READMEs and API docs (if appropriate)

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• I have added tests that prove my fix is effective or that my feature works (if appropriate)
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By submitting this pull request, I confirm that my contribution is made under the terms of the Apache 2.0 license.

[unprovable]

I'm guessing given this was submitted over two weeks ago and no comments have been forthcoming that this probably isn't going anywhere?

This gate makes a lot of the research I'm currently doing much more workable, hence the code was sent up. Can someone close this (and the other related PR's) if it's not going to be used? Thanks :) M.

[kshitijc]

Thanks for this PR @unprovable and apologies for missing this earlier. Could you please run tox -e linters for fixing the file formatting ?

[unprovable]

Hello! No worries - and yes, sorry, forgot to run that. Ran it on all the repos to be sure, but only changes made to the sdk repo. Commited and pushed up.

[codecov]

Codecov Report

Merging #297 (e2f7d97) into main (21466b3) will not change coverage.
The diff coverage is 100.00%.

@@            Coverage Diff            @@
##              main      #297   +/-   ##
=========================================
  Coverage   100.00%   100.00%           
=========================================
  Files           63        63           
  Lines         4221      4236   +15     
  Branches       581       581           
=========================================
+ Hits          4221      4236   +15     

Impacted Files	Coverage Δ
src/braket/circuits/gates.py	100.00% <100.00%> (ø)

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[kshitijc]

Let's revert tox.ini here as well before we merge. Thanks!

[kshitijc]

Thank you for contributing to enhance the Braket SDK and being patient as we worked through the PRs, @unprovable! Great work!

[unprovable]

Thank you for all your help! :D Very nice experience doing these PR's for sure!