[unitaryHACK] Create a Pytorch simulator #1225

[Slimane33]

Context:
Create a quantum simulator with PyTorch.

Description of the Change:
A new device default.qubit.torch is created. It allows all quantum operations and measurements to be performed within the PyTorch worlkflow.

Benefits:
It allows end-to-end GPU computation and integration of quantum circuits with the torch interface of Pennylane. A fully working example can be found here: https://colab.research.google.com/drive/1Xb_-l3TIOZhbDw6K9jO34oDgDqzs3o7V?usp=sharing
All the gates implemented with Tensorflow have been reimplemented and seem to work.

Remaining work:

1. The plugin is not fully tested. When I run the line pl-device-test --device default.qubit.torch --shots None
   I get the following error

/Users/slimane/Desktop/pennylane/pennylane/devices/tests/test_wires.py:65: 
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 
pennylane/qnode.py:555: in __call__
    res = self.qtape.execute(device=self.device)
pennylane/tape/tape.py:1264: in execute
    return self._execute(params, device=device)
//anaconda3/lib/python3.7/site-packages/autograd/tracer.py:48: in f_wrapped
    return f_raw(*args, **kwargs)
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 

self = <AutogradQuantumTape: wires=[-1, -2], params=0>, params = (), device = <DefaultQubitTorch device (wires=2, shots=None) at 0x1a5fb4e278>

    @autograd.extend.primitive
    def _execute(self, params, device):
        # unwrap all NumPy scalar arrays to Python literals
        params = [p.item() if p.shape == tuple() else p for p in params]
        params = autograd.builtins.tuple(params)
    
        # unwrap constant parameters
        self._all_params_unwrapped = [
            p.numpy() if isinstance(p, np.tensor) else p for p in self._all_parameter_values
        ]
    
        # evaluate the tape
        self.set_parameters(self._all_params_unwrapped, trainable_only=False)
        res = self.execute_device(params, device=device)
        self.set_parameters(self._all_parameter_values, trainable_only=False)
    
        if self.is_sampled:
            return res
    
>       if res.dtype == np.dtype("object"):
E       TypeError: Cannot interpret 'torch.float64' as a data type

pennylane/interfaces/autograd.py:171: TypeError

Since it seems to be a fundamental error of incompatibility between torch.dtypeand numpy.dtype, I don't understand why I am still able to normally run the circuit.

2. Writing the appropriate unit test test_default_qubit_torch.py

3. Check formatting

Possible drawbacks:
More maintenance, torch operations are more different of numpy ones than tensorflow ones are.
Autograd in Pytorch is very sensitive. For example this formulation of RZ gate works

def RZ(theta, device=None):
    theta = torch.as_tensor(theta, dtype=C_DTYPE, device=device)
    p = torch.exp(-0.5j * theta)
    return p * torch.tensor([1, 0], dtype=torch.complex128) + torch.conj(p) * torch.tensor([0, 1], dtype=torch.complex128)

while this one doesn't

def RZ(theta, device=None):
    theta = torch.as_tensor(theta, dtype=C_DTYPE, device=device)
    p = torch.exp(-0.5j * theta)
    return torch.tensor([p, torch.conj(p)], dtype=torch.complex128)

Related GitHub Issues:
#1225

This is a collective contribution from: @arshpreetsingh, @PCesteban, @artm88, @charmerDark, @mkasmi, @Slimane33

[josh146]

Thanks @Slimane33! Looking forward to reviewing this, simply let us know via a comment in the PR when this is ready for review (or, alternatively, if you have any questions).

The plugin is not fully tested. When I run the line pl-device-test --device default.qubit.torch --shots None
I get the following error

Hmm, it seems that the Autograd interface is not compatible with the PyTorch device. This might be because the device test suite is defaulting to diff_method="parameter-shift", interface="autograd".

Instead, we would like to use diff_method="backprop", interface="torch". Perhaps the device test suite needs to be updated to support this?

More maintenance, torch operations are more different of numpy ones than tensorflow ones are. Autograd in Pytorch is very sensitive. For example this formulation of RZ gate works

In this particular example @Slimane33, could you do?

return torch.diag([p, torch.conj(p)])

[Slimane33]

Instead, we would like to use diff_method="backprop", interface="torch". Perhaps the device test suite needs to be updated to support this?

How can we change that? The test suite works for default.qubit.tf which uses diff_method="backprop", interface="tf".

return torch.diag([p, torch.conj(p)])

It does not work because torch.diagreturns an 2D tensor given 1D tensor. The following line doesn't work either

return torch.diag(torch.tensor([[p, 0], [0, torch.conj(p)]], dtype=C_DTYPE, device=device))

[albi3ro]

@josh146 @antalszava Ready to override and merge from my side.

[co9olguy]

🎉
Congrats @PCesteban @arshpreetsingh @Slimane33!

[arshpreetsingh]

Congrats @PCesteban @arshpreetsingh!

Thanks @co9olguy ! and Great efforts from @Slimane33 as well.