That all works great, except I run into trouble when trying to apply the channels to qubits and 1 & 3 or qubits 2 & 4(for example). Seems like some default "ordering" behavior with channels that I don't see with the QuantumOperators.

So, changing your code to

ops = {QuantumOperator["XX", {2, 3}], 
    QuantumOperator["YY", {2, 3}]} Sqrt[.5];
channel = QuantumChannel[ops]

applies the channel to qubits 2&3 just fine.

But similar code fails to apply the channel to qubits 2&4 and throws an error saying the Order size should be less than or equal to the number or qudits. Here is the code I tried for applying the channel to qubits 2&4.

ops = {QuantumOperator["XX", {2, 4}], 
    QuantumOperator["YY", {2, 4}]} Sqrt[.5];
channel = QuantumChannel[ops]

Note this same kind of code works fine for QuantumOperators, just not the Channels.

Cool, I have it working now after the bug fix.

This isn't really a bug, as I have found a work around, but thought I'd bring it up as a potential upgrade.

I've noticed that composing channels seems to get bogged down fairly quickly compared to composing quantum operators. For context, I've constructed a 2-qubit depolarizing channels to apply along with each two-qubit gate in my circuit.

   TQDepol[\[Epsilon]_] := 
  Sqrt[\[Epsilon]/
   15.0] {QuantumOperator["IX"], QuantumOperator["IY"], 
    QuantumOperator["IZ"], QuantumOperator["XI"], 
    QuantumOperator["XX"], QuantumOperator["XY"], 
    QuantumOperator["XZ"], QuantumOperator["YI"], 
    QuantumOperator["YX"], QuantumOperator["YY"], 
    QuantumOperator["YZ"], QuantumOperator["ZI"], 
    QuantumOperator["ZX"], 
    Sqrt[\[Epsilon]/15.0] QuantumOperator["ZY"], 
    QuantumOperator["ZZ"], 
    Sqrt[1 - \[Epsilon]]/Sqrt[\[Epsilon]/15.0] QuantumOperator["II"]};

TQDepolChannel[\[Epsilon]_, i_, j_] := 
 QuantumChannel[TQDepol[\[Epsilon]], {i, j}]

I can compose a couple of these maps, like this works just fine:

TQDepolChannel[\[Epsilon], 1, 2]@TQDepolChannel[\[Epsilon], 3, 4]

But the calculation quickly bogs down if I try to compose 3 or more of these channels. My work around is to apply the channels to a state. For example, this composition takes a very long time to evaluate,

TQDepolChannel[\[Epsilon], 1, 2]@ TQDepolChannel[\[Epsilon], 1, 2]@TQDepolChannel[\[Epsilon], 3, 4]

But this evaluates pretty quickly

TQDepolChannel[\[Epsilon], 1, 2]@ TQDepolChannel[\[Epsilon], 1, 2]@TQDepolChannel[\[Epsilon], 3, 4]@QuantumState["0000"]

While the second option is fast, it would sometimes be better to calculate the map for an arbitrary initial state. Maybe the slowdown comes from dealing with super-operators that act on density matrices and perhaps moving to the Liouville representation where the density matrix is vectorized will help - just speculating.

Anyway, thank you for the help.

Wonderful, everything is working beautifully now.

YES! That did it....THANK YOU!