Autograd for quantum circuits

[Zohim Chandani]

I am working with quantum circuits and curious to learn about how autograd works in this instance.

I know other libraries like Pennylane offer differentiation of quantum circuits via autograd however I am trying to understand how to do this with CUDA Quantum.

See code below and the error I am receiving:

!pip install cuda-quantum

import cudaq
from cudaq import spin 

def qnn(theta_val): 

    kernel, thetas = cudaq.make_kernel(list)

    qubits = kernel.qalloc(1)    

    kernel.rx(thetas[0], qubits[0])
    
    hamiltonian = spin.z(0)
    
    return cudaq.observe(kernel, hamiltonian, theta_val).expectation()

One can think of qnn as a neural network where the aim is to optimise thetas[0] just like we optimise the weights and biases of a NN. Moreover, rx is just a 2 by 2 matrix which should be differentiable.

from autograd import grad 

gradf = grad(qnn)

gradf(2.4)

---------------------------------------------------------------------------
RuntimeError                              Traceback (most recent call last)
Cell In[54], line 3
      1 gradf = grad(qnn)
----> 3 gradf(2.4)

File ~/.local/lib/python3.10/site-packages/autograd/wrap_util.py:20, in unary_to_nary.<locals>.nary_operator.<locals>.nary_f(*args, **kwargs)
     18 else:
     19     x = tuple(args[i] for i in argnum)
---> 20 return unary_operator(unary_f, x, *nary_op_args, **nary_op_kwargs)

File ~/.local/lib/python3.10/site-packages/autograd/differential_operators.py:28, in grad(fun, x)
     21 @unary_to_nary
     22 def grad(fun, x):
     23     """
     24     Returns a function which computes the gradient of `fun` with respect to
     25     positional argument number `argnum`. The returned function takes the same
     26     arguments as `fun`, but returns the gradient instead. The function `fun`
     27     should be scalar-valued. The gradient has the same type as the argument."""
---> 28     vjp, ans = _make_vjp(fun, x)
     29     if not vspace(ans).size == 1:
     30         raise TypeError("Grad only applies to real scalar-output functions. "
     31                         "Try jacobian, elementwise_grad or holomorphic_grad.")

File ~/.local/lib/python3.10/site-packages/autograd/core.py:10, in make_vjp(fun, x)
...
      7 kernel.rx(thetas[0], qubits[0])
      9 hamiltonian = spin.z(0)
---> 11 return cudaq.observe(kernel, hamiltonian, theta_val).expectation()

RuntimeError: Invalid list-like argument to Kernel.__call__()

Any insight would be much appreciated. Thanks