[BUG] Documentation inconsistently states that GlobalPhase acts on all wires

[dime10]

Expected behavior

While any operator can be extended to act on a larger system by adding Identity tensor products, it is generally understood that the number of target wires in an operator is in reference to the smallest representation of the operator.

Given that the smallest representation of the GlobalPhase operator is a 1x1 matrix ( e ^ -i phi ), and the number of wires n relates to the matrix dimensions as 2^n x 2^n, this is consistent with saying the operator acts on 0 wires, rather than all wires.

Another reason to this why this notion is useful is that it demonstrates the operation can be applied anywhere in the circuit with equivalent results (i.e. it commutes with all other gates), because its wires do not overlap with other gates.

Finally, it becomes obvious that GlobalPhase cannot be acting on all wires as it would be otherwise impossible to control without having overlapping target and control wires.

Actual behavior

Additional information

While mathematically this is the most natural interpretation, draw the gate might require special handling.

Source code

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Tracebacks

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System information

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Existing GitHub issues

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