OpenQASM 3 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 powering modifier pow(r) can be used to represent the r-th power of any gate g via pow(r) @ g, where r can either be an integer or a floating point number.

The case where r is a floating-point number needs to be handled by computing the principal logarithm of the unitary that represents g. This might be tricky in general.

The case where r is an integer can be naively solved by repeatedly applying g. If r <0, pow(r) @ g can be translated to inv @ pow(-r) @ g. Several simplifications might be possible here, e.g., the powers of phase gates can easily be computed by appropriately scaling the respective parameter. In its simplest form, pow(2) @ s = z.

At the very least, support for the case where r is an integer shall be provided, which provides much greater flexibility for describing circuits in a standardized way.

MQT Core's OpenQASM parser is already capable of correctly parsing the pow modifier, but lacks support for actually translating it to an appropriate operation in MQT Core:

It should be possible to handle this pretty similarly to the mqt.core.ir.operations.Operation.invert and the mqt.core.ir.operations.Operation.get_inverted methods.

For the actual implementation, it would be reasonable to consider how Qiskit is handling this, e.g.

• https://github.com/Qiskit/qiskit/blob/511ecbf74e5f251e5d1e0607e646e132c9d87d5b/qiskit/circuit/gate.py#L63-L94
• https://github.com/Qiskit/qiskit/blob/511ecbf74e5f251e5d1e0607e646e132c9d87d5b/qiskit/circuit/library/standard_gates/rz.py#L148-L150

I also like this trick for the Python bindings:
https://github.com/Qiskit/qiskit/blob/511ecbf74e5f251e5d1e0607e646e132c9d87d5b/qiskit/circuit/gate.py#L96-L97