Interesting. I agree a follow up result would be fascinating. w.r.t. imaginary numbers and tensor flow, as you may have come across at some point, you can alwa

Interesting. I agree a follow up result would be fascinating. w.r.t. imaginary numbers and tensor flow, as you may have come across at some point, you can always map a quantum circuit over to one that only uses real valued amplitudes at the cost of just a single ancila qubit. Just replace i with |1> on the ancila and all multiplications by a phase with a controlled rotation on the ancila. In other words, the phase is a qubit the universe gives you for free.