I need to draw a quantum circuit in Clifford+T library and obtain automatically its transformation matrix. (I received a response to this part of my question before in the link: How can I obtain transformation matrix of a quantum circuit in the Qiskit?) and now I want to do this work as a parametric. For example, I want to define gate T as $$ \begin{pmatrix} 1 & 0 \\ 0 & w \end{pmatrix} $$ where $w=\frac{(1+i)}{\sqrt{2}}$, and I want to obtain the transformation matrix of the circuit with parameter $w$ and not as numeric. How can I do this?
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As of Qiskit 0.23.0 that's not yet supported.
The reason is mainly that such a simulator would be very slow as we would have to use SymPy's matrix multiplication for symbolic expressions. This is not really feasible for more than 5 or 6 qubits -- depending on your machine specs. Also, the output can become a gigantic symbolic expression pretty quickly and therefore likely only of limited use.
That being said, you can of course write your own script for a symbolic simulator: all you have to do is replace matrix multiplications with SymPy multiplications. A good starting point could be the quantum_info.Operator that uses straightforward NumPy multiplications and could probably be generalized easily.
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1$\begingroup$ Could you please send an example of what you are saying? thanks $\endgroup$ Commented Oct 28, 2020 at 10:01