Support for the inversion modifier of OpenQASM 3.0

[burgholzer]

The new OpenQASM standard introduces gate modifiers in order to more efficiently describe quantum circuits. Any modifier mod can be applied to a gate g via mod @ g. For more details, see Section 4.2 in https://arxiv.org/pdf/2104.14722.pdf or the Live Specification.

The inversion modifier inv can be used to invert any gate g via inv @ g. The inverse of any gate can be computed as:

• For any unitary operation U = U_m-1 ... U_0 its inverse U^-1 is defined by reversing the order of operations and inverting each individual gate, i.e., U^-1 = U_0^-1 ... U_m-1^-1.
• The inverse of a controlled operation is defined as the controlled inverse operation, i.e., inv @ ctrl @ g = ctrl @ inv @ g.
• inv @ U(a, b, c) = U(-a, -c, -b) and inv @ gphase(a) = gphase(-a)

Note that the global phase gate gphase(a) is not yet introduced and its implementation is left for another issue at the moment.

We should be able to handle many of these inversions in a cleverer fashion, e.g., if it is known, that a gate is self-inverse, or e.g., in case of the phase gate, where the inverse is obtained by negating the parameter.

Enhancing the OpenQASM parser with this feature provides greater flexibility for describing circuits in a standardized way.

Tasks

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1. Add support for the inverse modifier to mqt-core itself Add invert functionality for quantum operations #416
2. Add support for the inverse modifier to the QASM (3.0) parser